On Apr 17, 2005, at 21:58, Kevin Venzke wrote:
plurality
That doesn't work unless you count the total number of people "who think
that the winner is not the first choice of the most voters." Otherwise
you have everyone revolting who doesn't get their first choice.
Yes. I'm just trying to demonstrate that there are different ways of measuring the dissatisfaction of voters. Pairwise margins is one but not the only one.
If one wants to see that "weakest pairwise opposition margin"
explanation in a positive light, then one may think that each candidate
corresponds to some alternative policy. There are thus as many policies
as there were candidates. In this situation one would compare these
policies every day in a similar manner as one compared candidates on
the election day.
I didn't understand this paragraph...
My idea was to demonstrate that the competitive setting between candidates on which the voters based their voting may continue to live also after the elections. In other words, the margins that were used when counting the votes have some natural interpretations (debate and comparison between left wing, right wing, green or other policy) also in the life after elections.
I think it is ok to elect e.g. the Condorcet loser if all the other alternatives are even worse (typically a very strongly looped Smith set).
But the other alternatives are only "even worse" according to MinMax.
If the voters preferring Smith members to the Condorcet loser were
given the chance to change their votes, they would do so, to change your
perception that all of the Smith members were worse.
Yes, many other methods do not find others "even worse", but if MinMax it is considered to be a (generally accepted) sincere voting method, then that selection must be right in some elections. (From a MinMax perspective the voters seem to dislike any proposed alternative winner more (= happy to change her to some other named candidate) than they dislike the Condorcet loser.)
I don't know what you mean by "true clones." A method that chokes on "fake clones" will also choke on "true clones" since it can't tell the difference.
With true clones I meant situation where one party has set several candidates (that appear next to each others in all votes) and it would have had also the possibility of setting only one candidate. Fake clones would be ones that are always grouped but just by accident.
It still makes no difference, since a method can't tell the two types of
clones apart.
I think we agree on that. But since the true closes are not known, then it may be as wrong to interpret all possible clones as members of one party than it is to treat all of them as individual candidates. One just doesn't know. And if one changes the winner based on a false clone assumption, then one may violate the rights of the candidate that would have won without the clone assumption.
The thing that would change this, is if you want to argue that sometimes Smith or clone independence causes a worse candidate to be elected. But I don't think that's what you're saying.
Actually I do. I don't know the clone world well enough to say anything
on that but I can make a claim on the Smith set. My claim is that
minmax (margins) is a SVM.
But I don't find your reasoning persuasive, since if there were hypothetically
the ability to obtain "additional votes" to create a Condorcet winner, then
why couldn't there be the ability for voters to alter their votes so as to
avoid the election of the Condorcet loser?
I agree that the "additional votes" are not something that would materialize, they are just a tool for imagination when comparing different outcomes of the election. I try to focus on the (hopefully) sincere votes given at the first and only round in the elections. Depending on what the sincere opinions (votes) are people might or might not have interest to form a coalition against the Condorcet loser (if there was a second round in the election (which I hope there will not be)).
I can't remember if you and James used this scenario:
20 A>B>C>D 20 B>C>A>D 20 C>A>B>D 13 D>A>B>C 13 D>B>C>A 13 D>C>A>B
Not exactly but close enough to serve as a good example.
You could imagine that it would be slightly easier for the D voters to get
the additional voters necessary to make D the CW. But it seems to me easier
to imagine that the voters solidly committed to {a,b,c} would just compress
their rankings.
If there was a second round, A, B and C supporters would have an interest to join forces against D. The needs of A, B and C supporters would be served better. But needs of voters in general would be served worse (if MinMax is used as the SVM). Better not tell to A, B and C about this possibility :-). Maybe the voting method should not help them implementing the strategy.
If A, B and C are true clones and all belong to party "ABC", then the situation changes a bit. We could expect that A, B and C are friendly competitors and they now regret that they didn't arrange a pre-election where one of A, B and C would have been elected as the only "ABC" party candidate for the main election.
If we do not elect D, we may violate one of the principles of basic ranking based election, namely the fact that only relative preferences should be considered, not their strengths. Vote A>B>C>D should mean A>B, A>C, A>D, B>C, B>D and C>D and nothing more (not e.g. A>B>C>>>>D which could be a good guess if A, B and C were true clones).
Let's assume for a while that A, B and C are false clones. I'll add some sincere rating style information in the votes (">>>>").
20 A>>>>B>C>D 20 B>>>>C>A>D 20 C>>>>A>B>D 13 D>>>>A>B>C 13 D>>>>B>C>A 13 D>>>>C>A>B
Now we have four separate parties. All voters like their own first priority candidate but find all others really bad. Electing the candidate of the largest party "D" doesn't look that bad any more. I'm of course fighting against myself now when giving another chosen meaning (separate party interpretation instead of the clone party interpretation) to the votes. MinMax lies somewhere between these two interpretations. It is just one way to read the neutral comparison information (A>B, A>C, A>D, B>C, B>D, C>D) and evaluate each candidate separately, without trying to think what kind of alliances voters might have or could make, and how they could change their votes strategically, and without trying to linearize the group preferences.
Did I have any luck in trying to find arguments to justify the (so neglected) MinMax as a sincere voting method?
BR, Juho
P.S. Note also the other example that I discussed with James. This one doesn't have any clones, and A, B and C are not as likely to agree on a joint best candidate.
101: A>B>X>C
101: B>C>X>A
101: C>A>X>B
100: X
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