[EM] Condocet with many candidates - two round elections considered
Dear all, dear Markus Schulze, after having presented Condorcet elections to some people in the Czech green party, the following question came up. Condorcet elections might work with three candidates, but what about if there are twenty of them, will the system work and elect the best candidate? Q1: What would you answer for Condorcet elections in general and Schulze-method elections in particular? Q2: Specifically, would you recommend a two-round construct, i.e. the three best candidates (or x best?) meet in the second round. Q3: Would such a two-round system help to deal with the case of the "dark horse" winning with long beat-paths and people being dissatisfied with the election? Q4: If yes, how many candidates should be in the second round and how should they be selected (Schulze ranking?)? One such mis-election with dissatisfied voters would be enough to discredit Condorcet elections in our party and two-round elections might give an additional sense of security for some voters in the face of a novel and fairly complex election system. In the Czech republic we currently use two-round elections. However, if two round Condorcet elections bring no additional value, then there is no need to complicate an elegant election system. Thanks for your advice. Best regards Peter Zborník Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Thoughts on a nomination simulation
Hello, The last thing I did with my simulation is check whether on average a candidate would prefer to have withdrawn (considering the results of thousands of trials of one position) than stand, with the assumption that they care what happens when they lose. (I'm not sure that's actually a good assumption: It would be better to assume the voters are the ones who care, and don't support a candidate who spoils the election.) I got odd results. It could very well be a bug. But for example I found that (sincere) FPP had very few scenarios where a candidate would prefer to exit the race. Maybe it's because I had filtered out uncompetitive elections. But, even if FPP can handle some three-way races doesn't mean that we can score FPP based on them, with the assumption that they will occur. That seems like a big problem with my simulation, that there are always three candidates, and no check for incentives for more or fewer to be nominated. Over the past couple of years I've made a couple attempts at writing a nomination simulation, where candidates in turn decide whether they want to stand somewhere else in issue space. To this I could add the possibility of exiting or entering the race. I've had problems getting this simulation to work well at all, but assuming I could figure it out, I might be able to discover specific stable situations for a given method (with a given strategy and information availability). Though this still would not (easily) give me probabilities of scenarios occuring. I guess for each method I would have a fairly short list of stable positions, and could find average utilities for each position. I'm curious if anyone else has put thought into this topic... Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condocet with many candidates - two round elections considered
Hi Peter, --- En date de : Mer 16.6.10, Peter Zbornik a écrit : >Dear all, dear Markus Schulze, > >after having presented Condorcet elections to some people in the Czech >green party, the following question came up. >Condorcet elections might work with three candidates, but what about if >there are twenty of them, will the system work and elect the best >candidate? In my opinion, in theory, Schulze performs exactly as well with many as with few candidates. >Q1: What would you answer for Condorcet elections in general and Schulze- >method elections in particular? I would not say Condorcet in general is excellent at this, but Condorcet fans tend to prefer methods that don't break when you have many candidates. >Q2: Specifically, would you recommend a two-round construct, i.e. the >three best candidates (or x best?) meet in the second round. The only reason I would recommend something like this is if you expect that voters may not be familiar with the strongest candidates. If voters do not obtain *new* knowledge between rounds, and their preferences don't change, then the pairwise contests among them are going to be exactly the same, and the Schulze result would most likely be the same. >Q3: Would such a two-round system help to deal with the case of the "dark >horse" winning with long beat-paths and people being dissatisfied with >the election? If the "dark horse" can win in this way (more likely: he wins because everyone gives him a mid-range preference and he defeats everyone) he will most likely still win when you eliminate all but a few candidates. So again, a second round only makes a difference if the voters are supposed to get new information and change their preferences. The ordinary two-round method is different from this because when you eliminate candidates, the "best" candidate could very easily change, since it's all based (in theory) on who is everyone's favorite candidate. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condocet with many candidates - two round elections considered
Hi Kevin, thanks for your view on the topic. In election-theoretic language, what criterion is used to describe, that a method performs as well with many as with few candidates? There is a list of criterias in the table at: http://en.wikipedia.org/wiki/Schulze_method#Comparison_with_other_preferential_single-winner_election_methods, but I don't know which it is (clone-independence? Maybe some other criterion too?). Peter On 6/16/10, Kevin Venzke wrote: > > Hi Peter, > > --- En date de : Mer 16.6.10, Peter Zbornik a écrit : > >Dear all, dear Markus Schulze, > > > >after having presented Condorcet elections to some people in the Czech > >green party, the following question came up. > >Condorcet elections might work with three candidates, but what about if > >there are twenty of them, will the system work and elect the best > >candidate? > > In my opinion, in theory, Schulze performs exactly as well with many as > with few candidates. > > >Q1: What would you answer for Condorcet elections in general and Schulze- > >method elections in particular? > > I would not say Condorcet in general is excellent at this, but Condorcet > fans tend to prefer methods that don't break when you have many candidates. > > >Q2: Specifically, would you recommend a two-round construct, i.e. the > >three best candidates (or x best?) meet in the second round. > > The only reason I would recommend something like this is if you expect > that voters may not be familiar with the strongest candidates. If voters > do not obtain *new* knowledge between rounds, and their preferences don't > change, then the pairwise contests among them are going to be exactly > the same, and the Schulze result would most likely be the same. > > >Q3: Would such a two-round system help to deal with the case of the "dark > >horse" winning with long beat-paths and people being dissatisfied with > >the election? > > If the "dark horse" can win in this way (more likely: he wins because > everyone gives him a mid-range preference and he defeats everyone) he will > most likely still win when you eliminate all but a few candidates. So > again, a second round only makes a difference if the voters are supposed > to get new information and change their preferences. > > The ordinary two-round method is different from this because when you > eliminate candidates, the "best" candidate could very easily change, since > it's all based (in theory) on who is everyone's favorite candidate. > > Kevin Venzke > > > > > > Election-Methods mailing list - see http://electorama.com/em for list info > Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condocet with many candidates - two round elections considered
Hi Peter, --- En date de : Mer 16.6.10, Peter Zbornik a écrit : >thanks for your view on the topic. >In election-theoretic language, what criterion is used to describe, that a >method performs as well with many as with few candidates? >There is a list of criterias in the table >at:http://en.wikipedia.org/wiki/Schulze_method#Comparison_with_other_prefer >ential_single-winner_election_methods, but I don't know which it is (clone- >independence? Maybe some other criterion too?). Unfortunately this is a difficult criterion to try to define. Independence of clones is probably the best one. It says performance won't degrade by cloning candidates or consolidating a set of clones into one candidate. But it doesn't say anything about what happens if you just add a lot of unrelated candidates. Actually the criterion there called "Independence of Smith-dominated alternatives" is helpful also as it means that every candidate in the election either has a beatpath to every other candidate, or else has no effect on the outcome. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condocet with many candidates - two round elections considered
On Jun 16, 2010, at 4:34 PM, Peter Zbornik wrote: Dear all, dear Markus Schulze, after having presented Condorcet elections to some people in the Czech green party, the following question came up. Condorcet elections might work with three candidates, but what about if there are twenty of them, will the system work and elect the best candidate? Condorcet methods work quite as well with more than three candidates. Some problems even get smaller when the number of candidates increases (maybe majority of them???). Q1: What would you answer for Condorcet elections in general and Schulze-method elections in particular? Different Condorcet methods are very similar in real life elections. The first thing that might cause different results when compared to some other methods is that the Schulze method uses winning votes to determine the strength of pairwise preferences. Other characteristic features of the Schulze method are that in case of a top level cycle it uses uses beatpaths and always elects from the Smith set. The difference to other common Condorcet methods is quite marginal here. In general the answers from practical elections point of view are very similar to all Condorcet methods. Different Condorcet methods meet different criteria and give different results in some specific examples. These properties can be used to promote one method or another, or oppose them, but as already said, from practical elections point of view the differences are very small. Q2: Specifically, would you recommend a two-round construct, i.e. the three best candidates (or x best?) meet in the second round. No, Condorcet methods can handle all this in one round. I can understand that if people are used to having two rounds then it would be nice to first see who the leaders are and what other voters were thinking, and only then make the final decisions. One could handle this as well by arranging first a test election (or one or more polls) and then the final round that would include all the candidates. If there are very many candidates then it might be practical if some of them would not participate in the final round (to ease the task of voting), but I don't see any other reasons for arranging the final round with few candidates only. (Multiple rounds make strategic voting slightly easier but I don't expect strategic voting to be a problem if the number of voters is higher than say 10.) Q3: Would such a two-round system help to deal with the case of the "dark horse" winning with long beat-paths and people being dissatisfied with the election? I don't think so. Condorcet methods allow also candidates that do not have high number of first preferences to win. I.e. also good compromise candidates from smaller groupings do have a chance if the supporters of the largest groupings generally like that candidate and rank her second after their own candidate. Other kind of "dark horses" are probably not a problem. They could be a problem only if the voters start doing something irrational in wide scale, like ranking some bad candidates above all the serious candidates. Strategic voting could be one more way to try to introduce "black horses", but I don't believe that to be a problem, and second round would not help. Q4: If yes, how many candidates should be in the second round and how should they be selected (Schulze ranking?)? (I said "no" but...) Any proportional ranking based approach would be fair in the sense that it would pick candidates from all segments of the party. But that would work also against the target of electing a candidate that all like. And in that process one could also eliminate some candidate that would be the winner at the second round (assuming that opinions would change a bit and the first ranked (Schulze ranking) candidate would not win). Therefore it would be more natural to pick candidates that got good (single-winner) Condorcet results at the first round. This approach could look a bit biased sine the centrist / "liked by all" candidates would be over-represented. So, if there are not too many candidates, maybe better to keep all of them also at the final round. Keeping them all may also give more complete/ accurate information on how liked each one of them is. One such mis-election with dissatisfied voters would be enough to discredit Condorcet elections in our party and two-round elections might give an additional sense of security for some voters in the face of a novel and fairly complex election system. In the Czech republic we currently use two-round elections. However, if two round Condorcet elections bring no additional value, then there is no need to complicate an elegant election system. Yes, I can understand that people that are used to a two-round method may feel like being surprised if the method elects someone already at the first round, especiall
