Re: [EM]Definite Majority Choice, AWP, AM
Dear Chris! You wrote: I like this table. Thanks. Doesn't AM look like the most natural and balanced? Yes, but that's only an aesthetical judgement... I was wondering if it is possible in AM for a candidate who is both the sincere CW and sincere AW to successfully Buried, and I've come up with an example that shows that unfortunately it is, but AWP and DMC likewise fail in the same example. But not DFC (Democratic Fair Choice aka Random Ballot from Forest's P), as I will show below! Sincere preferences: 48: ABC 01: ACB 03: BAC 48: CBA B is the CW and AW. Also DFC elects B here. Then 45 of the 48 AB voters Bury B strongly, i.e. with both rankings and approval, while the other 3 of the 48 only Bury with their rankings (not approving C). [...] All three methods elect the Burier's candidate, A. But DFC elects A only with 52% probability, and C with 48% probability. This means the Buriers would get their least prefered candidate with a large probability, which should deter them from strategizing. When there are three candidates in the top cycle, AM has the property that the candidate with the lowest voted approval score can't win. But that's also true for DMC and DFC since that candidate is always strongly defeated. Jobst wrote: Here you state the obvious problem when looking at both approval and defeat information. Forest's ingenious argument was that we should at least not elect a candidate where both kinds of information agree that the candidate is defeated, leaving us with his set P of candidates which are not strongly defeated. But when we take both kinds of information serious, it does not seem appropriate to me to always elect a candidate from the two extremes of P like Approval and DMC do. Still, DMC has the obvious advantage of extreme simplicity. I would find it much more natural if the winner was somewhere in the middle of P! Doesn't Approval Margins fill the bill? Welcome to the AM fan club! I don't know... Which cycle resolution technique does AM use? The claim that the winner belongs to P seems to hold at least when you use an immune cycle resolution technique like that of Beatpath, RP, or River... Yours, Jobst Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM]Definite Majority Choice, AWP, AM
Hello James and All, On Mar 26, 2005, at 14:05, James Green-Armytage wrote: Yes, but you've not yet understood the virtue of cardinal-weighted pairwise and approval-weighted pairwise. I request that you read my cardinal pairwise paper, as most of the arguments used therein apply to AWP as well. http://fc.antioch.edu/~james_green-armytage/cwp13.htm No Condorcet method can escape the possibility of the burying strategy, but CWP and AWP make it so that you can't change the result from a sincere CW to someone who is very *different* from the sincere CW (except by large cycle strategies that are probably to complex to be realistic). I think there is some confusion here. My intention was not to criticize the cardinal pairwise or other methods but just to comment on the (voting method independent) evaluation criteria that were used when studying the voting examples. My statement was thus that if sincere votes would be X but real votes are Y, it is very difficult (maybe not possible in practice) to construct a voting method that would take X into account when making decisions. This is because only Y is known and it is too difficult to guess what X was (or to identify which individual votes are strategic in Y). We can only use some generic means (=no reference to the actual sincere votes X) when trying to eliminate strategies. Agreed? Concerning the rest of your mail I think your analysis of this example is good, and related voting methods that add new information to basic ranking are a very fruitful area of study. Since I commented the evaluation criteria only, my intention was not to say that K/Kerry should not win this election. I only said that being a sincere Condorcet winner is not a good argument to favour K. I agree that the ratings give additional information that can be used to determine how the cycles should be solved, and in this case evidence supports Kerry quite well. I believe I'm quite in line with you here. The best voting methods or voting organizers can do in this situation is to try to discourage strategic voting. If the reward-strength/probability of a given strategy obviously outweighs the risk strength/probability, then we should assume that voters will tend to use the strategy. Perhaps they won't, but we should err on the side of caution, especially where flagrant incursions are concerned. Anything else would be naive and dangerous. I agree. But in addition to risk strength/probability we should cover also things like difficulty to understand/apply, difficulty to agree on the strategy etc. Also the level of distortion (a strategy may lead e.g. to election of the second best or the worst candidate) should be taken into account when evaluating the need to defend against different strategies. Happy birthday to you. Best Regards, Juho Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM]Definite Majority Choice, AWP, AM
