[EM] a simple, ISDA-compliant method, not as great as I thought

[Kristofer Munsterhjelm]

On 4/17/23 22:42, Filip Ejlak wrote:
> Oh, good example. I mean, the FPC scores are different - 16:17:15 and 
> 16:15:17 respectively - but it unfortunately still gives a nonmonotonic 
> result (chaging A to C).
> 
> Standard FPC behaves in a more logical way here, changing B to C as B 
> gets lowered. I don't know, perhaps there could exist some middle ground 
> between sequential elimination and lack thereof? (not Smith//FPC, it is 
> still susceptible to clones.) Or it can be an entirely wrong tree to be 
> barking up... Although for me this idea still looks temptingly nice.

First of all, welcome! It's always nice to see new people on the list :-)

The usual middle point between elimination and none is below-average 
elimination like what Carey does to be monotone in the three-candidate 
case. However, you would probably lose ISDA this way, and it doesn't 
necessarily work for larger number of candidates.

Other ideas I've been thinking about include an idea of somehow making 
A's score the maximum through some elimination sequence that always 
favors A. E.g. let X be a sequence of the candidates except for A and 
two others, so that when you eliminate one after another (in the order 
of the sequence) then the (k+1)-th candidate in the sequence is never 
ranked first by first preference Copeland once the k first candidates 
are eliminated. Then A's score is the score in the final first 
preference Copeland election after everybody but A and the two others 
are eliminated, when the sequence is chosen to maximize A's score in 
this way, where the idea is that the max operator forces monotonicity. 
But I never managed to make that concrete. Perhaps something along those 
lines could work, though, but it would be much more hairy than plain FPC.

-km