Re: [EM] Condocet with many candidates - two round elections considered
On Jun 16, 2010, at 9:34 AM, Peter Zbornik wrote: after having presented Condorcet elections to some people in the Czech green party, the following question came up. Condorcet elections might work with three candidates, but what about if there are twenty of them, will the system work and elect the best candidate? one serious problem that *any* ranked-order system has is if there are more candidates than ranking levels on the ballot. it means that after you rank your top, say, five candidates, you have no ability to weigh in on the rest of the candidates and it might be one of those candidates who ends up battling against another of the unranked candidates. all unranked candidates are essentially tied for last place and you are prevented from ranking Satan or Beelzebub or Hitler lower than a dozen other candidates that you might not care so much about. i think that ballot access rules, that limit the number of candidates to around the number of ranking levels, is the answer. Q1: What would you answer for Condorcet elections in general and Schulze-method elections in particular? Q2: Specifically, would you recommend a two-round construct, i.e. the three best candidates (or x best?) meet in the second round. Q3: Would such a two-round system help to deal with the case of the "dark horse" winning with long beat-paths and people being dissatisfied with the election? i am less concerned about the DH problem than many here are. if Liberals rank the DH above the Conservative candidate, it means they like the DH better. if Conservatives rank the DH above the Liberal, it means they like the DH better than the Liberal. if the DH ends up winning with very few first choice votes, then the DH may very well be the most acceptable compromise candidate over either or any of the polarized candidates that have more first choice support. remember, assuming a Condorcet winner exists, electing *anyone* other than the Condorcet winner means that you are electing someone when a majority of voters have agreed that some other specific candidate is better and have explicitly marked their ballots as so. you can call that specific candidate that the majority of voters preferred a "Dark Horse", but that's just a label. the fact is that candidate is still preferred by a majority of voters over any other specific candidate. if you are taking the stated preferences of the voters at face value, how can you decide on anyone else and call that election reflective of the will of the voters? now, if *no* Condorcet winner exists, then that's a different story. perhaps (instead of Schulze) electing the Smith set candidate with the most first-choice votes might prevent the Dark Horse from winning, but i think that the Schulze winner is a better choice (if they happen to be different). Q4: If yes, how many candidates should be in the second round and how should they be selected (Schulze ranking?)? i dunno about a party election, but in a general election one of the main problems is that only a fraction (around 50%) of the original voters show up for the second-round runoff. that's one of the main reasons for settling the election on a single Election Day. -- r b-j r...@audioimagination.com "Imagination is more important than knowledge." Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condocet with many candidates - two round elections considered
All common Condorcet methods work fine also with multiple candidates (although not all methods meet exactly the same criteria). The first problem are probably human behaviour related, i.e. people start hating the voting process if it is too tedious, and they may not rank all relevant candidates, and that may lead to some distortion in the results. Juho On Jun 16, 2010, at 5:51 PM, Kevin Venzke wrote: Hi Peter, --- En date de : Mer 16.6.10, Peter Zbornik a écrit : thanks for your view on the topic. In election-theoretic language, what criterion is used to describe, that a method performs as well with many as with few candidates? There is a list of criterias in the table at:http://en.wikipedia.org/wiki/Schulze_method#Comparison_with_other_prefer ential_single-winner_election_methods, but I don't know which it is (clone- independence? Maybe some other criterion too?). Unfortunately this is a difficult criterion to try to define. Independence of clones is probably the best one. It says performance won't degrade by cloning candidates or consolidating a set of clones into one candidate. But it doesn't say anything about what happens if you just add a lot of unrelated candidates. Actually the criterion there called "Independence of Smith-dominated alternatives" is helpful also as it means that every candidate in the election either has a beatpath to every other candidate, or else has no effect on the outcome. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Irrelevant Ballots Independent Fallback Approval (IBIFA)
"Irrelevant Ballots Independent Fallback Approval" (IBIFA) is the name I've settled on for the method I proposed in a May 2010 EM post titled "Bucklin-like method meeting Favorite Betrayal and Irrelevant Ballots". http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html In that post I wrote that it uses multi-slot ratings ballots, and defined the 4-slot version: *Voters fill out 4-slot ratings ballots, rating each candidate as either Top, Middle1, Middle2 >or Bottom. Default rating is Bottom, signifying least preferred and unapproved. > > >Any rating above Bottom is interpreted as Approval. > > >If any candidate/s X has a Top-Ratings score that is higher than any other >candidate's approval >score on ballots that don't top-rate X, elect the X with the highest TR score. > > >Otherwise, if any candidate/s X has a Top+Middle1 score that is higher than >any other candidate's >approval score on ballots that don't give X a Top or Middle1 rating, elect the >X with the highest >Top+Middle1 score. > > >Otherwise, elect the candidate with the highest Approval score.*(Obviously >other slot names are possible, such as 3 2 1 0 or A B C D or Top, High >Middle, Low Middle, Bottom.) The 3-slot version: *Voters fill out 3-slot ratings ballots, rating each candidate as either Top, Middle >or Bottom. Default rating is Bottom, signifying least preferred and unapproved. > >Any rating above Bottom is interpreted as Approval. > >If any candidate/s X has a Top-Ratings score that is higher than any other >candidate's approval >score on ballots that don't top-rate X, elect the X with the highest TR score. > >Otherwise, elect the candidate with the highest Approval score.* > It can also be adapted for use with ranked ballots: *Voters rank the candidates, beginning with those they most prefer. Equal-ranking and truncation are allowed. Ranking above at least one other candidate is interpreted as Approval. The ballots are interpreted as multi-slot ratings ballots thus: An approved candidate ranked below zero other candidates is interpreted as Top-Rated. An approved candidate ranked below one other candidate is interpreted as being in the second-highest ratings slot. An approved candidate ranked below two other candidates is interpreted as being in the third-highest ratings slot (even if this means the second-highest ratings slot is left empty). An approved candidate ranked below three other candidates is interpreted as being in the fourth-highest ratings slot (even if this means that a higher ratings slot is left empty). And so on. Say we label these ratings slot from the top A B C D etc. A candidate X's A score is the number of ballots on which it is A rated. A candidate X's A+B score is the number of ballots on which it is rated A or B. A candidate X's A+B+C score is the number of ballots on which it is rated A or B or C. And so on. If any candidate X has an A score that is greater than any other candidate's approval score on ballots that don't A-rate X, then elect the X with the greatest A score. Otherwise, if any candidate X has an A+B score that is greater than any other candidate's approval score on ballots that don't A-rate of B-rate X, then elect the X with the greatest A+B score. And so on as in the versions that use a fixed number of ratings slots, if necessary electing the most approved candidate.* This is analogous with ER-Bucklin(whole) on ranked ballots: http://wiki.electorama.com/wiki/ER-Bucklin Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Condorcet question - why not bullet vote
Dear all, dear Markus Schulze, I got a second question from one of our members (actually the same guy which asked for the first time): If I just bullet vote in a Condorcet election, then I increase the chances of my candidate being elected. If I have a second or third option, the chances of my prefered candidate to win is lowered. Q: In this case why should any voter not bullet-vote? I have some clue on how to answer, but not enough for an exhaustive answer. My argument starts: If I vote for a candidate who has >50% of the votes, then it does not matter if there is a second or third choice. If my prefered candidate A gets <50% of the votes, then it makes sense to support a second choice candidate B. However if the supporters of B only bullet vote, then maybe B's supporters get an advantage over A? ... at this point I realize, that I don't know enough about Condorcet and/or Schulze to answer the question. Why is it not rational to bullet vote in a Condorcet election if you are allowed not to rank some candidates? I guess you have discussed this question a zillion of times, so please forgive my ignorance. Maybe you could help me out with this one. Peter Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
On Jun 16, 2010, at 1:30 PM, Peter Zbornik wrote: Dear all, dear Markus Schulze, I got a second question from one of our members (actually the same guy which asked for the first time): If I just bullet vote in a Condorcet election, then I increase the chances of my candidate being elected? If there is a Condorcet Winner (CW), the answer is "no". If there is no CW, then we have a "Condorcet paradox" or a "cycle" where Candidate Rock beats Candidate Scissors, Candidate Scissors beats Candidate Paper, and Candidate Paper beats Candidate Rock. Then I won't say whether the answer is "no" for sure, but I am still convinced that cycles are rare and that a method like Schulze or Ranked Pairs resolves the cycles meaningfully. If I have a second or third option, the chances of my prefered candidate to win is lowered? Same answer as above. If there is a CW, the answer is "no, it does not hurt your favorite. It makes no difference to your favorite." Q: In this case why should any voter not bullet-vote? The whole idea is to allow the voter expressivity in all election possibilities and to not burden the voter with the need to think or vote strategically. If the voter thinks that Candidate A is a better choice than Candidate B (that is, if the election was a 2-person race between A and B, this voter would vote for A), then the voter ranks A above B and that's that. Nothing more to worry about. If the voter would vote for Candidate C over B in a 2-person race but not over A in a different 2-person race, then that voter would rank A highest, C next, followed by B last. Bullet voting for A does not help A any more than ranking A highest and mutes this voter regarding a possible decision between B and C. I have some clue on how to answer, but not enough for an exhaustive answer. My argument starts: If I vote for a candidate who has >50% of the votes, then it does not matter if there is a second or third choice. If my prefered candidate A gets <50% of the votes, then it makes sense to support a second choice candidate B. However if the supporters of B only bullet vote, then maybe B's supporters get an advantage over A? No, not if either A or B (or C) end up as the Condorcet Winner. ... at this point I realize, that I don't know enough about Condorcet and/or Schulze to answer the question. Why is it not rational to bullet vote in a Condorcet election if you are allowed not to rank some candidates? Because you lose your voice in a potentially decisive election between two candidates, neither whom are your favorite but one of them you hate. I guess you have discussed this question a zillion of times, so please forgive my ignorance. It's what it's all about. According to my "Gospel of Fair Elections according to Condorcet", there are really no downsides if there is a clear Condorcet Winner (and I disagree with most of the rest of this mailing list about the "Dark Horse pathology"). And I believe that cycles (where there *is* no CW) are rare. That's my religion. -- r b-j r...@audioimagination.com "Imagination is more important than knowledge." Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
