Selling a vote

A voting function is a rule that determines the outcome of an election: taking the voters' votes as input, a voting function selects the winning candidate from the set of candidates receiving some vote. A voting function is immune to vote selling when, given that neither voter i nor voter j votes for the winning candidate, a change ceteris paribus in i's vote cannot make the candidate for which j votes the winner. It is shown that voting functions immune to vote selling have either a dictator (a voter who always determines the winning candidate) or a dictated candidate (a candidate who becomes the winner by just receiving some vote).