[EM] Fixing IRV

[Richard Moore]

Roy wrote:
> a similar situation arises in all Smith set results. I don't see an 
> opportunity for non-monotonicity in this example; I would like to see 
> an example that demonstrates it. Perhaps a situation with inner and 
> outer Smith sets?

The best bet is to find a case where swapping the rankings 
of two candidates on one ballot changes the order of 
elimination in a key way. If

(1) X is originally eliminated at some stage, and Y 
subsequently wins, and
(2) swapping Y and Z on some ballot that originally has Y 
ranked lower than Z causes Z to be eliminated at that stage 
instead of X, and
(3) X's continued presence after that stage causes Y to lose 
instead of win,

then you have your example.

(I would think that a proof of Riker's theorem -- if that's 
the correct name -- would involve showing that such an 
example exists for every "elimination method". Obviously 
such a proof wouldn't apply to methods that eliminate 
candidates after, or at the same time as, the winner is 
determined.)

> Is anybody (besides me) interested in pursuing this method further? 
> It's not that it's a technically better method than any other 
> Condorcet method; it just offers a more pursuasive argument to IRV 
> advocates, because it's better than IRV by their own standard 
> (majority rule).

Many people here are pessimistic about getting the IRV 
people to accept any variations, even those variations that 
bring in a majoritarian standard. Such methods have been 
suggested before. Nevertheless, it might be worth 
investigating its other properties, such as strategic 
criteria compliance.

Richard