Alejandro Saporiti

Single-Crossing, Strategic Voting and the Median Choice Rule

This paper studies the strategic foundation of the Representative Voter Theorem (Rothstein in: Pub Choice 72:193–212, 1991), also called the “second version” of the Median Voter Theorem. As a by-product, it also considers the existence of strategy-proof social choice functions over the domain of single-crossing preferences. The main result shows that single-crossing constitutes a domain restriction over the real line that allows not only majority voting equilibria, but also non-manipulable choice rules. In particular, this is true for the median rule, which is found to be group strategic-proof over the full set of alternatives and over every nonempty subset. In addition, the paper also examines the relation between single-crossing and order-restriction. And it uses this relation together with the strategy-proofness of the median rule to prove that the outcome predicted by the Representative Voter Theorem can be implemented in dominant strategies through a simple mechanism. This mechanism is a two-stage voting procedure in which, first, individuals select a representative among themselves, and then the winner chooses a policy to be implemented by the planner.

Political motivations and electoral competition: Equilibrium analysis and experimental evidence

We study both theoretically and experimentally the complete set of Nash equilibria of a classical one-dimensional, majority rule election game with two candidates, who might be interested in power as well as in ideology, but not necessarily in the same way. Apart from obtaining the well known median voter result and the two-sided policy differentiation outcome, the paper uncovers the existence of two new equilibrium configurations, called ‘one-sided’ and ‘probabilistic’ policy differentiation, respectively. Our analysis shows how these equilibrium configurations depend on the relative interests in power (resp., ideology) and the uncertainty about voters’ preferences. The theoretical predictions are supported by the data collected from a series of laboratory experiments, as we observe convergence to the Nash equilibrium values at the aggregate as well as the individual levels in all treatments, and the comparative statics effects across treatments are as predicted by the theory.

Bertrand Competition in Markets with Fixed Costs

This paper provides necessary and sufficient conditions for the existence of a pure strategy Bertrand equilibrium in a model of price competition with fixed costs. It unveils an interesting and unexplored relationship between Bertrand competition and natural monopoly. That relationship points out that the non-subadditivity of the cost function at the output level corresponding to the oligopoly break-even price, denoted by D(pL(n)), is sufficient to guarantee that the market sustains a (not necessarily symmetric) Bertrand equilibrium in pure strategies with two or more firms supplying at least D(pL(n)). Conversely, the existence of a pure strategy equilibrium ensures that the cost function is not subadditive at every output greater than or equal to D(pL(n)).

Securely implementable social choice rules with partially honest agents

We study a social choice model with partially honest agents, and we show that strategy-proofness is a necessary and sufficient condition to achieve secure implementation. This result provides a behavioral foundation for the rectangularity property; and it offers as a by-product a revelation principle for secure implementation with partial honesty. We apply the implementation concept to a single-crossing voting environment, and we prove that it characterizes, in combination with unanimity, the family of augmented representative voter schemes.