The strategic sincerity of approval voting
Manipulation of voting rules has been studied to a large extent. As pointed out by Downding and van Hees (2008), smarter voters have an advantage from insincere behavior, so that there is some interest in studying the strategic sincerity of voting rules. The paper under review considers the unique scoring rule that ensures no-skipping sincerity for three candidates, i.e., approval voting, with respect to incentives for sincerity. Following the argument of \textit{R. B. Myerson} that in large games there should be some uncertainty about the number of players in the game [J. Econ. Theory 94, No. 1, 7--45 (2000; Zbl 1044.91004)], the author considers Poisson games with an expected number of \(n\) players. In general, none of the different definitions of sincerity from the literature is satisfied in this framework. For a known number of players the situation is different, as shown in [\textit{J.-F. Laslier}, ``The leader rule: a model of strategic approval voting in a large electorate'', J. Theor. Polit. 21, No. 1, 113--136 (2009; \url{doi:10.1177/0951629808097286 })]. In the present paper ``two main rationales for the violation of sincerity'' are identified. For one of these a sufficient condition for avoidance is given. Other rank scoring rules are discussed too.
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