Abstract
Under approval voting, each voter can nominate as many candidates as she wishes and the election winners are those candidates that are nominated most often. A voter is said to have voted sincerely if she prefers all those candidates she nominated to all other candidates. As there can be a set of winning candidates rather than just a single winner, a voter’s incentives to vote sincerely will depend on what assumptions we are willing to make regarding the principles by which voters extend their preferences over individual candidates to preferences over sets of candidates. We formulate two such principles, replacement and deletion, and we show that, under approval voting, a voter who accepts those two principles and who knows how the other voters will vote will never have an incentive to vote insincerely. We then discuss the consequences of this result for a number of standard principles of preference extension in view of sincere voting under approval voting.
Highlights
Approval voting (AV) is a voting procedure that allows each voter to approve of as many candidates as she desires and that declares the candidate(s) collecting the most approvals the winner(s) of the election (Weber 1978; Brams and Fishburn 1978, 2007; Laslier and Sanver 2010)
For instance, by Sanver (2010), despite its prominent position amongst the major voting procedures, AV does not directly fit into the standard model of voting used in social choice theory
We define our model and state the main problem we shall address. (An important detail of the model, namely how voters extend their preferences over individual candidates to sets of candidates, will largely be relegated to Sect. 3.)
Summary
Approval voting (AV) is a voting procedure that allows each voter to approve of as many candidates as she desires and that declares the candidate(s) collecting the most approvals the winner(s) of the election (Weber 1978; Brams and Fishburn 1978, 2007; Laslier and Sanver 2010). The assumptions we shall work with concern the principles by which a voter will extend her preferences over individual candidates to a preference order over (nonempty) sets of candidates when considering what ballot to submit This is a well-studied problem in social choice theory, often referred to as ranking sets of objects (see, e.g., Barberà et al 2004; Gärdenfors 1976; Kelly 1977; Kannai and Peleg 1984; Nitzan and Pattanaik 1984; Puppe 1995; Can et al 2009; Erdamar and Sanver 2009; Geist and Endriss 2011) and we shall be examining incentives to vote sincerely under AV for a range of different such principles proposed in the literature.
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