[EM] Sincere methods

[Juho Laatu]

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