[EM] A Clone Free Metric on ballots

[Kristofer Munsterhjelm]

On 04/03/2021 08.50, Forest Simmons wrote:
> A lot of good ideas have died on the vine because clones were ignored.
> The three best ones are Borda, Copeland, and Kemeny.
> 
> The key to fixing them is to make appropriate use of lotteries that
> re-distribute the probability of an alternative to the members of the
> clone set that takes its place. We have mentioned a few of them and have
> shown how to use them to fix Borda and Copeland in recent posts to this
> EM list.

I think this is related to a pattern that often shows up: that when you
generalize certain methods that reweight candidates, you end up
reweighting the voters instead.

Consider, for instance, party list. Traditional Sainte-Lague type party
list works by electing a candidate from the party with the greatest
(adjusted) support, then recalculating that party's adjusted support to
be penalized by 1/3, 1/5, 1/7 etc.

Now suppose you want to generalize this to Approval. Then there's no
easy way to adjust the parties' support because a voter may vote for
many different parties at once. So what does proportional approval
voting do? It reweights the voters instead.

However much overlap there may be between candidates, a voter is always
a single voter. So this sort of "probability of voters doing X"
perspective may be useful more generally.