Hi Juho, Some replies follow, on the subject of voter strategy and approval-weighted pairwise. These comments should also be helpful for others who don't understand why I consider AWP to be clearly better than DMC and AM. The voting method sees only the altered votes. Although the sincere CW would be K, a voting method that elects K is not necessarily good. In this case votes 4: BDK were altered. But as well it could have been that those votes were sincere and for example votes 4: KBD were altered. Lets say that the sincere votes of those K supporters are 4: KDB. If that was the case, then the sincere CW would have been D. Yes, but you've not yet understood the virtue of cardinal-weighted pairwise and approval-weighted pairwise. I request that you read my cardinal pairwise paper, as most of the arguments used therein apply to AWP as well. http://fc.antioch.edu/~james_green-armytage/cwp13.htm No Condorcet method can escape the possibility of the burying strategy, but CWP and AWP make it so that you can't change the result from a sincere CW to someone who is very *different* from the sincere CW (except by large cycle strategies that are probably to complex to be realistic). In this example, Kerry is similar to Dean, while Kerry and Dean are different from Bush. How do I define similar and different? The average rating differentials on preferences between two candidates. This is straight out of my cardinal pairwise paper, section 7.a. Changing the winner from Kerry to Bush is what I call a flagrant incursion (one that causes a very high-priority defeat to be overruled by a false defeat). Changing the winner from Dean to Kerry (as in your scenario) does not fit this definition. A flagrant incursion undermines the intent of the voters much more severely than a non-flagrant incursion. Furthermore, Kerry voters planning a burying strategy against Dean risk much more than Bush voters planning a burying strategy against Kerry. This is in part because Dean cannot possibly stand a chance of being elected without the help of Kerry supporters; if the Kerry supporters get wind of the strategy ahead of time and respond in kind, Bush's victory is assured. Bush, on the other hand, has no similar allegiance with Kerry or Dean, and Bush supporters on the whole have less to lose if Dean and Kerry supporters get alienated from them (because, for the most part, they already are). It is in this way that CWP and AWP distribute strategic incentive in roughly inverse proportion to strategic ability. Section 7.b. This is perhaps the best possible anti-strategic property to have; if we accept that at least some group of voters is likely to have a burying opportunity against the sincere CW, it is much better for this group to consist of voters who don't prefer some candidate on the opposite side of the political spectrum to the CW. So, it looks to me that in the example above the voting methods should behave as if there was a sincere cycle and not favour K any more than the others. First of all, as Mike said, ignoring voter strategy won't make it go away. However, I can make a very strong argument for CWP and AWP in sincere voting scenarios as well. Let's say that second set of votes are sincere, as you suggest. Bush beats Dean, and most of the BD voters feel strongly about that preference (44 out of 52 place their cutoff between Bush and Dean). Kerry beats Bush, and most of the KB voters feel strongly about that preference (46 out of 51 place their cutoff between Kerry and Bush). Dean beats Kerry, but only a small portion of the voters feel strongly about the DK preference. Hence, if you have to overrule one defeat, I argue that the DK defeat is the most appropriate one to overrule. Do you see how this makes common sense? The best voting methods or voting organizers can do in this situation is to try to discourage strategic voting. If the reward-strength/probability of a given strategy obviously outweighs the risk strength/probability, then we should assume that voters will tend to use the strategy. Perhaps they won't, but we should err on the side of caution, especially where flagrant incursions are concerned. Anything else would be naive and dangerous. Sincerely, James Green-Armytage http://fc.antioch.edu/~james_green-armytage/voting.htm + APPENDIX: My example from 9/22/04 http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-September/013936.html 3 candidates: Kerry, Dean, and Bush. 100 voters. Sincere preferences 19: KDB 5: KDB 4: KBD 18: DKB 5: DKB 1: DBK 25: BKD 23: BDK Kerry is a Condorcet winner. Altered preferences 19: KDB 5: KDB 4: KBD 18: DKB 5: DKB 1: DBK 21: BKD 23: BDK 4: BDK (these are sincerely BKD) There is a cycle now, KBDK happy birthday to me ... happy birthday to me .. *sigh* .. Election-methods mailing list -
Re: [EM]Definite Majority Choice, AWP, AM
