[EM] Example of participation/no-show paradox with Condorcet?

[Allen Smith]

In message <20051105190824.26835.qmail at web26807.mail.ukl.yahoo.com> (on 5
November 2005 20:08:24 +0100), stepjak at yahoo.fr (Kevin Venzke) wrote:
>Allen,
>
>--- Allen Smith <easmith at beatrice.rutgers.edu>:
>> I agree that in most cases some method of solving (top) cycles is
>> necessary. (But not in all - there are some purposes for which a full-scale
>> Condorcet winner is what is desirable, and if there isn't one, no winner
>> should be selected; for instance, election to a collegium with life
>> terms.)
>
>But as far as Participation is concerned, you don't obtain compliance by
>specifying that no one wins when there's no CW. Suppose that nobody wants
>a cycle, and everyone prefers any winner to no winner. Suppose X is the
>CW. Then it's possible that adding ballots will change the winner from X to
>nobody, unless these ballots don't rank X below anyone.

I would not recommend a strict Condorcet requirement when any likelihood was
present of nobody wanting a cycle.

>Suppose the additional voters *want* to create a cycle. Then it could be
>that their sincere vote actually eliminates a cycle that already existed.

Exactly how does one do a sincere vote in favor of a cycle?

>I think you overestimate the problem. For one thing, a voter is not likely
>to have information to determine that a sincere vote is more harmful for him
>than abstaining. But even if he does have this information, he can probably
>also come up with an insincere vote that is at least as effective.

True, especially for methods allowing tie votes.

>> (I am currently contemplating a Schwartz/Approval combo.)
>
>The most obvious ones are to eliminate the approval loser until one candidate
>beats everyone left, or to explicitly reduce to Schwartz and take the approval
>winner of those candidates.

The latter is what I am considering, with a threshold being marked by the
voter but subject to adjustment up/down the ranking so that the approval
votes from the voter are not wasted (either by no approved-of candidates
being among the Schwartz set or by all approved-of candidates being among
the Schwartz set). I am also contemplating the results of the following
rules for deciding in _favor_ of there being a tie vote (partially to allow
for more effectiveness of the Schwartz set as opposed to the Smith set),
with X being votes for x, Y being votes for y, I being indifferent between X
and Y, and M being a constant:
    A. abs(X - Y) <= min(I, M*(I+X+Y)); or
    B. (I/(I+X+Y)) > max(0.5, (max(X,Y)/(X+Y))).
M is set high enough that outcomes that are so close as to be brought into
rational dispute (e.g., Florida in 2000) are considered ties.

Candidates not marked on the ballot are tied for last place. If the
threshold is not marked by the voter, and there were unmarked candidates,
then said threshold goes (initially) right above the umarked
candidates. Otherwise, an unmarked threshold goes halfway down the list of
candidates, going toward halfway down the ranking if halfway down the list
of candidates would put it in the middle of a tie. (I am contemplating
whether an automated Approval strategy - automated initial placement of the
threshold - based on (among the Schwartz set) initial first-place votes,
ITV, or another mechanism might work better, but have concerns regarding
strategic vulnerabilities and - depending on what mechanism was used - the
amount of data that would need to be retained.)

>I still favor my "improved Condorcet//Approval" method, which nearly satisfies
>Condorcet, and also avoids "favorite betrayal" incentive. That is, you can
>never cause one of your first-place candidates to win by lowering another of
>them in your ranking.

Ah; http://wiki.electorama.com/wiki/Improved_Condorcet_Approval?
Interesting; will take a further look, thanks!

     -Allen

-- 
Allen Smith			http://cesario.rutgers.edu/easmith/
September 11, 2001		A Day That Shall Live In Infamy II
"They that can give up essential liberty to obtain a little temporary
safety deserve neither liberty nor safety." - Benjamin Franklin