[EM] Majority winner set

[MIKE OSSIPOFF]

> >Take another look at my definition of sincere voting. It doesn't
> >say that sincere voting must be nonstrategic. With a rank method
> >the only sincere ballot is a sincere ranking of all the candidates.
>
>Why do you have to rank all the candidates in order for it to be a sincere
>ballot?  In fact, I think that the opposite could be true (see below).

Maybe. Then my definition could be greatly shortened. I'd felt that
not expressing a sincere preference when there voting system gives no
reason not to is an insincere nonvoting of that preference, an insincere
statement that the candidates are equally good. But yes, there's a
case for saying the only insincere ballot is one which votes an
unfelt pairwise preference. That's because not voting either over the
other could be interpreted as not saying anything about their relative
merit, rather than saying that they're equally good. That sounds just
as valid, and would simplify my definition.

Anyway, I claim that in Approval, when it's impossible to vote
2 preferences on the same ballot, it isn't insincere to not combine
them, because not doing the impossible doesn't count as an
act of any kind, and so it isn't an insincere act. Hence the way I
worded my definition. But if we agree that the only insincere vote
is one which votes an unfelt preference, then my definition can be
much shortened.

> >In Plurality, the only sincere ballot is one that votes for one's
> >sincere favorite. But in Approval, I'm not sure what you'd want to call
> >a sincere ballot.
>
>I think that a sensible definition of sincere voting, encompassing all
>voting methods, is as follows;
>
>A voter votes sincerely where no candidate x is voted below another
>candidate y, if the voter actually prefers x to y.  In situations where a
>voter does not prefer one candidate to another, and is allowed by the 
>method
>to express the equality of those candidates on the ballot without
>compromising the validity of that vote or preventing the voter for
>expressing other sincere preferences, then the vote must show those
>candidates as equal on the ballot.


Ok, you've removed the insincere label from not voting a felt
preference, and, as I said, there seems to be a perfectly valid case
for regarding it that way.

Where I simply referred to voting a preference that isn't a sincere
preference, you allow the voter to do that under conditions where
he rates the candidates equal, but voting them so would interfere with
voting other preferences. I've got to check out how that will act
differently from my wording. If you already know, tell me. Maybe when
I study your example, that will answer my question.

Of course anytime two or more different definitions are reasonable, but
only some of them act with all criteria & all methods in keeping with
how the criteria are intended, then there's a case for using one of
those definitions. I don't know yet how these different definitions
would act differently. So far I don't know if there are situations
where voting 2 candidates equal would interfere with the voting of
some preference. Again, a study of your example might show a situation
like that.

Mike Ossipoff


>
>This definition would mean that in a rank ballot with three candidates
>A,B,C, and the voter preferring A to B and C, but not having a preference
>between B and C, then voting A first, and not numbering the others, is the
>only sincere vote possible.  If you add candidate D, whom the voter likes
>less than all the other candidates, then there are five (or seven) sincere
>ways of voting;
>A1
>A1,B2
>A1,C2
>A1,B2,C3 (with or without D4)
>A1,C2,B3 (with or without D4)
>
>In a cumulative voting situation, it would allow a voter to give two
>candidates the same number of votes, even if that voter prefers one
>candidate to another, but doesn't allow a voter to give a different number
>of votes to two candidates liked the same.  I could extrapolate to the 
>other
>methods, but I won't bother at the moment.
>
>The definition is broad enough to define a wide range of voting choices as
>sincere, and also allows for a distinction between sincere strategic voting
>and insincere strategic voting.  Whether this is a good thing or not, I
>don't know, but I think the definition is intuitively correct, as well as
>applicable to all methods & situations.


>

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