[EM] Favorite Betrayal and Condorcet

[Kevin Venzke]

Hi Forest, I don't follow what you say below. The DSV method should surely operate on
sincere ballots to find the promised equilibrium. So every favorite F should already be
approved.

The easiest illustrative situation is where there is no CW (either sincere or voted), but
some voters can abandon one of their first preferences in order to give a different first
preference a win that makes them the CW.

Kevin



Le lundi 18 avril 2022, 18:11:37 UTC−5, Forest Simmons <forest.simmons21 at gmail.com> a écrit : 

Your comments remind me that (if I remember correctly) there is supposed to always exists a Nash equilibrium approval ballot set which elects the sincere CW candidate when one exists. 

But a DSV method that finds such an equilibrium (along with its concomitant candidate) would have to satisfy the FBC, since any one voter defecting from that equilibrium to approve her favorite F would get away with it ... if the winner changed at all it would have to change to F.

So all we need is a constructive proof of the alleged Nash Equilibrium existence.

Can someone clear up this mystery?