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

[Allen Smith]

In message <20051105212238.14536.qmail at web26810.mail.ukl.yahoo.com> (on 5
November 2005 22:22:38 +0100), stepjak at yahoo.fr (Kevin Venzke) wrote:
>
>Basically, I can't see a way of amputating scenarios without a CW, and thereby
>meaningfully obtain compliance with criteria that are normally incompatible
>with Condorcet.

Understand.

>> >> (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).
>
>Unfortunately, I believe this will create a monotonicity problem.

Urr? Oh dear, I'll have to check more closely into this...

>> 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.
>
>But this seems to create more opportunities to dispute ties rather than fewer,
>unless I'm missing something.

I can see that argument. (The above would work with an M of 0. Quite a bit
of it has the same intent, as far as I can tell, as your "Tied at the top" -
great minds think alike? :-}) The idea in regard to M is that it is easier
to detect fraud or error (which is in turn more possible/likely the closer
the vote counts are) with the approval aspect of the voting via, e.g., an
independent summation (at least of the counts prior to threshold
adjustment).

>> 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.)
>
>Monotonicity, again. (But I don't mean to say that you need to value
>monotonicity. It just seems to be a fairly easy criterion to satisfy, so
>it's noticeable if you don't.)

Indeed; I had intended to satify it. (Among ones not intended to be
satisfied are Consistency (gerrymandering exists even in systems technically
satisfying Consistency) and Independence of Irrelevant Alternatives.)

	   -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