Arrow's original proof of his impossibility theorem proceeded in two steps: showing the existence of a decisive voter, and then showing that a decisive voter is a dictator. Barbera replaced the decisive voter with the weaker notion of a pivotal voter, thereby shortening the first step, but...

This chapter surveys the literature on strategy proofness from a historical perspective. While I discuss the connections with other works on incentives in mechanism design, the main emphasis is on social choice models.

Economists have used the term “nonbinary” to describe both choice functional nonbinariness (choice functions that cannot be rationalized as the maximizing outcome of a binary preference relation) and structural nonbinariness (the structure of the model dictates that pairs of alternatives do...

This article surveys the literature that investigates the consistency of Arrow's social choice axioms when his unrestricted domain assumptions are replaced by domain conditions that incorporate the restrictions on agendas and preferences encountered in economic environments. Both social welfare...

Any procedure of social choice makes use of some types of information and ignores others. For example, the method of majority decision concentrates on people's votes, but pays no direct attention to, say, their social standings, or their prosperity or penury, or even the intensities of their...