Peter Zbornik wrote: Dear all, dear Markus Schulze, I got a second question from one of our members (actually the same guy which asked for the first time): If I just bullet vote in a Condorcet election, then I increase the chances of my candidate being elected. If I have a second or third option, the chances of my prefered candidate to win is lowered. Q: In this case why should any voter not bullet-vote? I have some clue on how to answer, but not enough for an exhaustive answer. I would say that the answer is contingency. Say that your favorite is A, and it's uncertain whether B or C is more popular, but you prefer B to C. Then, bullet-voting A might give you A instead of B (which would be good), but it might also give you C rather than B (which would be bad) because you falsely reported that it doesn't matter to you whether B or C wins. A bit more formally, consider this: C is the current CW and B is just short of beating him, while A is far behind. If two voters vote A > B = C, then nothing happens, but by voting A > B > C, B now beats C and wins. Also note that voting for additional candidates doesn't harm the outcome unless you, by doing so, set up or help others set up a cycle. If X is the CW and beats others by a lot of votes, then voting others ahead of X doesn't itself do anything harmful; the only potential for harm occurs in the domain of the cycle. Similarly, for the "advanced methods" (Schulze, Ranked Pairs, and so on), ranking candidates that end up outside of the Smith set doesn't do any harm either, because these methods satisfy Independence of Smith-dominated alternatives (also called "local IIA"). To sum all of that up: bullet-voting is like driving straight in a game of Chicken. Sure, you might benefit by doing so, but you may also crash and get a very bad outcome. In addition, the advanced methods pass criteria that both narrow down the situations where sincerity will backfire, as well as the degree to which it would do so; an ISDA-compliant method must obviously elect from the Smith set in the first place, for instance. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
Hi Peter, My quick responses to this: --- En date de : Mer 16.6.10, Peter Zbornik a écrit : >I got a second question from one of our members (actually the same guy >which asked for the first time): >If I just bullet vote in a Condorcet election, then I increase the chances >of my candidate being elected. >If I have a second or third option, the chances of my prefered candidate >to win is lowered. None of this is guaranteed. Actually listing additional preferences can also help a preferred candidate. >Q: In this case why should any voter not bullet-vote? You should not bullet vote if the possible use of voting for a second preference outweighs the likelihood that the second preference will hurt your first preference. It is not obvious that a voter should be trying to support his favorite candidate to the exclusion of everything else. He should be trying to get the best result possible on average. >My argument starts: >If I vote for a candidate who has >50% of the votes, then it does not >matter if there is a second or third choice. >If my prefered candidate A gets <50% of the votes, then it makes sense >to support a second choice candidate B. >However if the supporters of B only bullet vote, then maybe B's >supporters get an advantage over A? Yes, that can happen. But it doesn't follow from this, that everybody should bullet-vote. If A and B are similar candidates then all of these voters benefit from the A>B votes even though the B voters only voted B and denied A chance to win. Most likely if the A voters bullet-voted also, then some other candidate would win. >... at this point I realize, that I don't know enough about Condorcet >and/or Schulze to answer the question. > >Why is it not rational to bullet vote in a Condorcet election if you are >allowed not to rank some candidates? It could be rational in some cases, but it is not rational in general. In general it makes sense to express your preferences. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
Hi Kristofer, thanks for a detailed answer. As you answer contingency, it might be beneficial to turn the question around. In what situations will bullet voting help my candidate to win (considering the advanced Condorcet systems)? Peter On Wed, Jun 16, 2010 at 8:14 PM, Kristofer Munsterhjelm < km-el...@broadpark.no> wrote: > Peter Zbornik wrote: > >> Dear all, dear Markus Schulze, >> >> I got a second question from one of our members (actually the same guy >> which asked for the first time): >> If I just bullet vote in a Condorcet election, then I increase the chances >> of my candidate being elected. >> If I have a second or third option, the chances of my prefered candidate >> to win is lowered. >> Q: In this case why should any voter not bullet-vote? >> I have some clue on how to answer, but not enough for an exhaustive >> answer. >> > > I would say that the answer is contingency. Say that your favorite is A, > and it's uncertain whether B or C is more popular, but you prefer B to C. > Then, bullet-voting A might give you A instead of B (which would be good), > but it might also give you C rather than B (which would be bad) because you > falsely reported that it doesn't matter to you whether B or C wins. > > A bit more formally, consider this: C is the current CW and B is just short > of beating him, while A is far behind. If two voters vote A > B = C, then > nothing happens, but by voting A > B > C, B now beats C and wins. > > Also note that voting for additional candidates doesn't harm the outcome > unless you, by doing so, set up or help others set up a cycle. If X is the > CW and beats others by a lot of votes, then voting others ahead of X doesn't > itself do anything harmful; the only potential for harm occurs in the domain > of the cycle. > > Similarly, for the "advanced methods" (Schulze, Ranked Pairs, and so on), > ranking candidates that end up outside of the Smith set doesn't do any harm > either, because these methods satisfy Independence of Smith-dominated > alternatives (also called "local IIA"). > > To sum all of that up: bullet-voting is like driving straight in a game of > Chicken. Sure, you might benefit by doing so, but you may also crash and get > a very bad outcome. In addition, the advanced methods pass criteria that > both narrow down the situations where sincerity will backfire, as well as > the degree to which it would do so; an ISDA-compliant method must obviously > elect from the Smith set in the first place, for instance. > Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
2010/6/16 robert bristow-johnson > > On Jun 16, 2010, at 1:30 PM, Peter Zbornik wrote: > > Dear all, dear Markus Schulze, >> >> I got a second question from one of our members (actually the same guy >> which asked for the first time): >> If I just bullet vote in a Condorcet election, then I increase the chances >> of my candidate being elected? >> > > If there is a Condorcet Winner (CW), the answer is "no". If there is no > CW, then we have a "Condorcet paradox" or a "cycle" where Candidate Rock > beats Candidate Scissors, Candidate Scissors beats Candidate Paper, and > Candidate Paper beats Candidate Rock. Then I won't say whether the answer > is "no" for sure, but I am still convinced that cycles are rare and that a > method like Schulze or Ranked Pairs resolves the cycles meaningfully. Would that it were this easy. But there could be an honest CW, and bullet voting creates an artificial cycle. Simple case: 40 C>B>A 30 B>A>C 30 A>B>C B is the clear CW: wins 60/40 against C, and 70/30 against B. But if the A voters bullet vote, then there is a Condorcet cycle, because now B loses 30/40 against C. Some tiebreaking methods deal with this situation better than others. But if they twist themselves up in enough knots to avoid this problem, then they give results which are very hard to defend if half the A voters were really A>C>B voters who truncated lazily. Anyway, you cannot give simple guarantees like the one you stated above. JQ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
Hi Peter, --- En date de : Mer 16.6.10, Peter Zbornik a écrit : >In what situations will bullet voting help my candidate to win >(considering the advanced Condorcet systems)? The simplest is probably the one you gave. For example: 43 A 27 B vs. B>C 30 C>B If B voters don't give any second preference then generally B will win (depending perhaps on the particular method). But if B voters give a second preference for C then C will win. If B voters believe C voters will give them support then they could decide to bullet vote, as they can be confident that A will either win outright (as majority favorite) or suffer a pairwise defeat worse than B's loss to C. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
Some more viewpoints that were not covered very well yet. 1) Typical (=all common) Condorcet methods make pairwise comparisons and derive the results from those comparisons. Changing one's vote from A>B>C to A>B=C does not change the pairwise comparison results of ones favourite (A) against the others. The second vote does say B=C although the true opinion of the voter is B>C. That helps C and hurts B when these two are compared (these might be the two strongest candidates, and not indicating one's opinion in this pairwise comparison could change the winner from (sincere) B to C). 2) There are few cases where not giving one's sincere opinion may improve the result. It is however a fact that in almost all situations giving one's sincere preferences is the wisest thing the voter can do. It is not easy to identify and efficiently use those exceptional cases in Condorcet elections. For a regular voter in large public elections sincerity is clearly the best strategy to follow. Juho On Jun 16, 2010, at 8:30 PM, Peter Zbornik wrote: Dear all, dear Markus Schulze, I got a second question from one of our members (actually the same guy which asked for the first time): If I just bullet vote in a Condorcet election, then I increase the chances of my candidate being elected. If I have a second or third option, the chances of my prefered candidate to win is lowered. Q: In this case why should any voter not bullet-vote? I have some clue on how to answer, but not enough for an exhaustive answer. My argument starts: If I vote for a candidate who has >50% of the votes, then it does not matter if there is a second or third choice. If my prefered candidate A gets <50% of the votes, then it makes sense to support a second choice candidate B. However if the supporters of B only bullet vote, then maybe B's supporters get an advantage over A? ... at this point I realize, that I don't know enough about Condorcet and/or Schulze to answer the question. Why is it not rational to bullet vote in a Condorcet election if you are allowed not to rank some candidates? I guess you have discussed this question a zillion of times, so please forgive my ignorance. Maybe you could help me out with this one. Peter Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Condorcet question - why not bullet vote?
