A tight quantitative version of Arrow's impossibility theorem

Approval voting and Arrow's impossibility theorem

Approval voting has attracted considerable interest among voting theorists, but they have rarely investigated it in the Arrovian framework of social welfare functions (SWF) and never connected it with Arrow’s impossibility theorem. This note explores these two directions. Assuming that voters have dichotomous preferences, it first characterizes approval voting in terms of its SWF properties and...

Game Theory Lecture Notes by the Gibbard Satterthwaite Theorem and Arrow's Impossibility Theorem

Note: This is a only a draft version, so there could be flaws. If you find any errors, please do send email to [email protected]. A more thorough version would be available soon in this space. 1 The Gibbard–Satterthwaite Impossibility Theorem We have seen in the last section that dominant strategy incentive compatibility is an extremely desirable property of social choice functions. Howeve...

Welfarist-consequentialism, similarity of attitudes, and Arrow's general impossibility theorem

Arrow's Impossibility Theorem Without Unanimity

Arrow’s Impossibility Theorem states that any constitution which satisfies Transitivity, Independence of Irrelevant Alternatives (IIA) and Unanimity is a dictatorship. Wilson derived properties of constitutions satisfying Transitivity and IIA for unrestricted domains where ties are allowed. In this paper we consider the case where only strict preferences are allowed. In this case we derive a ne...

Arrow ' s Theorem with a Fixed Feasible Alternative *

Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if ...