[EM] AERLO loses any FBC. MMPO is Approval. Still the best public method.

Kevin Venzke stepjak at yahoo.fr
Sun Jun 19 14:59:17 PDT 2005


--- MIKE OSSIPOFF <nkklrp at hotmail.com> a écrit :
> And when, with that method, in an acceptable/unacceptable situation, a voter 
> uses his/her best strategy, protecting the acceptable candidates by AERLO 
> and power truncation, then MMPO with power truncation becomes identical with 
> Approval for that voter.
> CR, when voters use their best strategy, also becomes identical to Approval. 
> Maybe that's true of all FBC-complying methods. Forest and Kevin, why not 
> check out the other FBC-complying methods, such as       tMMWV and the other 
> t methods described by Kevin. And like the Ordered-Bucklin variant that 
> Forest described, if it meets FBC.

Well, as far as "tC//A," or "Improved Condorcet Approval," I don't believe that
the optimal strategy is to only use the extremes. If you vote A>B, and this
causes B to fail to be the CW, then your vote is compressed and you automatically
vote for both A and B equally. B has a pretty good chance of still winning. B
might ultimately lose, but you do obtain the opportunity to have A win instead
of supporting A and B equally from the start.

If you're talking about a voter in an acceptable/unacceptable situation, then
probably he won't bother to use lower ranks. It seems like a tall order to
get around this...

Assume that the voter just has some candidates he wants to rank, and some
he doesn't. A nice criterion would say that no shuffling of the ranked candidates
can cause the win to move from a ranked candidate to an unranked candidate, or
(obviously) vice versa. But I can't think what would satisfy this criterion other
than Approval with a ranking stapled to it.

> How good properties and criterion compliances can be offered by 
> FBC-complying rank methods, with and without enhancements? So far MMPO has 
> been discussed. I'm suggesting that Forest and Kevin discuss some of the 
> other FBC-complying rank methods.

tC//A aka ICA satisfies Plurality, Minimal Defense (if using a fully ranked ballot),
SDSC (ditto), FBC, and Monotonicity. It fails Condorcet (technically), Participation,
LNHarm, and Clone-Winner.

I currently wonder whether SDSC, FBC, and Clone-Winner are compatible in a
method more complicated than Approval.

It's possible to define a weakened version of Condorcet which ICA would satisfy:

"If there is at least one candidate X such that for any other candidate Y,
v[x,y]+t[x,y]>=v[y,x], then one such candidate must be elected."

Oddly, Condorcet doesn't imply this "weak" Condorcet. Also, this "weak" Condorcet
seems incompatible with Clone-Winner.

Kevin Venzke


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