Talk:Distributed Score Voting
On your criteria table, you say that DSV passes the participation criterion while failing the consistency criterion. These two criteria are mathematically equivalent in single winner elections so if your method fails consistency it must also fail participation. Condorcet methods are also incompatible with the participation, favorite betrayal, and IIA criteria, thus DSS must fail favorite betrayal and IIA as well. I'm not sure about some of the other criteria that you claim DSV passes, though the number of criteria that you got wrong already puts into question the validity of the entire table. User:ParkerFriedland , 00:29, February 8, 2020
- Could you give me a reference to the proof that consistency and participation are equivalent? To my knowledge, Descending Acquiescing Coalitions passes participation but not consistency since, to quote w:Consistency criterion,
It has been proven a ranked voting system is "consistent if and only if it is a scoring function"(H. P. Young, "Social Choice Scoring Functions", SIAM Journal on Applied Mathematics Vol. 28, No. 4 (1975), pp. 824–838.), i.e. a positional voting system. Borda count is an example of this.
- Woodall states that DAC passes participation in his article "Monotonicity and Single-Seat Election Rules". Kristomun (talk) 09:56, 8 February 2020 (UTC)
- I'd guess the reasoning for why consistency and participation are equivalent is that if you have a group of voters before and after adding in a voter, participation requires that voter not to get a worse result from voting, while consistency considers the voter a second "group" of voters who, when their vote fuses with the first group, shouldn't change the winner if they personally voted for the winner as their 1st choice. BetterVotingAdvocacy (talk) 16:10, 9 February 2020 (UTC)
Sorry, when I was evaluating the criteria I considered a counting method different from the written one. Now I have also fixed it in the wiki (it was a small change in point 3) so I will re-evaluate the various criteria. In particular:
- participation criterion, consistency criterion, favorite betrayal criterion: you are right, they are not satisfied.
- IIA: this is particular because two candidates X and Y who aren't part of the Smith set are simply excluded (therefore the interests of the group on X with respect to Y aren't evaluated). The interests towards X and Y are evaluated only when they fall into the Smith set and in this case, it can be said that adding an irrelevant candidate, the interests of the group towards X and Y don't change. User:Aldo Tragni, 11:52, February 8, 2020
- Every voting method that passes the majority criterion fails IIA, see the Wikipedia article. What you're talking about sounds like ISDA, which by the way is mutually incompatible with IIA, since ISDA implies the majority criterion. . BetterVotingAdvocacy (talk) 00:45, 9 February 2020 (UTC)
- You're right, in the Smith set I have to apply extra rules to reduce it in order to satisfy the IIA; specifically I have to reduce the possible condorcet paradox to a group of only 3 best candidates in a cyclical path; I'm looking for a definition for this but for now the maximum I have found is Smith set. Aldo Tragni (talk) 13:59, 9 February 2020 (UTC)
- You forgot to sign your post, btw. But look, here's an example of how every voting method that always elects the majority's 1st choice has to fail IIA:
- 25 A>B>C
- 40 B>C>A
- 35 C>A>B
- Your voting method guaranteeably elects one of these candidates. Now, if we eliminate one of the losing candidates, we find that there's another candidate who is a majority's 1st choice (if A wins, eliminate B who lost, and now C wins. If B wins, eliminate C and A wins. If C wins, eliminate A and B wins), and so they must win, violating IIA. It is a very specific criterion, and I think you're possibly discussing something completely new. But unfortunately, the only reasonable voting methods I'm aware of that pass IIA are Approval and Score Voting, and that too only under contrived conditions. https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives#Criticism_of_IIA BetterVotingAdvocacy (talk) 13:24, 9 February 2020 (UTC)
- I didn't have time to correct my previous answer. The IIA that is satisfied concerns the set (IIA*), that is:
- IIA: A is preferred to B. If I add C, then A continues to be preferred over B.
- IIA*: X is a set containing all the preferred candidates over B. If I add C a less appreciated candidate (in head-to-head) than the candidates in X and B, then all candidates in X continue to be preferred over B.
- - B is outside the Smith set: Smith set = X and the candidate added C would lose both against B and X leaving B (and C) outside the Smith set.
- - B is inside the Smith set: adding C could not get B out of the Smith set; at most C could enter the Smith set. In the Smith set the score voting is applied to choose the winner Aldo Tragni (talk) 14:00, 9 February 2020 (UTC)
- That is, as best as I can tell, ISDA (Independence of Smith-dominated Alternatives). https://en.wikipedia.org/wiki/Independence_of_Smith-dominated_alternatives. Also, just as a note, if the "eliminate the worst, redistribute points" procedure is done to the candidates within the Smith Set, that seems equivalent to Smith//IRV, while if you're correct about this being Score Voting in the Smith Set, then it's equivalent to Smith//Score. BetterVotingAdvocacy (talk) 16:10, 9 February 2020 (UTC)
- Yes, basically it's one Smith//Score that adds a couple of rules to handle the multi-winner case. Aldo Tragni (talk) 19:33, 9 February 2020 (UTC)