[EM] Majority Loser & Mutual 3rd Dominant Set Criterion. Equalling votes.

[MIKE OSSIPOFF]

Majority Loser (MLC) and a criterion requiring choice from what James has 
called a mutual 3rd dominant seet are really just re-statements of MMC, 
differing from it only in degree. MLC is just a  special special case that's 
even more special, as compared to MMC.

And, just as with MMC, it remains true for those other 2 criteria that the 
examples showing that IRV meets them point to WDSC & FBC failure examples 
for IRV.

In James Majority Loser example for Approval, the Approval voting isn't 
plausible.

It's true that Approval can have the co-operation/cefection dilemmas that 
James described. But I've already told why it isn't so important. When B 
wins by defection, when A is CW, it isn't a majority rule violation. There 
will almost always be an indication that A or B is more popular than the 
other, more deserving of being the AB compromise, or is the inbetween 
compromise with C, if such a comproimise is needed.

And the example suggests that A & B are fairly similar. Of course the more 
similar they are, the less it matters which one wins, and the less voters 
will be inclined to risk defection.

And I've suggested an enhancement for avoiding that dilemma, in much the 
same way that ATLO avoids it in wv Condorcet:

The voter could designate some of hir votes "equalling votes" or "reciprocal 
votes".

An equalling vote can raise the vote total of a candidate to whom it's given 
up to that of the candidates to whom the voter gives ordinary votes, but no 
higher. Or, probably better yet,  up to 1 vote fewer than the vote total of 
the candidates to whom that voter has given ordinary votes.

Reciprocal votes are more difficult to defne, and may not be useful:

Equalling votes sound much simpler to define and count. I'm not sure that my 
definition of reciprocal votes is in finished form yet, or that reciprocal 
votes is a usable idea. Reciporocal votes, as I've defined them so far, may 
be full of problems.

A "reciprocal vote" for a candidate C, given by voter V, counts only if the 
ballots giving to C an ordinary vote also give an ordinary or reciprocal 
vote to candidates to whom V gives ordinary votes, in sufficient percentage 
so that their lack isn't the reason why C wins instead of a candidate to 
whom V has given an ordinary vote.

But equalling votes would get rid of the co-operation/defection dilemma for 
Approval.

I wouldn't initially propose Approval with equalizing votes. I'd propose it 
as a later enhancement, especially at such time as the 
co-operation/defection dilemma became widely perceived as a problem for 
Approval. Simple: If it becomes a problem, then solve it with equalling 
votes.

There could even be different kinds of equalling votes. A kind that protects 
only the candidates to whom that voter has given an ordinary vote. (That's 
the kind that I defined above). And maybe a kind that similarly protects all 
the candidates from that candidate to whom that voter gave the equalling 
vote.

Of course Approval's co-operation/defection dilemma could also be solved by 
discussion among the A & B voters. Someone might argue that that doesn't 
count for much, since such discussion could similarly alleviate all problems 
of all methods. But I'm only suggestsing it as a solution for one particular 
special situation in Approval. Other than that situation, Approval holds its 
own very well without the discusion, and without equalling votes.

Mike Ossipoff

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