[EM] Smith Sets with 3 members
There's been a lot of argument on the list over how to resolve the lack of a Condorcet winner. With 3 members in the Smith set I see some easy resolutions that aren't feasible for 3 members. With 4 members, 2 of them will have 2 victories apiece and 2 of them will have 1 victory apiece (only counting victories against other members of the Smith set). It would seem reasonable to limit our attention to the 2 with the most victories, and then select whichever of those defeats the other. With 5 members, 3 structures are possible: 1) All 5 have 2 victories apiece 2) One has 3 victories, 3 have 2 victories, 1 has 1 victory. 3) 2 have 3 victories, 2 have 1 victory, 1 has 2 victories. For case 2 it seems reasonable to elect the person with 3 victories. For case 3 it seems reasonable to pick whichever of the top 2 can defeat the other. For case 1 the problem is similar to when you have 3 candidates in the Smith set. I won't enumerate all of the possibilities with six members, but by drawing diagrams I've seen that you can have a case where 3 members win equal numbers of victories, and more victories than any other candidate. Among those 3 there can be a Condorcet Winner, or not, depending on the results. I realize that elections with more than 3 candidates in the Smith set are rather unlikely, but the case with 4 is not totally out of the question, and it seems to present an easy resolution. Does anybody see a problem with that method of resolution for 4 members in the Smith set? I haven't thought about it in depth. Alex Small
Re: [EM] Smith Sets with 3 members
On Tue, 26 Feb 2002, Markus Schulze wrote: Dear Alex, methods that always choose one of the candidates with the largest number of pairwise victories are called Copeland methods. The main problem of Copeland methods is that they are manipulable by clones in a very straight forward manner. It seems to me that another problem of Copeland methods is that they encourage favorite betrayal in the same way IRV does: if your compromise has a better chance of winning the election than your favorite, but your favorite has a good chance of beating your compromise, then you (and like minded voters) vote your compromise above your favorite to maximize your compromise's chance of getting one more win. Forest
[EM] Cumulative Repeated Approval Balloting for DSV
The goal of maximizing voting power while minimizing manipulability seems to be an elusive will 'O wisp. However, in committees and other small groups one option is repeated balloting. For example, approval ballots can be repeated N times or until the ballots stabilize, whichever comes first. One problem with this method is that when there is no Condorcet Winner, the ballots may cycle radically, and the N_th time cutoff more or less randomly chooses a member of the cycle. When approaching the N_th balloting, various factions may try to trick others with feigned mutual support right up to but not including the last ballot. Or on the other hand, they may stubbornly bullet up through the penultimate balloting hoping that they will be used as a lesser evil compromise on the last vote by other factions. In other words, repeated approval balloting can be a game of chicken or prisoners dilemma or high stakes poker. Repeated plurality balloting is worse, yet that is what Lorrie Cranor used as her main example of Declared Strategy Voting (DSV). It seems to me that it would add stability and remove some of the high stakes poker feeling if the approval totals were accumulated for each candidate, and that the win would go to the first candidate to reach total approval of, say, K*M, where K is the number of candidates and M is the number of voters. After each balloting the cumulative approval totals of the candidates would be shown in a bar graph, with previous levels marked by color changes, and the K*M goal clearly marked as well. The voters would have a good enough idea of the progression to make a reasonable decision of how far down to approve in the next balloting. Drastic last minute changes in strategy would not be enough to make up for the cumulative trend, so approval increments would not gyrate wildly. How does DSV relate to this? The proposed version of DSV (Cumulative Repeated Approval Balloting Declared Strategy Voting or CRAB_DSV) would take as input each voter's relative utilities for the various candidates in the form of some kind of CR ballot, say the Five Slot Grade Ballot (possibly with plus and minus options for more resolution). The first balloting would be on the basis of each voter approving each of his/her above mean utility (i.e. above average grade) candidates. The subsequent approvals would be made with decision theoretic methods applied to the grade ballots in conjunction with the candidates' approval statistics, i.e. the statistics described by the bar graphs mentioned above. I believe that CRAB_DSV would overcome most if not all of the disadvantages of the version of DSV that Ms. Cranor devoted most of her attention to in her dissertation. In particular, it has the stability of her stochastic ballot by ballot version and the repeatability of her non-random repeated balloting version. Since Cranor's DSV was based on plurality, it bore a certain similarity to IRV, though less manipulable. Imagine doing repeated plurality balloting. Compare that with repeated approval balloting, and finally compare that with cumulative repeated approval balloting, and I think you can see a definite progression towards stability. Cumulative repeated plurality balloting would add some stability to Cranor's version, but it seems to me it would be the stability of getting into a rut, and being unable to move to a better rut, whereas approval doesn't penalize tentative testing of the waters in various directions in search for a better equilibrium. CRAB_DSV would allow voters to submit sincere grade ballots without fear of regret. The decision theoretic calculations automatically optimize the approval votes according to the information that becomes available at the end of each round of repeated balloting. Sophisticated voters have no advantage over the naive. If they think they do, they can limit their grades to A's and F's, for example, and the DSV calculations will automatically cast each of their ballots with all A's translated as approvals and all F's translated as non-approvals. The method is not summable in polynomial size data structures, but an approximation can be done in O(K^3) where K is the number of candidates. That's enough for now. Forest
