[EM] Condorcet as compromising DSV, and multiwinner ideas

[Kevin Venzke]

Hi Kristofer,

Sticking to the first topic:

Kristofer Munsterhjelm via Election-Methods <election-methods at lists.electorama.com> a écrit :
> Suppose that we have a Plurality election and that A wins, but B is the
> CW. Then the voters who preferred B to A could all compromise for B and
> make B win; and no other faction would be able to change the result
> after the voters compromised.[1]
> 
> (If there's a cycle, then repeating this reasoning would make the winner
> sequence follow the Smith set cycle.)
> 
> So in some sense, electing the CW executes a majority-compromise on
> behalf of the voters when such an opportunity exists, without the voters
> having to guess ahead of time who they're supposed to compromise for.
> 
> [1] This might even work with equal-rank as long as the voters who are
> indifferent between A and B either stay out of the strategy or lean A or
> B equally often, but I'm not sure if the "no other faction would be able
> to change the result" part would hold.

Regarding the footnote, I don't think it makes sense in a DSV thought experiment
for voters indifferent between some A and B to lift a single finger to stop one of
the two from winning vs. the other. (Not to mention that if they do, this could
potentially mean that they use a compromise strategy of raising an equal-bottom
candidate to the top.)

I mainly want to note then, that given this, and given the presence of some
incomplete rankings, it is not the case that all Smith set members could take a
turn at becoming first preference winner. I think this is not a bad reminder that
the Smith set can include candidates whose presence methods really ought to be
"independent of."

Kevin
votingmethods.net