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Participants, James G-A and I have have been discussing his "Voting Methods:definitions and criteria" page off-list, but James now thinks it would be a good idea if we took it on to the list, starting with this my most recent message to him. The quotes are all of James G-A or myself. James,
Probably this one:The plurality criterion might be a good one to add. Should I cite Woodall for that? If so, which paper of his? http://groups.yahoo.com/group/election-methods-list/files/wood1994.pdf In my message I deliberately referred to a "version" of the Plurality criterion, because as I recently pointed out in an EM message addressed to Russ, Woodall likes to economise on axioms and so doesn't include the common-sense axiom that two ballots that differ only in that one doesn't rank the one candidate the other specifically ranks last should be treated/interpreted as identical. http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/014958.html ["Plurality: if some candidate x has more first-preference votes than some other candidate y has votes in total, then x's probability of election must be greater than y's." In his papers, Woodall likes to economise on axioms; so doesn't include the common-sense axiom that a ballot that leaves one candidate unranked should be treated/regarded the same as a ballot that ranks this candidate last and all the other candidates the same. His "votes in total" refers to explicit rankings in any position. Incorporating this axiom, a "version" of the Plurality criterion I like is "If some candidate x is ranked in first-place on more ballots than candidate y is ranked above equal-last, then y can't win".] For me, Plurality and Minimal Defense are the real clinching arguments that WV is better than Margins (defeat-droppers). But there are three plain rankings methods that I prefer to Defeat-Dropper (WV); and they are CDTT,IRV and SCRIRVE and CNTT,IRV. If by "listed" you mean "ranked", then yes. Sometimes Woodall's language seems to assume that the candidates' names are displayed somewhere,Frankly, I'm not sure if I fully understand LNH and LNH. "Adding a preference to a ballot must not decrease the probability of election of any candidate ranked above the new preference." Does that mean adding a candidate who was previously not listed on the ballot? and that voters vote on blank sheets of paper by writing down the names of candidates the voter wishes to "vote for" in order of preference with the highest-ranked at the "top" of the "list", and the most-preferred also written down "first" (in time). (That explains the "later" in LNHarm.) I think at one point Kevin Venzke came up with a "pairwise" version that is maybe a bit stronger: "Adding a vote to A's pairwise tally versus B must not reduce the chance of any candidate winning except B" (my paraphrasing) In the sense that it is equivalent to complete invulnerability to Burying, yes But that is a very expensive property that is incompatible even with Condorcet(Gross).So my LPC is based on Blake's "secret preferences criterion". It seems that LPC is a good indicator of burying vulnerability, no? I don't know how anyone can think that "monotonicity" (aka Woodall's Mono-raise) is worth mentioning (and/or worrying about) and at the same time wonder ifIMO, two "consistency" criteria that are of greater practical importance than the ones you list are "Mono-add-plump" and "Mono-append".Maybe, I don't know. Again, these criteria are not as widely accepted as monotonicity, participation, and consistency. They might have some merit, but I haven't personally discovered it yet. these two "have any merit". I personally think that Mono-raise is nice, but too expensive because its incompatible with Weak Burial Resistance. Most of the criteria are "nice" and have at least some strong aesthetic appeal, and the reason why we don't have a method that meets them all is that some are incompatible with others. They all have some "price". Some we insist on at any price because they are about the fundamental aim of the method. One of these for me is (Mutual ) Majority. Others are always on our shopping list mainly because they are so "cheap", like Mono-add-plump and Mono-append!. There was a blunder in some of my posts on this topic regarding ER-IRV(fractional). It is not easy to come up with a three candidate scenario in which the Pushover-compressionistsIn any case they both should definitely have a higher number than does plain IRV in the "paradoxical" row, and the number for ER-IRV(whole) should be 4 or 5.Why is that? You may have to refresh my memory since our discussion of ER-IRV(whole) was quite some time ago. I believe that I had a good conceptual reply to your last message on the topic, but I never got around to writing it. can succeed with all their supporters carrying out the strategy, but the strategy is still more tempting than in plain IRV. But there was nothing wrong with my example regarding ER-IRV(whole). 45:Right=Left>CentreRightThis would also work if the numbers 45/35/20 were replaced with 49/48/3. I suggest the right numbers in your "paradoxical" row should be IRV1, ER-IRV(fractional)2, ER-IRV(whole) 5! This is classic Ossipoff/Eppley/Tarr stuff from the Jurassic period of WV versus Margins. This is from Steve Eppley's site:Probably WV should have a lower number than Margins in the "compromising-reversal" row, because sometimes in WV compromising-compression can be an effective "defensive strategy" but to achieve the same effect those voters in Margins have to compromise-reverse.That's interesting. Would you mind showing me an example? It sounds familiar, but I don't have anything like that on the surface (of my mind, or of my voting files). http://alumnus.caltech.edu/~seppley/Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm Example 2: The non-drastic defense voting strategy. Suppose there are 3
alternatives x, y and z. Suppose the voters'
That is, 46% of the voters sincerely
prefer x over y and y over z, 10%
prefer y
The votes of the 46% who voted x
over z over y misrepresent their preferences I'm sorry to hear that. Here it is:I had a look at the weak burial resistance criterion, but I unfortunately found it somewhat confusing. "If x is the CW (and wins), and on more than 1/3 of the ballots ranked above y and z; and afterwards on some of the ballots that rank y above x and x not below z, z's ranking relative to x is raised while keeping y ranked above them both, then if there is a new winner it cannot be y." CNTT,IRV has that problem, but CDTT,IRV is less vulnerable to Burial than Defeat-Dropper(Winning Votes) or any other plain rankings method that meetsAs far as I understand CDTT-IRV, the basic strategic vulnerability is that if the sincere IRV winner X differs from the sincere Condorcet winner Y, X>Y voters will have an incentive to bury-reverse Y. Mutual Majority, Smith(Gross) and Clone Independence. Take this classic example: 49: A (sincere is A>B) 24: B 27: C>B The CNTT is the normal Smith set, that on these votes includes all the candidates. CNTT,IRV elects A. One of the definitions of the CDTT is "the set of candidates that all have a majority strength beat-path to the candidates that have one to them." The CDTT here is BC. In the IRV count, B is first eliminated and so C wins (an example of failing the Plurality criterion). The A supporters can do nothing to get A into the CDTT, but they can gain a result they prefer by voting sincerely. The B supporters can do theselves no harm by voting B>A if they want to. Of course, unlike plain IRV, it fails Later-no-Help. The C supporters help C by ranking B. The horror possible real-world scenario with this method is that a lot of voters are advised to truncate, producing the above election, by those whose agenda is to bring the method into disrepute so that they can get rid of it. But if the participants accept that the system is fair and permanently in place, and just try to get their preferred candidates elected, then it should work well. One possible political advantage of CDTT,IRV is that it can be sold as an improved form of IRV. I think that is better than jumping in front of the IRV movement and shouting "Go Back! IRV is evil!". Chris Benham |
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