Admissible and sincere strategies under approval voting

This essay reasses the assumptions of the Brams-Fishburn theory of approval voting, and proposes modifications to make the theory correspond better with likely voting choices. With a small number of candidates, voters who use the inadmissible strategy of voting for all candidates can help to produce a result that better reflects the voters' wishes than is possible with admissible strategies, so we propose a widening of the definition of admissibility to encompass this case. With more than three candidates, we define first-order admissible strategies, which are the most likely strategies to be used in practice, and are also strongly sincere, in that a vote for any candidate is always accompanied by votes for all more or equally-preferred candidates. Their number is less under approval voting than under plurality voting. Both proposed modifications strengthen the technical arguments favoring approval voting over plurality voting.