Hello Chris, I have one generic comment on evaluation of different voting methods. Examples that include both sincere votes and altered votes nicely demonstrate the possibilities of strategic voting, but when the voting method gets a pile of ballots to be counted, no knowledge of which votes are sincere is available. I'll modify one of the examples to show what I mean. On Mar 24, 2005, at 18:11, Chris Benham wrote: The first is copied from a Sep.22,04 James G-A post. 3 candidates: Kerry, Dean, and Bush. 100 voters. Sincere preferences 19: KDB 5: KDB 4: KBD 18: DKB 5: DKB 1: DBK 25: BKD 23: BDK Kerry is a Condorcet winner. Altered preferences 19: KDB 5: KDB 4: KBD 18: DKB 5: DKB 1: DBK 21: BKD 23: BDK 4: BDK (these are sincerely BKD) There is a cycle now, KBDK The voting method sees only the altered votes. Although the sincere CW would be K, a voting method that elects K is not necessarily good. In this case votes 4: BDK were altered. But as well it could have been that those votes were sincere and for example votes 4: KBD were altered. Lets say that the sincere votes of those K supporters are 4: KDB. If that was the case, then the sincere CW would have been D. Since the voting method can not know which votes are sincere and which not, I guess it should behave as the votes given in the election were the sincere votes. I can't find any good examples where the voting method would be able to identify some votes as insincere. Maybe in the case that all ballots that have X in the first place are identical one could guess that X supporters have agreed some strategy. But of course that could as well be their sincere uniform opinion. So, it looks to me that in the example above the voting methods should behave as if there was a sincere cycle and not favour K any more than the others. The best voting methods or voting organizers can do in this situation is to try to discourage strategic voting. Best Regards, Juho ((P.S. One possible deviation to this main rule is a voting method that is known to require some certain strategy from the voters (to give the best results). In this case one could assume in the result counting process of the voting method that all voters have voted according to this known strategy and results should therefore be calculated using this assumption. In this case the voting method of course could give unwanted results if all or majority of voters voted sincerely. Maybe one should redefine sincerity in this case = sincere votes are those that follow the recommended/expected voting practice and do that in the light of voter's sincere preferences.)) --end of message-- Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM]Definite Majority Choice, AWP, AM
Dear Chris! First, I'd like to emphasize that DMC, AWP, and AM can be thought of as being essentially the same method with only different definition of defeat strength, so it seems quite natural to compare them in detail as you started. Recall that the DMC winner is the unique immune candidate when defeat strength is defined as the approval of the defeating candidate, so with that definition, Beatpath, RP, and River become equivalent to DMC. Perhaps it is helpful to look at the defeat strength like this: When A defeats B, then the defeat strength is composed as a linear combination of the following three components: AM AWP DMC no. of voters approving A but not B + + + no. of voters approving A and B 0 0 + no. of voters approving B but not A - 0 0 My second point is this: Your wrote: I used to think that electing the voted approval loser was absurd if we assume that the votes are sincere, but by that logic we should resolve all top cycles by electing the Approval winner. From that point of view, sometimes electing the approval loser is only a degree worse than not always electing the approval winner! Here you state the obvious problem when looking at both approval and defeat information. Forest's ingenious argument was that we should at least not elect a candidate where both kinds of information agree that the candidate is defeated, leaving us with his set P of candidates which are not strongly defeated. But when we take both kinds of information serious, it does not seem appropriate to me to always elect a candidate from the two extremes of P like Approval and DMC do. Still, DMC has the obvious advantage of extreme simplicity. I would find it much more natural if the winner was somewhere in the middle of P! The simplest way to achieve this is to use Random Ballot among P, which adds two nice properties to the method: (i) Randomization for better long-time fairness and strategy-proofness, and (ii) taking into account the third major kind of preference information: direct support. In your second example, this would result in R with 61% probability and L with 39% probability, so that the R voters would take the risk of getting a worse outcome than before with 39% probability, which should suffice to deter them from using that strategy. The results of the first example were posted by me already. People who don't like randomization could instead use TAWS (Total Approval Winner Stays): Process the candidates in order of increasing approval, always keeping the winner of the pairwise contest between the next candidate and the candidate at hand. With a large number of candidates, I guess this will still give a winner more to the less approved end of P, but in your first example it elects B as DMC does, and in your second one L as AM and AWP do. Forest alternatively proposed to choose from P via IRV (not monotonic) or using Winner Stays as in TAWS but starting from the top candidate on a Random Ballot. Yours, Jobst Election-methods mailing list - see http://electorama.com/em for list info