Re: To Blake, re: strategy
MIKE OSSIPOFF wrote: Blake said: Some countries use plurality with successive elimination for things like leadership conventions. I think Americans use it for speaker of the house. Since the strategy is very similar, I think that awareness of strategy in one would be good evidence of awareness of strategy in the other. I reply: Sure, but there are also countries that use IRV, and that's obviously the best evidence about IRV in action. So do you think IRV's strategy problems are worse than successive elimination? If not, then a lack of strategy in successive elimination has to be taken as evidence of a lack of strategy in IRV. It's almost the same the method. I'd said: information from (2 by e-mail, one in person), none of whom know eachother, told me that it's common for preferrers of small parties to insincerely vote one of the big-2 parties' candidates in 1st place , to avoid wasting their vote. One of those Australian voters with whom I spoke had just voted in that way in the most recent election. But they all said that such voting is common in Australian IRV elections. Blake replied: I don't consider those people a representative sample. I reply: Fine. Do a proper scientific statistical study. In the meantime, the evidence that I've described is all that's been offered from Australia. We obviously have different opinions on what constitutes good evidence, and if anyone is still reading this discussion, they'll have their own opinion. Rob has quoted some results from Ireland that confirm IRV's spoiler problem, a problem closely associated with LO2E. I might also add that when IRV was adopted in Australia it was hoped that it would encourage parties to run more than 1 candidate per party. For the most part that hasn't happened. Well, I'm not the all-around IRV apologist. I would point out some problems with IRV myself. I was adressing the narrow point of whether a significant number of people use the compromising strategy in IRV. Blake continues: As well, their strategy does not appear to be rational. I reply: Excuse me for repeating this, but you may have missed it before: Say there are 3 candidates, Favorite, Middle, Worst. Say Middle is closer to Worst than to Favorite. Hardly an implausible assumption, since it's unlikely that Middle is exactly in the middle. Say that Favorite isn't expected to have a 1st choice majority. Not implausible either, since, if the candidates are roughly equal in 1st choice support, none has more than about 33% of the total 1st choice support. Now, if Favorite is your favorite, should you sincerely rank Favorite in 1st place? Why? Favorite can't win, based on our assumptions. If you rank Middle in 1st place, at least you might save Middle from immediate elimination, avoiding an avoidable Worst victory. Not only is insincerely ranking Middle in 1st place a rational strategy, but it's the only rational strategy for someone who prefers FavoriteMiddleWorst. I agree that strategy would be rational in that situation. I don't disagree with the principle that strategy may be rational in IRV (in fact I discuss this on my web site). It's just that the few times I've heard people quoted as saying that they favour strategy in IRV, they don't seem to understand it. They seem to believe in a plurality-style strategy of compromising towards the major parties. Blake replies: It's quite possible to want to avoid having people vote candidates equal to their favourites without advocating Strong FBC. Just as it is possible to want to reduce crime without believing in some unmeetable zero-crime criterion. I reply: Ok, so you're just saying that it's good to be able to guarantee that _sometimes_ voters won't regret that they didn't insincerely rank someone equal to their favorite, and that they sometimes won't regret that they didn't insincerely rank someone over their favorite. Sorry, but guarantees that contain the word sometimes or maybe don't sound very reassuring. I think what you're getting at is that, while Approval never gives any incentive to vote someone over your favorite, it routinely gives strategic need to rank someone equal to your favorite. In comparions, methods like IRV Ranked-Pairs(margins) sometimes _do_ give strategic need to vote someone over your favorite, but at least they sometimes don't give strategic need to vote someone equal to or over your favorite. And you consider that an advantage for IRV Ranked-Pairs(margins) over Approval. Is that it? For you, sometimes is good enough a guarantee. You have a gambling nature. If that was my argument, I wouldn't agree with it either. Saying that IRV sometimes doesn't give strategic need to vote someone equal to or over your favourite couldn't be used to justify anything. My argument was in terms of general
[EM] State Ordered to Replace Old Vote Machines
D- Another *hammer* order from the courts -- like Bush v. Gore, ___ U.S. ___ (2000). - Los Angeles Times State Ordered to Replace Old Vote Machines By Henry Weinstein February 14, 2002 A federal judge in Los Angeles on Wednesday ruled that California has to replace outmoded punch-card voting machines by the 2004 presidential election. U.S. District Judge Stephen V. Wilson's decision is the first ruling in the nation requiring the elimination of obsolete voting machines in the aftermath of the controversial 2000 presidential election. Similar suits are pending in a number of other states. The decision immediately affects nine California counties, including Los Angeles, which have about 8 million registered voters. Wilson rejected the position of California Secretary of State Bill Jones and several county voting officials who said that they did not have the millions of dollars needed to upgrade their systems and that it was not feasible to make a change until 2005. The judge issued a one-sentence order and attorneys said they anticipated he would provide a more detailed ruling later. A lawsuit over the machines had been set for trial Feb. 19. The ruling was hailed by Daniel Tokaji, an attorney for the American Civil Liberties Union of Southern California, which last year filed the lawsuit seeking to compel elimination of the machines. This landmark decision means that by 2004, 'hanging chad' machines will go the way of black-and-white TVs, eight-track tapes and the Edsel, Tokaji said. It does what the secretary of state should have done years ago: upgrade