[EM] MMPO, Majority, Condorcet failures

[Gervase Lam]

> Date: Mon, 20 Dec 2004 21:59:38 +1030
> From: Chris Benham 
> Subject: [EM] MMPO, Majority, Condorcet failures

> To me the price MMPO  (MinMax Pairwise Opposition) pays for strategy
> benefits you describe is just far too high,
> failing as it does (Mutual) Majority and  Clone-Winner.  (Also very
> unattractive to me is that it  combines meeting
> Later-no-harm with failing Later-no-help, and thus having a
> zero-information  random-fill incentive.)
>
> A method that seems to perform as well in all your 3-candidate scenarios
> with lots of lazy truncating voters, is
> Raynaud(Gross)  with  the tiebreaker suggested by Gervase Lam.  (It
> could also be called  Raynaud(opposing votes)
> or  Max Pairwise Opposition Elimination).
>
> This would fail  Mono-raise, but at least meet Clone Independence and
>  (Mutual) Majority.  So in my view it is  much
> better!  What do you think?

Mono-raise is Monotonicity isn't it?  Monotonicity says that if a 
candidate X is lowered in the ranking in a ballot, it should not increase 
the chances of X winning.  If Mono-raise is Monotonicity, then ouch!

Forest's very recent posts on IRNR may also be worth referring to because 
Raynaud(Opposing Votes) is just applying MMPO and then eliminating the 
last placed candidate in each round.  (Thread: Range Voting and Cardinal 
Ratings Runoff).  As a consequence, I don't think Smith//MMPO is quite 
a good thing either.

Monotonicity to me seems to be a very fundamental requirement for ranked 
election methods.  If I had to choose between Clone Independence and 
Monotonicity, but not both, then I think I would go for Monotonicity.

Just in case I don't read this list until next year, merry christmas 
everybody!

Thanks,
Gervase.