Who Wins and Loses Under Approval Voting? An Analysis of Large Elections

We fully describe the set of equilibrium winners in a model of strategic Approval voting. To this end, we introduce the concept of viable candidate: a candidate is viable if the number of voters who do not rank him last is larger than the number of voters who rank first any other candidate. If at most two candidates are viable, we prove that the unique equilibrium winner is the Condorcet Winner. For any election with more viable candidates, we show that for some utility profiles we can build an equilibrium in which all the viable candidates are tied for victory.