the infrastructure of our democracy by providing a voting system fit for use in the 21st century. The ACLU attorney said he hopes that the plaintiffs can now work out a consent decree with Jones that would provide a plan for the transition to newer, high-tech machines. Jones conceded last September that two types of punch-card voting machines approved for use in California were obsolete and needed to be replaced. However, in December, Jones said that it would invite disaster if some of the state's large counties were required to change systems by the 2004 presidential election. On Wednesday, Jones, who is running for governor in the Republican primary, said Judge Wilson has set a deadline that may be impossible for counties to meet with advanced voting technology. Several counties will have to scale back plans to adopt state-of-the art technology to meet the new deadline. Jones also said that unless California voters pass Proposition 41--a $200-million bond measure that would provide 3-to-1 matching grants to California counties for the purchase of new election equipment--on March 5, many counties will be unable to purchase new systems at all. State May Appeal or Seek a Stay Jones spokesman Alfie Charles said the secretary of state would decide whether to appeal the ruling after consulting with county voting officials. Other political sources said they believe that Jones will ask for a stay of the ruling. Conny McCormack, Los Angeles County's registrar-recorder, predicted that the ruling will throw our Los Angeles County election system into chaos. Requiring us to procure, test and install a new system in less than two years precludes us from replacing punch cards with modern touch screens because there are no funds currently available from the federal, state or county government to do so, McCormack said. She said attempting to make a transition more rapidly than is feasible could lead to more tabulating errors in the next election. The ultimate irony is this would be the exact opposite outcome of that sought by the plaintiffs, McCormack said. But Tokaji said evidence developed in the lawsuit, Common Cause vs. Jones, shows that the nine affected California counties can easily upgrade their systems in time for the 2004 presidential election. Los Angeles is the largest of the nine California counties that use the punch-card machines. In the November 2000 presidential election, 53.4% of California voters, including those in Los Angeles County, used machines for pre-scored punch cards, similar to those that created some of the problems with hanging and pregnant chads in Florida. Ballots cast using those machines accounted for 74.8% of all ballots that did not register a vote for president in California. The error rate for those machines was more than double that of any other system used in the state and three times as high as in Riverside County, which used high-tech touch-screen machines, according to the suit filed last April by the ACLU. The suit alleged that the wide variety of voting machines used in California resulted in sharply disparate levels of accuracy, with the consequence that a disproportionate number of votes are not counted in some counties--including Los Angeles. Moreover, the suit, filed on behalf of five nonprofit groups and eight
[EM] Margins vs. winning-votes
First, a quick point: There are (at least) two separate issues discussed on this list. One is methods themselves, like Ranked Pairs vs. SSD vs. IRV vs. Borda; this issue generates most of the interesting posts and debates. The other is the procedures of compiling the pairwise matrix for pairwise methods to operate on, like margins vs. winning-votes vs. all-votes (though I don't believe anyone still advocates all-votes). These two issues are entirely orthogonal-- any pairwise method can use either the margins or the winning-votes approach, and I think Markus still prefers win-or-tie-votes for the official definition of Schulze's Method. Now Mike Ossipoff wants to discourage strategic truncation, but he doesn't find it important not to encourage strategic equal rankings high in the ballot. I don't see truncations as anything but a specific case of equal rankings. To me, a vote of AB when there are five candidates is simply a vote of ABC=D=E. I don't think this case is any more special than a case like A=BC=DE. Mike does, his favorite criteria reflect that, and that's why he prefers winning-votes, which of course is perfectly fine for him. What hurts a candidate most using a winning-votes method is being ranked under another. Being ranked equal to another hardly hurts at all. On average, ranking two candidates equally hurts neither. It's good strategy to vote ties among candidates you like and be decisive among candidates you don't. On the other hand, margins methods don't favor one over the other on average. Sometimes voting two candidates equally helps them and sometimes it hurts them, but it always has the same expected effect as if you had flipped a coin between them. To me the bottom line is this: Any evil strategy that a margins method allows is possible in the corresponding winning-votes method, whether by flipping coins or by coordinated bloc voting. So, as Blake has explained, winning-votes prevents nothing. It only provides more strategic options for the insincere voter, and it punishes the voter who sincerely truncates. I would like to believe that winning-votes is effective, but since it's not, and margins is more intuitive and so much better on social utility, I prefer margins. In fact, the false assurance that winning-votes gives its fans reminds me of my favorite analogy of Mike's: someone sitting in the driver's seat of a car that's up on blocks, having fun turning the steering wheel back and forth (from his classic anti-IRV post http://groups.yahoo.com/group/election-methods-list/message/6500). Margins vs. winning-votes is obviously a religious argument, though, so I don't expect to change anyone's mind. It's a bit like Newcomb's Paradox (explained at http://www.magnolia.net/~leonf/paradox/newcomb.html), which people seem to resolve each way in roughly equal numbers, but each group is entirely convinced that the other is being silly. Personally, I'd like to concentrate on newer, more interesting debates. = Rob LeGrand [EMAIL PROTECTED] http://www.aggies.org/honky98/ __ Do You Yahoo!? Yahoo! Greetings - Send FREE e-cards for every occasion! http://greetings.yahoo.com
Re: [EM] Winning-votes intuitive?
