We propose the concept of level r consensus as a useful property of a preference profile which considerably enhances the stability of social choice. This concept involves a weakening of unanimity, the most extreme form of consensus. It is shown that if a preference profile exhibits level r...

Can neural networks learn to select an alternative based on a systematic aggregation of conflicting individual preferences (i.e. a 'voting rule')? And if so, which voting rule best describes their behavior? We show that a prominent neural network can be trained to respect two fundamental...

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.

Introduction -- Elementary Logic -- Sets, Relations, Functions -- Binary Relations -- Social Choice Theoretic Framework and Arrow Impossibility Theorem -- Some Important Value-Judgments, Rules and Theorems -- Implications of Weakening of Some of Arrow Conditions -- The Method of Majority...