Peter, If I just bullet vote in a Condorcet election, then I increase the chances of my candidate being elected. Bullet voting in an election using a method that complies with the Condorcet criterion does I suppose somewhat increase the chance of your candidate being the Condorcet winner. But all Condorcet methods fail Later-no-Help, and in some this effect is sufficiently strong for the method to have a "random fill" incentive. That means that if you know nothing about how other voters will vote you are probabilistically better off by strictly ranking all your least preferred candidates. 46: A>B 44: B 10: C Here A is the CW, but if the 44B voters change to B>C then Schulze(Winning Votes) elects B. Schulze (WV) also has a zero-info. equal-rank at the top incentive. So say you know nothing about how other voters will vote and you have a big gap in your sincere ratings of the candidates, then your best probabilistic strategy is to rank all the candidates in your preferred group (those above the big gap in your ratings) equal-top and to strictly rank (randomly if necessarily) all the candidates below the gap. Your question seems to come with assumption that the voter doesn't care much who wins if her favourite doesn't. Q: In this case why should any voter not bullet-vote? The voter might be mainly interested in preventing her least preferred candidate from winning. Bullet voting is then a worse strategy than ranking that hated candidate strictly bottom. Another Condorcet method is Smith//Approval(ranking). That interprets ranking versus truncation as approval and elects the member of the Smith set (the smallest subset S of candidates that pairwise beat any/all non-S candidates) that has the highest approval score. (Some advocate the even simpler Condorcet//Approval(ranking) that simply elects the most approved candidate if there is no single Condorcet winner.) In the example above the effect of the 44B voters changing to B>C is with those methods to make C the new winner. Those methods do have a truncation incentive, so then many voters who are mainly interested in getting their strict favourites elected will and should "bullet vote". What is wrong with that? Chris Benham Dear all, dear Markus Schulze,I got a second question from one of our members (actually the same guy which asked for the first time): If I just bullet vote in a Condorcet election, then I increase the chances of my candidate being elected. If I have a second or third option, the chances of my prefered candidate to win is lowered. Q: In this case why should any voter not bullet-vote? I have some clue on how to answer, but not enough for an exhaustive answer.My argument starts: If I vote for a candidate who has >50% of the votes, then it does not matter if there is a second or third choice. If my prefered candidate A gets <50% of the votes, then it makes sense to support a second choice candidate B. However if the supporters of B only bullet vote, then maybe B's supporters get an advantage over A? ... at this point I realize, that I don't know enough about Condorcet and/or Schulze to answer the question.Why is it not rational to bullet vote in a Condorcet election if you are allowed not to rank some candidates? I guess you have discussed this question a zillion of times, so please forgive my ignorance.Maybe you could help me out with this one. Peter Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Thoughts on a nomination simulation
Kevin Venzke wrote: Hello, The last thing I did with my simulation is check whether on average a candidate would prefer to have withdrawn (considering the results of thousands of trials of one position) than stand, with the assumption that they care what happens when they lose. (I'm not sure that's actually a good assumption: It would be better to assume the voters are the ones who care, and don't support a candidate who spoils the election.) I got odd results. It could very well be a bug. But for example I found that (sincere) FPP had very few scenarios where a candidate would prefer to exit the race. Maybe it's because I had filtered out uncompetitive elections. But, even if FPP can handle some three-way races doesn't mean that we can score FPP based on them, with the assumption that they will occur. That seems like a big problem with my simulation, that there are always three candidates, and no check for incentives for more or fewer to be nominated. I think that a nomination simulation would have to be more complex, to take feedback into account. Candidates would position themselves somewhere in opinion space, then move closer to the winners depending on the outcome of the simulation (and possibly decide to drop out if this would elect a candidate closer to their position). Even so, the simulation would fail to catch certain aspects of the election cycle itself. Consider a two party state under FPTP. In a pure opinion-space analysis, the two parties would converge on a common point (the "center") in an effort to eat into each others' voters, yet in reality that doesn't seem to happen - the Republican and Democratic parties appeal to different voters. Changes in voter sentiment might be able to handle some of that problem; by having voters change their opinions between elections, candidates know not to get too specialized (because it takes time to move about in opinion space). That would also limit stagnation in even advanced systems: if you have a Condorcet method and a party places itself at the (static) median voter, the game is over and all the other parties can just as well go home. There are other effects as well: Parties and candidates might also slide into corruption unless checked by competition. One could model that by a candidate wanting to both be elected and to be placed at a certain point in opinion space (individual corruption), or by candidates being attracted towards a certain area in opinion space (coordinated corruption, e.g. by lobbying). Candidates may be of use (as opposition), even if not elected - not sure how to model that; and the candidates, particularly organized ones, may choose to employ strategy if doing so is feasible (as the New York parties did under STV) - I'm not sure how to model that, either. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
On Jun 16, 2010, at 9:39 PM, Peter Zbornik wrote: In what situations will bullet voting help my candidate to win (considering the advanced Condorcet systems)? Here's one more example where a reasonably small number of strategic voters can change the result. 49: A 48: B>C 3: C>B If the three C voters will truncate then they will win instead of B in winning votes based Condorcet methods. Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Thoughts on a nomination simulation
Hi Kristofer, --- En date de : Mer 16.6.10, Kristofer Munsterhjelm a écrit : > I think that a nomination simulation would have to be more > complex, to take feedback into account. Candidates would > position themselves somewhere in opinion space, then move > closer to the winners depending on the outcome of the > simulation (and possibly decide to drop out if this would > elect a candidate closer to their position). It basically works (or will work) like this except I plan to have the movement be in a random direction. If the movement is unsuccessful then the change is undone and the next candidate gets to "go." It's an issue but hopefully not an insurmountable one that the proper place for the candidate to stand may be nowhere near where they are. > Even so, the simulation would fail to catch certain aspects > of the election cycle itself. Consider a two party state > under FPTP. In a pure opinion-space analysis, the two > parties would converge on a common point (the "center") in > an effort to eat into each others' voters, yet in reality > that doesn't seem to happen - the Republican and Democratic > parties appeal to different voters. A possible theory: They could not converge to the center because a third candidate could decide to sit on the outer side of one, and still be somewhat viable. So, a candidate needs to be far enough from the center to discourage a rival nomination from the same side. > Changes in voter sentiment might be able to handle some of > that problem; by having voters change their opinions between > elections, candidates know not to get too specialized > (because it takes time to move about in opinion space). That > would also limit stagnation in even advanced systems: if you > have a Condorcet method and a party places itself at the > (static) median voter, the game is over and all the other > parties can just as well go home. Well currently the median is not static. On average it is static, but in a given election it could move a bit. > There are other effects as well: Parties and candidates > might also slide into corruption unless checked by > competition. One could model that by a candidate wanting to > both be elected and to be placed at a certain point in > opinion space (individual corruption), or by candidates > being attracted towards a certain area in opinion space > (coordinated corruption, e.g. by lobbying). Those are definitely interesting ideas. One would have to figure out the formula that decides where increasing "electibility" is no longer desirable to a candidate. > Candidates may > be of use (as opposition), even if not elected - not sure > how to model that; and the candidates, particularly > organized ones, may choose to employ strategy if doing so is > feasible (as the New York parties did under STV) - I'm not > sure how to model that, either. I expect to have candidates behave naively since I don't want to pretend to know beforehand what kinds of "transformations" could be helpful to a candidate. I really hope to see odd equilibria in some methods that have never been considered. The idea of a candidate being nominated to improve expectation from the election, rather than getting that candidate elected, raises the issue of whether candidates are mainly concerned about being elected, or about the expectation for their supporters. Also, whether "withdrawal" from the election means that the candidate actually withdraws, or that the voters simply decide that they will ignore this candidate as unhelpful. In reality it's probably a combination of both. Kevin Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote?