Partial rankings are penalized. I don't think it would be a strong exaggeration to characterize this as the crux of your argument. You basically say, Ranked Pairs ignores partial rankings, while SSD does not. Since partial rankings are penalized, this allows those who are unaware of this in SSD to be victimized. The addendum to this is that people are not really going to be more inclined to truncate than they are to order-reverse anyway. I hope that no one doubts that the word penalized is justified. I mean, if my favourite is A, then on average, any complete ranking is better for electing A, than ranking A alone. I do doubt that the word penalized is justified. My example shows multiple instances of the opposite being the case. I guess the question of what constitutes penalized is an important one. Are you saying that the voters are penalized relative to their sincere ranking, or penalized relative to a strategic order reversal? Because there is a huge difference. Moreover, the latter is irrelevant to the margins vs. winning votes debate. Let's look at my example one more time: Sincere ranking: 49:BushGore 12:GoreBush 12:GoreNader 27:NaderGore Now, who benefits and who is hurt by truncation? Let's look at each faction. The 49 BushGore voters win the election for Bush by truncating in margins. In winning votes, they fail to change the outcome. In neither case does truncation hurt these voters. The fact that order reversal helps these voters (assuming everyone else votes sincerely) is irrelevant to the discussion. Remember, we're only seeking to find who is penalized by truncation. The 27 NaderGore voters... yes. They are penalized by truncation, no doubt. This is equally true in margins and winning votes, however. The second choice of the 12 GoreNader voters is largely irrelevant. Nader is more or less guaranteed to lose big pairwise to Bush in this election anyway. So truncation is neither good nor bad for them. In the case of the 12 GoreBush voters, truncation is a poor strategy in margins. It will have little impact unless there is a huge amount of order-reversal in the Bush camp, at which point it throws the election to Nader. In winning votes, however, truncation more or less guarantees a Gore victory, regardless of order-reversal from the BushGore voters. So, if you're scoring at home, that's one clear penalty for truncation in either margins or winning votes, one totally irrelevant choice about truncation in either margins or winning votes, one case where truncation helps in margins but not in winning votes, and one case where truncation hurts a little in margins, but helps in winning votes. It's worth noting that the one time truncation helps in winning votes, it enforces majority rule, while the one time it helps in margins, it allows a minority to defeat the sincere CW. Let me repeat your previous statement: if my favourite is A, then on average, any complete ranking is better for electing A, than ranking A alone. I have seen no evidence to this effect. What I have seen suggests that the effect of truncation varies wildly from case to case, and that election results in winning votes tend to be less negatively effected by truncation. On the margins side, we don't want to impose any particular penalty for leaving candidates unranked, since we want this to be a reasonable option for people. Winning votes provides this option. Margins doesn't really, since your ballot effectivelly gets randomly completed if you leave it incomplete. This means we can't set up specific penalties against insincere partial rankings without mind-reading). We note that although people can gain through truncation, they can also lose by it. True. So our goal is to pick the system that seems to reward sincere rankings as oppose to insincere partial rankings. From what I have seen, that would imply winning votes is a better method. It's not like it's a good strategy in general. We note that if voters behave rationally the whole issue is moot. No strategy is good in general. Different situations demand different strategies. But I'm not convinced that insincere partial rankings are always a suboptimal strategy in margins. It seems reasonable that there could be a situation in margins where truncation will order the victories just so, while order reversal will push the winning margin high enough that another camp could manipulate the results even further with order-reversal of their own. -Adam
