Automated Analysis of Social Choice Problems: Approval Elections with Small Fields of Candidates

We analyse the incentives of a voter to vote insincerely in an election conducted under the system of approval voting. Central to our analysis are the assumptions we make on how voters deal with the uncertainty stemming from the fact that a tie-breaking rule may have to be invoked to determine the unique election winner. Because we only make very weak assumptions in this respect, it is impossible to obtain general positive results. Instead, we conduct a fine-grained analysis using an automated approach that reveals a clear picture of the precise conditions under which insincere voting can be ruled out. At the methodological level, this approach complements other recent work involving the application of techniques originating in computer science and artificial intelligence in the domain of social choice theory.