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Some Implications of Arrow's Theorem for Voting Rights

Hayden, Grant M. - 2022

Arrow's theorem proves that no voting procedure can meet certain conditions of both fairness and logic. In this note, Grant Hayden explores the ramifications of the theorem for qualitative vote dilution. After describing Arrow's argument, Mr. Hayden considers four democratic voting procedures...

Persistent link: https://www.econbiz.de/10014081971

A Pedagogical Proof of Arrow's Impossibility Theorem

Dardanoni, Valentino - 2001

In this note I consider a simple proof of Arrow's Impossibility Theorem (Arrow 1963). I start with the case of three individuals who have preferences on three alternatives. In this special case there are 133 possible combinations of the three individuals' rational preferences. However, by...

Persistent link: https://www.econbiz.de/10014137645

From Paired Comparisons and Cycles to Arrow’s Theorem

Saari, Donald G. - 2019

Persistent link: https://www.econbiz.de/10012880787

A Graphical Analysis of Some Basic Results in Social Choice

Cantillon, Estelle; Rangel, Antonio - 2021

We use a simple graphical approach to represent Social Welfare Functions that satisfy Independence of Irrelevant Alternatives and Anonymity. This approach allows us to provide simple and illustrative proofs of May's Theorem, of variants of classic impossibility results, and of a recent result on...

Persistent link: https://www.econbiz.de/10013236834

Chapter 3 Domain restrictions

Gaertner, Wulf - In: Handbook of social choice and welfare : volume 1, (pp. 131-170). 2002

This chapter discusses different types of domain restrictions. We begin by analyzing various qualitative conditions on preference profiles. Value-restricted preferences (with single-peaked preferences as one of its subcases), limited agreement as well as antagonistic and dichotomous preferences...

Persistent link: https://www.econbiz.de/10014023840

Chapter 2 Categories of arrovian voting schemes

Aleskerov, Fuad - In: Handbook of social choice and welfare : volume 1, (pp. 95-129). 2002

which the individual opinions about the alternatives are defined, as well as to the form of desired social decision. These … types of rules are Social Decision Rules, Functional Voting Rules, and Social Choice Correspondences. Consideration is given … schemes are given. The notion of “rationality” of individual opinions and social decision is described. Various types of …

Persistent link: https://www.econbiz.de/10014023841

Chapter 1 Impossibility theorems in the arrovian framework

Campbell, Donald E.; Kelly, Jerry S. - In: Handbook of social choice and welfare : volume 1, (pp. 35-94). 2002

Given a set of outcomes that affect the welfare of the members of a group, K.J. Arrow imposed the following five conditions on the ordering of the outcomes as a function of the preferences of the individual group members, and then proved that the conditions are logically inconsistent: • The...

Persistent link: https://www.econbiz.de/10014023842

Chapter Twenty-Five. Strategyproof Social Choice

Barberà, Salvador - In: Handbook of social choice and welfare : volume 2, (pp. 731-831). 2011

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.

Persistent link: https://www.econbiz.de/10014025183

Chapter Nineteen. Nonbinary Social Choice

Rajat, Deb - In: Handbook of social choice and welfare : volume 2, (pp. 335-366). 2011

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...

Persistent link: https://www.econbiz.de/10014025189

Chapter Seventeen. Arrovian Social Choice Theory on Economic Domains

Le Breton, Michel; Weymark, John A. - In: Handbook of social choice and welfare : volume 2, (pp. 191-299). 2011

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...

Persistent link: https://www.econbiz.de/10014025191