Chris, thanks for pointing these things out. I didn't know about the Later-no-Help. You write: "But all Condorcet methods fail Later-no-Help, and in some this effect is sufficiently strong for the method to have a "random fill" incentive." Do you know for which Condorcet methods this effect is sufficiently strong to have a random fill incentive? You write: "That means that if you know nothing about how other voters will vote you are probabilistically better off by strictly ranking all your least preferred candidates." Is this claim possible to prove or is it at least supported by some evidence? As for the no info, equal rank - this is a rational strategy when you have no info. In real life you have a lot of information about the expected voting behavior of others. Peter On Wed, Jun 16, 2010 at 9:11 PM, Chris Benham wrote: > Peter, > > If I just bullet vote in a Condorcet election, then I increase the chances > of my candidate being elected. > > Bullet voting in an election using a method that complies with the > Condorcet criterion does I suppose > somewhat increase the chance of your candidate being the Condorcet winner. > > But all Condorcet methods fail Later-no-Help, and in some this effect is > sufficiently strong for the method > to have a "random fill" incentive. That means that if you know nothing > about how other voters will vote > you are probabilistically better off by strictly ranking all your least > preferred candidates. > > 46: A>B > 44: B > 10: C > > Here A is the CW, but if the 44B voters change to B>C then Schulze(Winning > Votes) elects B. > > Schulze (WV) also has a zero-info. equal-rank at the top incentive. So say > you know nothing about > how other voters will vote and you have a big gap in your sincere ratings > of the candidates, then your > best probabilistic strategy is to rank all the candidates in your preferred > group (those above the big > gap in your ratings) equal-top and to strictly rank (randomly if > necessarily) all the candidates below > the gap. > > Your question seems to come with assumption that the voter doesn't care > much who wins if her favourite > doesn't. > > Q: In this case why should any voter not bullet-vote? > > The voter might be mainly interested in preventing her least preferred > candidate from winning. Bullet > voting is then a worse strategy than ranking that hated candidate strictly > bottom. > > Another Condorcet method is Smith//Approval(ranking). That interprets > ranking versus truncation as > approval and elects the member of the Smith set (the smallest subset S of > candidates that pairwise beat > any/all non-S candidates) that has the highest approval score. > > (Some advocate the even simpler Condorcet//Approval(ranking) that simply > elects the most approved > candidate if there is no single Condorcet winner.) > > In the example above the effect of the 44B voters changing to B>C is with > those methods to make C > the new winner. > > Those methods do have a truncation incentive, so then many voters who are > mainly interested in > getting their strict favourites elected will and should "bullet vote". > > What is wrong with that? > > Chris Benham > > > > > > > Dear all, dear Markus Schulze,I got a second question from one of our > members (actually the same guy which asked for the first time): If I just > bullet vote in a Condorcet election, then I increase the chances of my > candidate being elected. If I have a second or third option, the chances of > my prefered candidate to win is lowered. Q: In this case why should any > voter not bullet-vote? I have some clue on how to answer, but not enough > for an exhaustive answer.My argument starts: If I vote for a candidate > who has >50% of the votes, then it does not matter if there is a second or > third choice. If my prefered candidate A gets <50% of the votes, then it > makes sense to support a second choice candidate B. However if the > supporters of B only bullet vote, then maybe B's supporters get an > advantage over A? ... at this point I realize, that I don't know enough > about Condorcet and/or Schulze to answer the question.Why is it not > rational to > bullet vote in a Condorcet election if you are allowed not to rank some > candidates? I guess you have discussed this question a zillion of times, so > please forgive my ignorance.Maybe you could help me out with this one. >Peter > > > > Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
Juho, we have the example 49: A 48: B>C 3: C>B you wrote to me: "- C loses to B, 3-48. In winning votes the strength of this loss is 48. - B loses to A, 48-49. In winning votes the strength of this loss is 49. - A loses to C, 49-51. In winning votes the strength of this loss is 51." Thus: "If the three C voters will truncate then they will win instead of B in winning votes based Condorcet methods." This is correct, if proportional completion is not used (see page 42 in http://m-schulze.webhop.net/schulze2.pdf) If proportional completion is used (which I would recommend) then B wins. If proportional completion is used, then we need to fill in the preferences of the ones who did not vote: We have 100 voters. - C loses to B, 3-48, means 49 voters did not vote. We split each voter into two: the first has weight 3/51 of a vote and the second 48/51, which gives a total score of 49*3/51+3 vs 49*48/51+48 - B loses to A, 48-49, means 3 voters did not vote. We split each voter into two: the first has weight 48/97 and the second 49/97, which gives a total score of 3*48/97+48 vs 3*49/97+49 - A loses to C, 49-51, means all voters voted. Thus after the proportional completion, the vote tally is the following: - C loses to B, 5,88-94,12. In winning votes the strength of this loss is 94,12. - B loses to A, 49,48-50,52. In winning votes the strength of this loss is 50,52. (delete this link first) - A loses to C, 49-51. In winning votes the strength of this loss is 51. Thus B wins if proportional completion is used. C wins without proportional completion. Best regards Peter Zborník On Wed, Jun 16, 2010 at 9:35 PM, Juho wrote: > On Jun 16, 2010, at 9:39 PM, Peter Zbornik wrote: > > In what situations will bullet voting help my candidate to win >> (considering the advanced Condorcet systems)? >> > > Here's one more example where a reasonably small number of strategic voters > can change the result. > > 49: A > 48: B>C > 3: C>B > > If the three C voters will truncate then they will win instead of B in > winning votes based Condorcet methods. > > Juho > > > > > > > > Election-Methods mailing list - see http://electorama.com/em for list info > Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
So, why bother to vote for one or more? There are two leaders, and I have a preference (or three of which I prefer one or two).. I see clones so, if I like what they are, I should vote for all of them. I like what I hear of a candidate, so hope to attract more like this one, even if they are not getting many votes this time. Therefore: Among the leaders it matters, so you vote if you care. Among the also-rans it does not matter, so you vote if you care. Among those who might be on the edge of a significant vote count it only matters if the one you consider bullet voting, and the one you are considering as an option, are both on the edge such that you could regret whatever you do, that it is time to worry. So vote if you care, for voting can either help or hurt. The studying here mostly makes headaches. Dave Ketchum On Jun 16, 2010, at 2:20 PM, Kevin Venzke wrote: Hi Peter, My quick responses to this: --- En date de : Mer 16.6.10, Peter Zbornik a écrit : I got a second question from one of our members (actually the same guy which asked for the first time): If I just bullet vote in a Condorcet election, then I increase the chances of my candidate being elected. If I have a second or third option, the chances of my prefered candidate to win is lowered. None of this is guaranteed. Actually listing additional preferences can also help a preferred candidate. Q: In this case why should any voter not bullet-vote? You should not bullet vote if the possible use of voting for a second preference outweighs the likelihood that the second preference will hurt your first preference. It is not obvious that a voter should be trying to support his favorite candidate to the exclusion of everything else. He should be trying to get the best result possible on average. My argument starts: If I vote for a candidate who has >50% of the votes, then it does not matter if there is a second or third choice. If my prefered candidate A gets <50% of the votes, then it makes sense to support a second choice candidate B. However if the supporters of B only bullet vote, then maybe B's supporters get an advantage over A? Yes, that can happen. But it doesn't follow from this, that everybody should bullet-vote. If A and B are similar candidates then all of these voters benefit from the A>B votes even though the B voters only voted B and denied A chance to win. Most likely if the A voters bullet-voted also, then some other candidate would win. ... at this point I realize, that I don't know enough about Condorcet and/or Schulze to answer the question. Why is it not rational to bullet vote in a Condorcet election if you are allowed not to rank some candidates? It could be rational in some cases, but it is not rational in general. In general it makes sense to express your preferences. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
Hi Peter, --- En date de : Mer 16.6.10, Peter Zbornik a écrit : >Thus: "If the three C voters will truncate then they will win instead of B >in winning votes based Condorcet methods." > >This is correct, if proportional completion is not used (see page 42 >in http://m-schulze.webhop.net/schulze2.pdf) >If proportional completion is used (which I would recommend) then B wins. If you are using proportional completion (or "symmetric completion") then you're not using winning votes, you're using margins. Juho advocates MinMax(margins) which is why he posted this example (Schulze is usually assumed to use winning votes), and also why he didn't like it when I pointed out that clone independence and ISDA were the probable answers to your criteria question Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Thoughts on a nomination simulation
Kevin Venzke wrote:
Hi Kristofer,
--- En date de : Mer 16.6.10, Kristofer Munsterhjelm a
écrit :
I think that a nomination simulation would have to be more
complex, to take feedback into account. Candidates would
position themselves somewhere in opinion space, then move
closer to the winners depending on the outcome of the
simulation (and possibly decide to drop out if this would
elect a candidate closer to their position).
