[EM] Re: MMPO, Majority, Condorcet failures

[Gervase Lam]

> Date: Sun, 19 Dec 2004 18:56:17 +0100 (CET)
> From: Kevin Venzke
> Subject: [EM] MMPO, Majority, Condorcet failures

> 29 B
> 19 A>B
> 9 A>C
> 43 C
>
> CW is C, but the MMPO winner is A.
>
> This scenario is particularly interesting because A is either
> a "weak centrist" candidate, or else someone taking advantage
> of the Later-no-help failure. This might be pretty bad. Suppose
> the following results are predicted:
>
> 49 Bush
> 24 Gore
> 27 Martian candidate
>
> All the Martian supporters need to do is vote "Martian>Gore" to
> ensure a Martian-Gore tie. The only way this can be countered
> is by Bush and/or Gore voters having the strategic sense to vote
> "Bush>Gore" or "Gore>Bush" (keeping in mind that MMPO satisfies
> Later-no-harm, and so can't make their favorite lose).

I think that this shows that all voters really should rank all of the 
candidates, with no equal rankings.  In fact, random ranking is better 
than truncation.  Those who think that random ranking is a bad thing won't 
like this at all.

This makes me think of the comparison between MinMax(Winning votes) and 
MinMax(Margins).  Those who think that random ranking susceptibility is a 
bad thing tend to prefer margins.  (Do Later-no-harm compliant methods 
inherently encourage random ranking?)  Those who think that truncation 
susceptibility is a bad thing tend to prefer winning votes.

Personally, I think truncation susceptibility should be avoided more than 
random ranking susceptibility.  On average, random ranking can cause the 
same problems as truncation.

Whereas truncation causes the same change (or non-change, depending on 
your point of view) in the pairwise contests when each ballot is tallied 
in turn, random ranking doesn't.  There will be slight "perturbations" 
which are only cancelled out by tallying up more ballots.  However, these 
additional ballots may cause other "perturbations."

Therefore, to me I think random ranking is risky.  You might as well put 
down your sincere ranking.

Strictly speaking this does not help the voters who have a sincere ranking 
that are actually truncated rankings.  Personally, I would give voting 
instructions to the voters on the lines of, "It is in your own interest to 
rank every candidate."  In other words, for each candidate, please DECIDE 
whether the other candidates are better or worse in comparison.  Don't sit 
on the fence.

As a result, the sincere rankings would have no tied or truncated 
rankings.  Such rankings may make MMPO more able to handle awkward 
scenarios.

Thanks,
Gervase.