Toward Applicable Social Choice Theory: A Comparison of Social Choice Functions under Spatial Model Assumptions

1978 ◽  
Vol 72 (4) ◽  
pp. 1341-1356 ◽  
Author(s):  
John R. Chamberlin ◽  
Michael D. Cohen
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Monte Carlo Study ◽  
Performance Criteria ◽  
Alternative Methods ◽  
Choice Functions ◽  
Presidential Primary ◽  
Formal Framework ◽  
Social Choice Functions

This article develops a formal framework to aid political designers in the comparison of social choice functions. It generalizes earlier assumptions of “impartial culture” so that we may begin to investigate the effect of politically interesting variations on the probability that different social choice functions will satisfy given performance criteria. As an application of the framework, a detailed Monte Carlo study compares the ability of four different social choice functions to select a Condorcet winner when voter preference orders have been generated from a spatial representation of ideal points and alternatives. We also investigate the potential of alternative methods of selecting winners in presidential primary elections.

In Praise of Manipulation

2007 ◽  
Vol 38 (1) ◽  
pp. 1-15 ◽  
Author(s):  
KEITH DOWDING ◽  
MARTIN VAN HEES
Keyword(s):  
Decision Making ◽  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Decision Making Process ◽  
Choice Functions ◽  
Social Choice Functions ◽  
Voting Procedures ◽  
Strategy Proofness

Many theorists believe that the manipulation of voting procedures is a serious problem. Accordingly, much of social choice theory examines the conditions under which strategy-proofness can be ensured, and what kind of procedures do a better job of preventing manipulation. This article argues that democrats should not be worried about manipulation. Two arguments against manipulation are examined: first, the ‘sincerity argument’, according to which manipulation should be rejected because it displays a form of insincere behaviour. This article distinguishes between sincere and non-sincere manipulation and shows that a familiar class of social choice functions is immune to insincere manipulation. Secondly, the ‘transparency’ argument against manipulation is discussed and it is argued that (sincere or insincere) manipulation may indeed lead to non-transparency of the decision-making process, but that, from a democratic perspective, such non-transparency is often a virtue rather than a vice.

Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule

1983 ◽  
Vol 77 (3) ◽  
pp. 718-733 ◽  
Author(s):  
John R. Chamberlin ◽  
Paul N. Courant
Keyword(s):  
Social Choice ◽  
Democratic Theory ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Proportional Representation ◽  
Choice Functions ◽  
Borda Rule ◽  
The Past ◽  
Majority Decision ◽  
Social Choice Functions

The development of social choice theory over the past three decades has brought many new insights into democratic theory. Surprisingly, the theory of representation has gone almost untouched by social choice theorists. This article redresses this neglect and provides an axiomatic study of one means of implementing proportional representation.The distinguishing feature of proportional representation is its concern for the representativeness of deliberations as well as decisions. We define a representative in a way that is particularly attentive to this feature and then define a method of selecting representatives (a variant of the Borda rule) which selects a maximally representative body. We also prove that this method of selection meets four social choice axioms that are met by a number of other important social choice functions (including pairwise majority decision and the Borda rule).

Rights and Social Choice: Is There a Paretian Libertarian Paradox?

1987 ◽  
Vol 3 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Jonathan Pressler
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Amartya Sen ◽  
Individual Rights ◽  
Choice Functions ◽  
General Consensus ◽  
Social Choice Functions ◽  
Original Theorem

In 1970 Amartya Sen exposed an apparent antinomy that has come to be known as the Paradox of the Paretian Libertarian (Sen, 1970b, pp. 152–57). Sen introduced his paradox by establishing a simple but startling theorem. Roughly put, what he proved was that if a mechanism for selecting social choice functions satisfies two standard adequacy conditions, there are possible situations in which it will violate either the very weak libertarian precept that every individual has at least some rights or the seemingly innocuous Paretian principle that an option should be judged unacceptable if there is an available alternative that everyone prefers to it. Many economists and philosophers have proposed solutions to Sen's problem, but there is no general consensus on what solution (if any) is correct. In the present paper I argue that Sen's original theorem fails to establish the existence of any conflict between libertarianism and Paretianism. Furthermore, I contend that Sen has misinterpreted certain other theorems which he has used to defend the existence of a paradoxical conflict between these two doctrines. In general, I try to show that whenever Sen posits a Paretian-libertarian conflict to explain an apparently troubling result in social choice theory, the difficulty can be better dealt with either by claiming that the theorem in question imposes overly strong background constraints on the form of social choice functions or by claiming that it relies on an unacceptable construal of individual rights.

Precursors to Public Choice

2019 ◽  
pp. 796-816
Author(s):  
Iain McLean
Keyword(s):  
Public Choice ◽  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Ancient Greek ◽  
The Social ◽  
Mathematical Skill ◽  
The Many ◽  
Selection Of

This chapter reviews the many appearances, disappearances, and reappearances of axiomatic thought about social choice and elections since the era of ancient Greek democracy. Social choice is linked to the wider public-choice movement because both are theories of agency. Thus, just as the first public-choice theorists include Hobbes, Hume, and Madison, so the first social-choice theorists include Pliny, Llull, and Cusanus. The social-choice theory of agency appears in many strands. The most important of these are binary vs. nonbinary choice; aggregation of judgement vs. aggregation of opinion; and selection of one person vs. selection of many people. The development of social choice required both a public-choice mindset and mathematical skill.

Full Implementation under Ambiguity

2021 ◽  
Vol 13 (1) ◽  
pp. 148-178
Author(s):  
Huiyi Guo ◽  
Nicholas C. Yannelis
Keyword(s):  
Social Choice ◽  
Expected Utility ◽  
Sufficient Conditions ◽  
Choice Functions ◽  
Maxmin Expected Utility ◽  
Special Cases ◽  
Social Choice Functions ◽  
Bayesian Implementation ◽  
Pareto Efficient ◽  
Choice Set

This paper introduces the maxmin expected utility framework into the problem of fully implementing a social choice set as ambiguous equilibria. Our model incorporates the Bayesian framework and the Wald-type maxmin preferences as special cases and provides insights beyond the Bayesian implementation literature. We establish necessary and almost sufficient conditions for a social choice set to be fully implementable. Under the Wald-type maxmin preferences, we provide easy-to-check sufficient conditions for implementation. As applications, we implement the set of ambiguous Pareto-efficient and individually rational social choice functions, the maxmin core, the maxmin weak core, and the maxmin value. (JEL D71, D81, D82)

Sign in / Sign up

Export Citation Format

Share Document