It basically works (or will work) like this except I plan to have the
movement be in a random direction. If the movement is unsuccessful then
the change is undone and the next candidate gets to "go." It's an issue
but hopefully not an insurmountable one that the proper place for the
candidate to stand may be nowhere near where they are.
The way I was considering would be to start with a bunch of random
candidates. Run the election. Each candidate then determines whether he
would have made his side better off if he didn't run, in which case he
removes himself from further rounds. Then the candidates that remain
update their position by moving closer to those on its side that are
above it in the social ordering, subject to possible counterbalancing
forces (warding off nominations on one's own side, for instance).
Finally, the voters' opinions change somewhat, to model a change of
opinion as may happen between elections.
The result would be a sort of attractor/k-means clustering type of
algorithm, where the dynamics would depend on the method in question.
One might also have new candidates appear - perhaps probabilistically
depending on distance to closest existing (or recently elected?) candidate.
Even so, the simulation would fail to catch certain aspects
of the election cycle itself. Consider a two party state
under FPTP. In a pure opinion-space analysis, the two
parties would converge on a common point (the "center") in
an effort to eat into each others' voters, yet in reality
that doesn't seem to happen - the Republican and Democratic
parties appeal to different voters.
A possible theory: They could not converge to the center because a
third candidate could decide to sit on the outer side of one, and still
be somewhat viable. So, a candidate needs to be far enough from the center
to discourage a rival nomination from the same side.
That is possible. Would primaries encourage that effect? If so, would we
expect parties in two-party states without voter primaries to be closer
to each other?
Changes in voter sentiment might be able to handle some of
that problem; by having voters change their opinions between
elections, candidates know not to get too specialized
(because it takes time to move about in opinion space). That
would also limit stagnation in even advanced systems: if you
have a Condorcet method and a party places itself at the
(static) median voter, the game is over and all the other
parties can just as well go home.
Well currently the median is not static. On average it is static, but in
a given election it could move a bit.
What I was thinking about here is that the median may change in a
consistent way. For instance, say that someone pulls off a particularly
large robbery in the country in question; this may shift the voters'
opinions to the "right/tough justice" area of opinion space; or the
voters may consider environmental concerns more important than earlier
and so shift in that direction. Events in the real world can change the
voter opinion.
In a simulation, I suppose the shifts would be modeled in a fairly
random manner, since it would be hard indeed to determine which model
would be most realistic. Perhaps some sort of 1/f noise would work so
that there is both slight/noisy changes and slow, large, consistent ones.
There are other effects as well: Parties and candidates
might also slide into corruption unless checked by
competition. One could model that by a candidate wanting to
both be elected and to be placed at a certain point in
opinion space (individual corruption), or by candidates
being attracted towards a certain area in opinion space
(coordinated corruption, e.g. by lobbying).
Those are definitely interesting ideas. One would have to figure out the
formula that decides where increasing "electibility" is no longer desirable
to a candidate.
I imagine electability would be the first priority (excepting idealist
candidates, but they aren't likely to be corrupted anyway). The
candidate would reason: better to be elected and make a compromise than
not make a compromise and not be elected. Within the space of positions
he can take and still be elected, however, the candidate would tend
towards a self-serving/corrupted point.
Cartel-like corruption ("what are you going to do, vote for a third
party?") would be more difficult to model. I'm not sure if they happen
consciously or if they're just a mutual laziness/implicit agreement by
both parties, a kind of "I won't lower my prices (approach the vote
Re: [EM] Condorcet question - why not bullet vote
On Jun 16, 2010, at 11:49 PM, Peter Zbornik wrote: Juho, we have the example 49: A 48: B>C 3: C>B you wrote to me: "- C loses to B, 3-48. In winning votes the strength of this loss is 48. - B loses to A, 48-49. In winning votes the strength of this loss is 49. - A loses to C, 49-51. In winning votes the strength of this loss is 51." Thus: "If the three C voters will truncate then they will win instead of B in winning votes based Condorcet methods." This is correct, if proportional completion is not used (see page 42 in http://m-schulze.webhop.net/schulze2.pdf) If proportional completion is used (which I would recommend) then B wins. Yes, the example applies to (typical) winning votes based methods. Other approaches like margins and the referenced approach may provide different results. If proportional completion is used, then we need to fill in the preferences of the ones who did not vote: We have 100 voters. - C loses to B, 3-48, means 49 voters did not vote. We split each voter into two: the first has weight 3/51 of a vote and the second 48/51, which gives a total score of 49*3/51+3 vs 49*48/51+48 - B loses to A, 48-49, means 3 voters did not vote. We split each voter into two: the first has weight 48/97 and the second 49/97, which gives a total score of 3*48/97+48 vs 3*49/97+49 - A loses to C, 49-51, means all voters voted. Thus after the proportional completion, the vote tally is the following: - C loses to B, 5,88-94,12. In winning votes the strength of this loss is 94,12. - B loses to A, 49,48-50,52. In winning votes the strength of this loss is 50,52. (delete this link first) What link? - A loses to C, 49-51. In winning votes the strength of this loss is 51. Thus B wins if proportional completion is used. C wins without proportional completion. There are many different approaches to measuring the preference strength of the pairwise comparisons. Winning votes and margins are the most common ones. The referenced approach would be a third approach. It seems to be the proportion of the given votes. Correct? 94,12 = 100/(3/48+1), i.e. the proportion of the preferences (48:3) scaled in another way (100/(1/x+1)) (Shortly back to the original question. Unfortunately I don't have any interesting proportion specific truncation related examples or properties in my ind right now.) Juho Best regards Peter Zborník On Wed, Jun 16, 2010 at 9:35 PM, Juho wrote: On Jun 16, 2010, at 9:39 PM, Peter Zbornik wrote: In what situations will bullet voting help my candidate to win (considering the advanced Condorcet systems)? Here's one more example where a reasonably small number of strategic voters can change the result. 49: A 48: B>C 3: C>B If the three C voters will truncate then they will win instead of B in winning votes based Condorcet methods. Juho Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
On Jun 17, 2010, at 12:29 AM, Kevin Venzke wrote: Hi Peter, --- En date de : Mer 16.6.10, Peter Zbornik a écrit : Thus: "If the three C voters will truncate then they will win instead of B in winning votes based Condorcet methods." This is correct, if proportional completion is not used (see page 42 in http://m-schulze.webhop.net/schulze2.pdf) If proportional completion is used (which I would recommend) then B wins. If you are using proportional completion (or "symmetric completion") then you're not using winning votes, you're using margins. The described algorithm seemed to make the completion in a "non- symmetric" way, leading to comparing the proportions of the A>B and B>A votes. Juho advocates MinMax(margins) which is why he posted this example Not really because of the minmax part but to cover also margins in addition to winning votes. (Schulze is usually assumed to use winning votes), and also why he didn't like it when I pointed out that clone independence and ISDA were the probable answers to your criteria question That was on the minmax part. Minmax doesn't meet the Smith criterion and clone independence (in some extreme situations). Also in this case I wanted to cover also those methods in the discussion (in addition to the usual Smith+WV ones and criteria that those methods meet). Kevin Venzke is usually more on the WV and Smith set line (right?). When it comes to real life elections I tend to think that all common Condorcet methods are pretty similar, and because of that similarity all the vulnerabilities and dramatic looking criteria do not mean that much in real elections. They make wonderful tools for propaganda though since one can construct dramatic looking (often just theoretical, not real life like) examples and criteria. All reasonable elections methods and all Condorcet methods violate some criteria that one probably would like to keep. It may also be that the best method (whatever that is) is one that violates numerous criteria but only slightly each one of them (and in situations that do not usually occur in real elections, or in some situations where the good looking criteria actually should be violated for some other more important reason). From practical Condorcet promotion point of view I don't recommend diving too deep in the world of different Condorcet variants and criteria. All typical Condorcet methods are exceptionally good single- winner methods for competitive environments. Better to concentrate on the properties of the Condorcet methods in general and just mention that there are different variants with slightly different properties. Btw, when it comes to different Condorcet methods and their differences (different results) in real life elections I expect the first differences to emerge in the margins vs. winning votes ((vs. other possible approaches)) front. The Smith set and cycle of four (or more) related differences are probably not as common. I assume reasonably sincere voters here. Also truncation may lead to missing the true Condorcet winner (but this is more difficult to measure since people truncated their votes and their true preferences were thus not recorded for analysis after the election). Juho Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Election calculator / Czech Green Party case
I wrote some code to study proportionality in the Czech Green Party
case. I uploaded some of that stuff also in the Internet in case you
are interested to experiment with it. The code is purely experimental
and draft and not very stable at the moment, i.e. no guarantees given,
but right now it seems to be operational at some level. You may check
it at http://electioncalculator.appspot.com/. At the moment the
proportional method does some exhaustive search over all the
combinations, so use it only with small number of candidates and
elected council members to avoid combinatorial explosion. (I'm
interested also in non-exhaustive versions but they are not good
enough to be used at the moment.)
