[EM] Fixing Kemeny-Young

[Kristofer Munsterhjelm]

On 14.01.2022 04:05, Forest Simmons wrote:
> I've always admired the basic idea of Kemeny-Young, namely a cost metric
> for conversion of one ranking into another ... simply the number of
> transpositions (elementary swaps) required.
> 
> The deal-breaker draw-back of the Kemeny cost metric is that it is clone
> dependent ... if it were independent of clones the " cost" of
> transposing AB to BA would be the same as the net cost of transposing
> the rank order of respective clones of A and B:
> 
> the order a1a2a3b1b2b3
>  to the order b3b2b1a3a2a1

Of course, I have to restate here that Ranked Pairs is such a method:
the metric is just leximax. (ordering a is better than ordering b if the
greatest pairwise victory consistent with a is higher than the greatest
pairwise victory consistent with b, with tiebreaks for second greatest,
third greatest, etc.) And it's cloneproof.

-km