Abstract
This chapter focuses on strategy-proofness and monotonicity. A game form (g.f.) describes any democratic decision rule that can be associated with a fixed society and set of outcomes. It is a more general object than a social choice function. When at least three different outcomes exist, the Gibbard-Satterthwaite theorem states that the only strategy-proof g.f. are dictatorial, that is, endow one particular agent with all decision power. When society (N) and the outcome space (A) are fixed, it is said that a decision process is democratic if it relies only on individual wills. It is formally described by a game form. A game form distributes exhaustively the decision power among individuals by endowing each agent with a fixed message space and converting any bundle of an agent's messages into a single outcome. Any social choice function can be viewed as a game form where the message space of every agent is L(A), the set of linear orderings of A, and S is the decision rule.
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