Social Choice Theory in HOL Arrow and Gibbard-Satterthwaite
نویسنده
چکیده
This article presents formalizations in higher-order logic of two proofs of Arrow’s impossibility theorem due to Geanakoplos. The Gibbard-Satterthwaite theorem is derived as a corollary. Lacunae found in the literature are discussed.
منابع مشابه
A topological proof of Eliaz's unified theorem of social choice theory
Recently Eliaz (2004) has presented a unified framework to study (Arrovian) social welfare functions and non-binary social choice functions based on the concept of preference reversal. He showed that social choice rules which satisfy the property of preference reversal and a variant of the Pareto principle are dictatorial. This result includes the Arrow impossibility theorem (Arrow (1963)) and ...
متن کاملBetween Arrow and Gibbard-Satterthwaite; A representation theoretic approach
A central theme in social choice theory is that of impossibility theorems, such as Arrow’s theorem [Arr63] and the Gibbard-Satterthwaite theorem [Gib73, Sat75], which state that under certain natural constraints, social choice mechanisms are impossible to construct. In recent years, beginning in Kalai [Kal01], much work has been done in finding robust versions of these theorems, showing “approx...
متن کاملThe Gibbard-Satterthwaite theorem of social choice theory in an infinite society and LPO (limited principle of omniscience)
This paper is an attempt to examine the main theorems of social choice theory from the viewpoint of constructive mathematics. We examine the Gibbard–Satterthwaite theorem [A.F. Gibbard, Manipulation of voting schemes: a general result, Econometrica 41 (1973) 587–601; M.A. Satterthwaite, Strategyproofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and soc...
متن کاملA Computer-Aided Proof to Gibbard-Satterthwaite Theorem
The Gibbard-Satterthwaite Theorem is a landmark result in both social choice theory and implementation theory, as it bridges normative and strategic analysis of voting problems. The theorem states that any social choice function that is strategy-proof and onto is also dictatorial. In this paper, we provide a computer-aided inductive proof for the theorem. We first show that this result holds if...
متن کاملArrow ’ s theorem and the Gibbard - Satterthwaite theorem : a unified approach *
The connection between Arrow’s theorem and the Gibbard-Satterthwaite theorem is further strengthened by providing a single proof that yields both results. 2001 Elsevier Science B.V. All rights reserved.
متن کامل