[EM] Sincere methods

[Jobst Heitzig]

Dear Juho and Kevin!

Juho answered to Kevin:
>> Is the "ability to defend against changing candidate X to some other
>> candidate Y" really a consideration in a strategy-free setting?
> 
> 
> Good question. I was afraid you would ask this :-). But yes, I think
> using this kind of arguments is ok since the actual election was seen as
> purely sincere. Word "defend" refers only to the situation after the
> elections. And also those "fights" after the elections are "straight
> forward attacks" and "free of strategical tactics".

I agree to this. I would say this kind of defending the candidate is not
a counter-strategic measure but a necessary part of the justification of
the winner. For example, when we consider approval and pairwise defeats
natural measures, then our sincere method should at least not elect
someone who is beaten by a more approved candidate. That is, our sincere
method should choose from Forest's set P.

>> 49 A
>> 24 B
>> 27 C>B
>>
>> I say the most intuitive winner is B. It's true that I have some strategy
>> concerns in mind.

>From the approval point of view, assuming the last 27 voters approve of
B, B is indeed an intuitive winner. But also C, although having only
half of that approval, but beating B, is natural.

>> For a practical method, I suggest that C be elected with 53%
>> probability, and
>> that B be elected with 47% probability. That's also due to strategic
>> concerns.

That's what DFC will do.

> Ok. You refer to practical voting methods here. Using random selection
> could be possible is SVMs too, but that would mean that there is no
> "complete SVM" (= method that would be able to always pick the winner)
> behind but only a set of sincere criteria that leave some space for
> picking any of the "good enough" candidates as the winner.

I don't understand this. DFC is a method that is always able to pick the
winner. It is based on the natural measures of approval and pairwise
defeats and on the principles of fair chances for all voters and
proportional representation in the long run. This makes it a perfectly
sincere method, even when you don't agree on the importance of these
measures and principles.

> I'm not quite sure if clone independence is a strategical defence
> criterion or a sincere criterion. Clones may also sometimes be real
> clones and sometimes not. Any good example in your mind for me to comment?

In my opinion, clone independence (aka component consistence) is a
sincere criterion since it can be interpreted like this: When a group of
candidates appears lumped together in all individual rankings, the
result should be the same as when first treating these "cloned"
candidates like one candidate and then, if that candidate wins, applying
the method again to the set of these cloned candidates.

Yours, Jobst