Example input:
method == Proportional
members == 5
ordered == 2
group == 2 aceg
group == 2 bdf
24 abcd
24 cbad
4 d
24 efgd
24 gfed
Button "Calculate" should do the job. In this input the used method is
obviously "Proportional". Number of council members is 5 ("members ==
5"). Two of the members will be elected using a proportional ranking
method ("ordered == 2"). There are two groups that each must get at
least two members (could be men and women). Different groups may
contain also same characters (candidates) and not contain some
characters in any of the groups although in the male/female case that
would not be very "natural" :-). And then there are the votes. The
requirement to achieve maximum proportionality and sufficient
participation of all the groups will not impact the ordered candidates
(i.e. the ordered candidates may distort proportionality a bit like in
the given example where d will be elected as the president, and
forcing sufficient representation of the groups may distort the
selection of the other members of the council a bit more since the
presidents will not participate in this game). Note that the "=="
parameters must be given in the first rows of the input. The
calculator is not very sensitive with respect to the format of the
input. It can eat all kind of strings with (optional) number at the
beginning of the row and all kinds of ASCII characters and equal signs
and English alphabet characters (candidates) later on the row.
These properties do cover most of the topics that were addressed in
the Czech Green Party discussions. (At least possibility of separate
votes for the presidents is still missing (maybe not a key feature but
somewhat interesting in theory).)
The given example contains some ties. Ties will be resolved using
random numbers. Ties will be indicated in the results (in the given
example both among the ordered candidates and sometimes also in the
composition of the whole council).
I included also some other buttons for some other methods. Clicking
button "PO" corresponds to having a "method == PO" parameter row among
the parameters at the beginning of the input. "PO" means proportional
order/ranking. The above mentioned additional parameters do not have
any influence in this method, except that it seems that the "members"
parameter will list given number of candidates from the beginning of
the ranking. (You should be able to reach the same results also with
the "Proportional" method and suitable parameters (all members/
candidates ordered).)
The "Proportional" method is a quite straight forward CPO-STV style
method that uses a Hare style quota (number of non-empty ballots
divided by the number of council members (not rounded/truncated)). The
weight of each vote that ranks some candidates that are in both
compared councils above the first candidate that will make the
difference between which alternative the vote supports will be reduced
by one quota (shared between all such votes). No negative weights
though. Equal ranking is allowed. Minmax(margins) is used to compare
different alternative council compositions and pick the winning one.
My current code is full of experimental and testing/debugging related
features but if needed I can extract some appropriate variant and
provide open source code for it. In this kind of complex methods open
source code and/or alternative implementations and/or reference
implementations are important to guarantee that the method (and the
implementation that will be used in the actual election) is correct
and does not contain any unintentional bugs nor any malicious
bugs/"features" (and also to make it easier for people to trust that
the system works as intended, not just to guarantee that it works as
intended).
Problem reports and other comments are welcome. I hope not too many
problem reports though :-). I will expand and improve (and otherwise
modify, maybe even destroy) the calculator when time allows and I have
the energy and ideas.
Juho
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
Hi Juho, --- En date de : Mer 16.6.10, Juho a écrit : > > If you are using proportional completion (or > "symmetric completion") then > > you're not using winning votes, you're using margins. > > The described algorithm seemed to make the completion in a > "non-symmetric" way, leading to comparing the proportions of > the A>B and B>A votes. I see... > > Juho advocates MinMax(margins) which is why he posted > this example > > Not really because of the minmax part but to cover also > margins in addition to winning votes. Not sure what you mean by that, as the example I posted works with both. > > (Schulze is usually assumed to use winning votes), and > also why he didn't > > like it when I pointed out that clone independence and > ISDA were the > > probable answers to your criteria question > > That was on the minmax part. Minmax doesn't meet the Smith > criterion and clone independence (in some extreme > situations). Also in this case I wanted to cover also those > methods in the discussion (in addition to the usual Smith+WV > ones and criteria that those methods meet). > > Kevin Venzke is usually more on the WV and Smith set line > (right?). I rarely advocate Smith. I find it such a weak criterion that it's not worth sacrificing much to satisfy it. I prefer CDTT or criteria that are reminiscent of it, geared towards respecting full majorities. > When it comes to real life elections I tend to think that > all common Condorcet methods are pretty similar, and because > of that similarity all the vulnerabilities and dramatic > looking criteria do not mean that much in real elections. > They make wonderful tools for propaganda though since one > can construct dramatic looking (often just theoretical, not > real life like) examples and criteria. I admit your truncation example was more dramatic than mine. Kevin Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Thoughts on a nomination simulation
Hi Kristofer, --- En date de : Mer 16.6.10, Kristofer Munsterhjelm a écrit : > >> Even so, the simulation would fail to catch > certain aspects > >> of the election cycle itself. Consider a two party > state > >> under FPTP. In a pure opinion-space analysis, the > two > >> parties would converge on a common point (the > "center") in > >> an effort to eat into each others' voters, yet in > reality > >> that doesn't seem to happen - the Republican and > Democratic > >> parties appeal to different voters. > > > > A possible theory: They could not converge to the > center because a > > third candidate could decide to sit on the outer side > of one, and still > > be somewhat viable. So, a candidate needs to be far > enough from the center > > to discourage a rival nomination from the same side. > > That is possible. Would primaries encourage that effect? If > so, would we expect parties in two-party states without > voter primaries to be closer to each other? I'm not sure. I tend to view primaries as one form of a phenomenon that will inevitably happen under FPP one way or another. If there's something important about them I guess it has something to do with timing... > >> There are other effects as well: Parties and > candidates > >> might also slide into corruption unless checked > by > >> competition. One could model that by a candidate > wanting to > >> both be elected and to be placed at a certain > point in > >> opinion space (individual corruption), or by > candidates > >> being attracted towards a certain area in opinion > space > >> (coordinated corruption, e.g. by lobbying). > > > > Those are definitely interesting ideas. One would have > to figure out the > > formula that decides where increasing "electibility" > is no longer desirable > > to a candidate. > > I imagine electability would be the first priority > (excepting idealist candidates, but they aren't likely to be > corrupted anyway). The candidate would reason: better to be > elected and make a compromise than not make a compromise and > not be elected. Within the space of positions he can take > and still be elected, however, the candidate would tend > towards a self-serving/corrupted point. Well electability would be a percentage. So assuming that's the final measure of the value of a position, I guess position on the "corruption axis" could work as a bonus/penalty to this measure. Not quite sure how it would work but I imagine the idea is that if you have two major parties, both parties can seem to conspire to nominate candidates in a region that no voters really like. At the moment I've added to my utility simulation the ability to iterate over some space rather than just be completely random. I'm checking all elections in 1D space with 9 positions allowed (evenly spaced) for just 729 possible elections (some redundant due to symmetry). Then I'm going to see if the methods differ, on these, with respect to which scenarios don't give any of the three candidates incentive to move. And then for the "stable" scenarios I'll check whether any candidates wanted to withdraw. Could be interesting, could be dull. Hopefully it will give me a sense of how productive a brand new simulation would be. Kevin Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Thoughts on a nomination simulation
On Jun 16, 2010, at 9:57 PM, Kevin Venzke wrote: Hi Kristofer, --- En date de : Mer 16.6.10, Kristofer Munsterhjelm > a écrit : Even so, the simulation would fail to catch certain aspects of the election cycle itself. Consider a two party state under FPTP. In a pure opinion-space analysis, the two parties would converge on a common point (the "center") in an effort to eat into each others' voters, yet in reality that doesn't seem to happen - the Republican and Democratic parties appeal to different voters. A possible theory: They could not converge to the center because a third candidate could decide to sit on the outer side of one, and still be somewhat viable. So, a candidate needs to be far enough from the center to discourage a rival nomination from the same side. That is possible. Would primaries encourage that effect? If so, would we expect parties in two-party states without voter primaries to be closer to each other? I'm not sure. I tend to view primaries as one form of a phenomenon that will inevitably happen under FPP one way or another. If there's something important about them I guess it has something to do with timing... Plurality NEEDS primaries because its voters can vote for only one. If X1 and X2 run for party X, without primaries, they can expect to each get only half the votes intended for party X. If Y1 is the only candidate for party Y, Y1 has a big advantage over X1 and X2. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Thoughts on a nomination simulation
