[EM] Condorcet Criterion for plurality.

[MIKE OSSIPOFF]

> >Condorcet's  Criterion:
> >
> >If there's a sincere CW, and everyone votes sincerely, then that
> >sincere CW should win.
> >
> >A voter votes sincerely if he doesn't vote a false preference or
> >leave unvoted a sincere preference that the balloting system in
> >use would have allowed him to vote in addition to the preferences

Craig L. said:

>This doesn't seem right.  Say I
>have a Condorcet system in which you can't indicate ties (must use
>sequential preferences: 1,2,3 etc), but you may truncate votes.  What is a
>sincere vote?

Ok, I think you got me on that one. It hadn't occurred to me that
a voting system could make it necessary to vote a false preference,
but IRV without equal rankings does.

I'd previously felt that a false preference is more insincere than
an unvoted sincere preference. Maybe, but if a sincere preference that's
very important to me requires voting a false one between two equally
good candidates, then of course I'm being much truer to myself if
I vote both preferences than neither of them.

You've shown that maybe my sincerity definition needs work if I'm
to be able to apply it to IRV without equal rankings--the usual form
of IRV. Though I haven't yet checked the situation out, it might be
that, using my present definition of sincere voting, IRV without
equal rankings might be a method that I don't want to apply my
criteria to. Just as it won't do to have a CC that Plurality passes,
and say "But we don't apply it to Plurality", similarly I shouldn't
have criteria that I don't want to apply to IRV. A criterion should
apply to all methods. If it ever acts contrary to how I want it to,
then it isn't quite the criterion that I want. So maybe it will be
necessary to change my definition of sincerity. Must check that out.

>There are situations in which you must either vote a false
>preference OR leave unvoted a sincere preference that the balloting allows
>you to vote.  Similarly, what of a plurality vote in which you like two
>candiates the same (your two favourites).  If you vote for one of them, is
>that an insincere vote?  If you don't vote at all, then you're leaving a
>preference unvoted that the system allows you to express (one of the
>favoured candidates over some other candidates).  There is a contradiction
>in the sincerity definiton.

Ok, but if I don't vote at all, I'm not a voter, and the sincerity
definition isn't about me. But you're right: If I like 2 candidates
equally, then it's impossible to vote sincerely by my definition,
in Plurality. Still, for purposes of testing for criterion failure
, I could always contrive an example where no one rates anyone equal,
and so Plurality will have sincere strategies for everyone, and
so the example complies with the premise (where it requires sincerity)
and so Plurality can fail.

But it certainly is contrary to my intent if it's impossible to
vote sincerely in Plurality if I like 2 candidates equally.

The definition definitely needs rewriting. Until it's rewritten,
some of my criteria maybe are as undefined as those of Markus. I say
"maybe" because I don't know if my incomplete sincerity definition will
actually pass methods that we all expect to fail, or fail methods we
all expect to pass. If so, then, with my existing sincerity definition,
my criteria aren't the criteria that I thought they were, and
a new sincerity definition is needed in order to make them work. I
don't know if the effect of my incomplete sincerity definition is that
bad, but I do know that it should be rewritten.

Thanks for pointing that out.

What was your sincerity definition again?

Mike Ossipoff

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