A Note on Binary Strategy-Proof Social Choice Functions - Achille Basile; Anna De Simone; Ciro Tarantino (Games, 2022)
Let <semantics>Φn</semantics> be the set of the binary strategy-proof social choice functions referred to a group of n voters who are allowed to declare indifference between the alternatives. We provide a recursive way to obtain the set <semantics>Φn+1</semantics> from the set <semantics>Φn</semantics>. Computing the cardinalities <semantics>|Φn|</semantics> presents difficulties as the computation of the Dedekind numbers. The latter give the analogous number of social choice functions when only strict preferences are admitted. A comparison is given for the known values. Based on our results, we present a graphical description of the binary strategy-proof social choice functions in the case of three voters.