Hi Dave, --- En date de : Mer 16.6.10, Dave Ketchum a écrit : > >> That is possible. Would primaries encourage that > effect? If > >> so, would we expect parties in two-party states > without > >> voter primaries to be closer to each other? > > > > I'm not sure. I tend to view primaries as one form of > a phenomenon that > > will inevitably happen under FPP one way or another. > If there's something > > important about them I guess it has something to do > with timing... > > Plurality NEEDS primaries because its voters can vote for > only one. If X1 and X2 run for party X, without > primaries, they can expect to each get only half the votes > intended for party X. If Y1 is the only candidate for > party Y, Y1 has a big advantage over X1 and X2. What I'm saying is that if we didn't have primaries, candidates would either drop out or voters would decide not to support them, so that there would still only be two viable candidates on election day. What I'm unclear on is what effect primaries have (or we should expect that they have) on candidate positions in comparison to just having candidates drop off as they start to lose in the polls. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Thoughts on a nomination simulation
On Jun 16, 2010, at 11:11 PM, Kevin Venzke wrote: Hi Dave, --- En date de : Mer 16.6.10, Dave Ketchum a écrit : That is possible. Would primaries encourage that effect? If so, would we expect parties in two-party states without voter primaries to be closer to each other? I'm not sure. I tend to view primaries as one form of a phenomenon that will inevitably happen under FPP one way or another. If there's something important about them I guess it has something to do with timing... Plurality NEEDS primaries because its voters can vote for only one. If X1 and X2 run for party X, without primaries, they can expect to each get only half the votes intended for party X. If Y1 is the only candidate for party Y, Y1 has a big advantage over X1 and X2. What I'm saying is that if we didn't have primaries, candidates would either drop out or voters would decide not to support them, so that there would still only be two viable candidates on election day. What I'm unclear on is what effect primaries have (or we should expect that they have) on candidate positions in comparison to just having candidates drop off as they start to lose in the polls. True that candidates can drop out, and some might respond to unexpected competition with such. Voters deciding not to support X1/ X2 is possible. My point was that plurality can be helped via primaries when your alternatives fail. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
Hi, Kevin, thanks for the comment. Well, it is true, that Schulze writes in http://m-schulze.webhop.net/schulze1.pdf, page 154, that "There has been some debate about how to define D [Schulze ranking relation] when it is presumed that on the one side each voter has a sincere linear ordering of the candidates, but on the other side some voters cast only a partial ordering because of strategic considerations. We got to the conclusion that the strength (N[e,f],N[f,e]) of the pairwise win ef ∈ A × A should be measured primarily by the absolute number of votes for the winner of this pairwise defeat N[e,f] and secondarily by the absolute number of votes for the loser of this pairwise defeat N[f,e]." However, for Schulze STV, proportional completion is used for incomplete orderings (see page 42 in http://m-schulze.webhop.net/schulze2.pdf). I thought, that Schulze STV reduces to Schulze Condorcet in the case where there is one seat. Now, this seems not to be the case when we have incomplete ballots (i.e. we allow for equal ranking of candidates), as Schulze Condorcet uses winning (and losing) votes and Schulze STV uses proportional completion before deciding upon winning votes. Maybe Markus Schulze could comment on this himself. I think proportional completion could be used in Schulze Condorcet, but there is obviously one big open question in this respect. Does Schulze Condorcet (proportional completion) meet the same criteria as Schulze (WV), http://en.wikipedia.org/wiki/Schulze_method#Satisfied_and_failed_criteria? Kevin, you seem to say that Shulze Condorcet (proportional completion) does meet the same criteria as Minimax(margins), quote "If you are using proportional completion (or "symmetric completion") then you're not using winning votes, you're using margins". Are you sure about this? Schulze Condorcet (proportional completion) gives different results than Schulze Condorcet (margins). For instance: Say we have two pairwise defeats and 100 voters - A vs B. First defeat A-B, 1-5. Margin gives 4 as the strength of the win. Proportional completion gives: 1+94*1/6 - 5+94*5/6=16,67-83,33, i.e. a margin of 66,67 (94 voters, each split into two with proportional weights). Second defeat A-B, 48-52. The margin is 4 both with proportional completion and without. Thus, it seems that proportional completion gives different results from both the winning (losing) votes approach and the margin approach for truncated Condorcet ballots. The natural question is: What are the differences in satisfied and failed criteria ( http://en.wikipedia.org/wiki/Schulze_method#Satisfied_and_failed_criteria) between Schulze Condorcet (proportional completion) and, Schulze Condorcet (WV)? Best regards Peter Zborník On Wed, Jun 16, 2010 at 11:29 PM, Kevin Venzke wrote: > Hi Peter, > > --- En date de : Mer 16.6.10, Peter Zbornik a écrit : > >Thus: "If the three C voters will truncate then they will win instead of B > >in winning votes based Condorcet methods." > > > >This is correct, if proportional completion is not used (see page 42 > >in http://m-schulze.webhop.net/schulze2.pdf) > >If proportional completion is used (which I would recommend) then B wins. > > If you are using proportional completion (or "symmetric completion") then > you're not using winning votes, you're using margins. > > Juho advocates MinMax(margins) which is why he posted this example > (Schulze is usually assumed to use winning votes), and also why he didn't > like it when I pointed out that clone independence and ISDA were the > probable answers to your criteria question > > Kevin Venzke > > > > > > Election-Methods mailing list - see http://electorama.com/em for list info > Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet question - why not bullet vote
On Thu, Jun 17, 2010 at 1:06 AM, Juho Laatu wrote: > On Jun 16, 2010, at 11:49 PM, Peter Zbornik wrote: > > Juho, > > we have the example > 49: A > 48: B>C > 3: C>B > > you wrote to me: > "- C loses to B, 3-48. In winning votes the strength of this loss is 48. > - B loses to A, 48-49. In winning votes the strength of this loss is 49. > - A loses to C, 49-51. In winning votes the strength of this loss is 51." > > Thus: "If the three C voters will truncate then they will win instead of B > in winning votes based Condorcet methods." > > This is correct, if proportional completion is not used (see page 42 in > http://m-schulze.webhop.net/schulze2.pdf) > If proportional completion is used (which I would recommend) then B wins. > > > Yes, the example applies to (typical) winning votes based methods. Other > approaches like margins and the referenced approach may provide different > results. > > > If proportional completion is used, then we need to fill in the preferences > of the ones who did not vote: > We have 100 voters. > - C loses to B, 3-48, means 49 voters did not vote. We split each voter > into two: the first has weight 3/51 of a vote and the second 48/51, which > gives a total score of 49*3/51+3 vs 49*48/51+48 > - B loses to A, 48-49, means 3 voters did not vote. We split each voter > into two: the first has weight 48/97 and the second 49/97, which gives a > total score of 3*48/97+48 vs 3*49/97+49 > - A loses to C, 49-51, means all voters voted. > > Thus after the proportional completion, the vote tally is the following: > - C loses to B, 5,88-94,12. In winning votes the strength of this loss > is 94,12. > - B loses to A, 49,48-50,52. In winning votes the strength of this loss > is 50,52. (delete this link first) > > > What link? > http://en.wikipedia.org/wiki/Schulze_method#The_Schwartz_set_heuristic, point 3 > > - A loses to C, 49-51. In winning votes the strength of this loss is 51. > > Thus B wins if proportional completion is used. C wins without proportional > completion. > > > There are many different approaches to measuring the preference strength of > the pairwise comparisons. Winning votes and margins are the most common > ones. The referenced approach would be a third approach. It seems to be the > proportion of the given votes. Correct? > Yes, the proportion is the same and the result is scaled up to the number of voters, and is suggested by Markus Schulze as mentioned below. Something similar (splitting up observations into two complementary) is done in statistics, when measuring the predictive strength of a logistic regression function on validation data. > > 94,12 = 100/(3/48+1), i.e. the proportion of the preferences (48:3) scaled > in another way (100/(1/x+1)) > > (Shortly back to the original question. Unfortunately I don't have any > interesting proportion specific truncation related examples or properties in > my ind right now.) > > Juho > > > > > > Best regards > Peter Zborník > > On Wed, Jun 16, 2010 at 9:35 PM, Juho wrote: > >> On Jun 16, 2010, at 9:39 PM, Peter Zbornik wrote: >> >> In what situations will bullet voting help my candidate to win >>> (considering the advanced Condorcet systems)? >>> >> >> Here's one more example where a reasonably small number of strategic >> voters can change the result. >> >> 49: A >> 48: B>C >> 3: C>B >> >> If the three C voters will truncate then they will win instead of B in >> winning votes based Condorcet methods. >> >> Juho >> >> >> >> >> >> >> >> Election-Methods mailing list - see http://electorama.com/em for list >> info >> > > > Election-Methods mailing list - see http://electorama.com/em for list info > > > > > Election-Methods mailing list - see http://electorama.com/em for list info > > Election-Methods mailing list - see http://electorama.com/em for list info
