SOCIAL CHOICE AND THE ARROW CONDITIONS

2014 ◽  
Vol 30 (3) ◽  
pp. 269-284 ◽  
Author(s):  
Allan F. Gibbard
Keyword(s):  
Social Choice ◽  
Social Preference ◽  
Preference Relation ◽  
Impossibility Result ◽  
Individual Preferences ◽  
System A ◽  
The Social ◽  
Liberum Veto

Arrow’s impossibility result stems chiefly from a combination of two requirements: independence and fixity. Independence says that the social choice is independent of individual preferences involving unavailable alternatives. Fixity says that the social choice is fixed by a social preference relation that is independent of what is available. Arrow found that requiring, further, that this relation be transitive yields impossibility. Here it is shown that allowing intransitive social indifference still permits only a vastly unsatisfactory system, a liberum veto oligarchy. Arrow’s argument for independence, though, undermines any rationale for fixity.

Condorcet Winners and the Paradox of Voting: Probability Calculations for Weak Preference Orders

1995 ◽  
Vol 89 (1) ◽  
pp. 137-144 ◽  
Author(s):  
Bradford Jones ◽  
Benjamin Radcliff ◽  
Charles Taber ◽  
Richard Timpone
Keyword(s):  
Decision Making ◽  
Computer Simulation ◽  
Social Choice ◽  
Individual Preferences ◽  
Weak Preference ◽  
The Social ◽  
Small Committee ◽  
Committee Decision Making ◽  
Preference Orders ◽  
Choice Literature

That individual preferences may he aggregated into a meaningful collective decision using the Condorcet criterion of majority choice is one of the central tenets of democracy. But that individual preferences may not yield majority winners is one of the classic findings of the social choice literature. Given this problem, social choice theorists have attempted to estimate the probability of Condorcet winners, given certain empirical or theoretical conditions. We shall estimate the probabilities of Condorcet winners and intransitive aggregate orders for various numbers of individuals with strong or weak preference orders across various numbers of alternatives. We find, using computer simulation, a stark contrast between these estimates assuming strong individual preferences and the estimates allowing for individuals' indifference between pairs of alternatives. In contrast to earlier work, which depends on the strong-preference assumption, we suggest that the problem is most acute for small committee decision making and least acute for mass elections with few alternatives.

scholarly journals Sports Tournaments and Social Choice Theory

Philosophies ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 28
Author(s):  
Rory Smead
Keyword(s):  
Social Choice ◽  
Social Preference ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Individual Preferences ◽  
Aggregation Methods ◽  
Dominance Relationships ◽  
Diverse Individual

Sports tournaments provide a procedure for producing a champion and ranking the contestants based on game results. As such, tournaments mirror aggregation methods in social choice theory, where diverse individual preferences are put together to form an overall social preference. This connection allows us a novel way of conceptualizing sports tournaments, their results, and significance. I argue that there are genuine intransitive dominance relationships in sports, that social choice theory provides a framework for understanding rankings in such situations and that these considerations provide a new reason to endorse championship pluralism.

FUZZY BLACK'S MEDIAN VOTER THEOREM: EXAMINING THE STRUCTURE OF FUZZY RULES AND STRICT PREFERENCE

2012 ◽  
Vol 08 (02) ◽  
pp. 195-217 ◽  
Author(s):  
MICHAEL B. GIBILISCO ◽  
JOHN N. MORDESON ◽  
TERRY D. CLARK
Keyword(s):  
Median Voter ◽  
Social Preference ◽  
Dimensional Space ◽  
Preference Relation ◽  
Strict Preference ◽  
Median Voter Theorem ◽  
The Social ◽  
Fuzzy Preference Relations ◽  
Simple Rules ◽  
Fuzzy Framework

Under certain aggregation rules, particular subsets of the voting population fully characterize the social preference relation, and the preferences of the remaining voters become irrelevant. In the traditional literature, these types of rules, i.e. voting and simple rules, have received considerable attention because they produce non-empty social maximal sets under single-peaked preference profiles but are particularly poorly behaved in multi-dimensional space. However, the effects of fuzzy preference relations on these types of rules is largely unexplored. This paper extends the analysis of voting and simple rules in the fuzzy framework. In doing so, we contribute to this literature by relaxing previous assumptions about strict preference and by illustrating that Black's Median Voter Theorem does not hold under all conceptualizations of the fuzzy maximal set.

Comments on the Judgment of Princeton

2012 ◽  
Vol 7 (2) ◽  
pp. 152-154 ◽  
Author(s):  
Richard E. Quandt
Keyword(s):  
Social Preference ◽  
Social Ranking ◽  
Second Best ◽  
Individual Preferences ◽  
The Social

Wine tastings inevitably involve some form of grading or ranking the wines, since the objective of tastings is to determine which wine is best, second best, etc., at least among the tasters on that particular occasion. Much has been written about the care that has to be taken that judges are not influenced by extraneous and irrelevant factors and that they do not influence one another. Ultimately, of course, the views of the judges need to be congealed in a single ranking that expresses the “social preference” among the wines. And therein lies the rub: how to aggregate individual preferences into a social ranking.

scholarly journals Impossibility theorems in multiple von Wright’s preference logic

2014 ◽  
Vol 59 (201) ◽  
pp. 69-84
Author(s):  
Branislav Boricic
Keyword(s):  
Social Choice ◽  
Social Preference ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Mathematical Economics ◽  
Preference Logic ◽  
Preference Relations ◽  
The Social ◽  
The Individual ◽  
Combining Logics

By using the standard combining logics technique (D. M. Gabbay 1999) we define a generalization of von Wright?s preference logic (G. H. von Wright 1963) enabling to express, on an almost propositional level, the individual and the social preference relations simultaneously. In this context we present and prove the counterparts of crucial results of the Arrow-Sen social choice theory, including impossibility theorems (K. Arrow 1951 and A. K. Sen 1970b), as well as some logical interdependencies between the dictatorship condition and the Pareto rule, and thus demonstrate the power and applicability of combining logics method in mathematical economics.

Positive Political Theory I: Collective Preference. By David Austen-Smith and Jeffrey S. Banks. Ann Arbor: University of Michigan Press, 1999. 208p. $39.50.

2001 ◽  
Vol 95 (2) ◽  
pp. 459-460
Author(s):  
Norman Schofield
Keyword(s):  
Political Theory ◽  
Social Preference ◽  
Preference Relation ◽  
Preference Aggregation ◽  
University Of Michigan ◽  
Social Rules ◽  
The Social ◽  
Ann Arbor ◽  
Collective Preference

This study is intended as the first of a two-volume presenta- tion of positive political theory. As the authors indicate in the preface, in this volume they develop what may be termed Arrovian direct preference aggregation, a theory that exam- ines the properties of a direct aggregation rule, f, mapping from a domain of preference profiles on a set, X. For any profile, , the image of f is a social preference relation denoted f( ). The social relation may exhibit maximal or unbeaten outcomes, mf( ), in X itself. Thus, the volume is concerned with the "classification" of all social rules that map from preference profiles into X itself.

scholarly journals The Death of Welfare Economics

2019 ◽  
Vol 51 (5) ◽  
pp. 827-865 ◽  
Author(s):  
Herrade Igersheim
Keyword(s):  
Social Welfare ◽  
Social Choice ◽  
Social Welfare Function ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Welfare Economics ◽  
Impossibility Result ◽  
Impossibility Theorem ◽  
Individual Values ◽  
The Social

The death of welfare economics has been declared several times. One of the reasons cited for these plural obituaries is that Kenneth Arrow’s impossibility theorem, as set out in his pathbreaking Social Choice and Individual Values in 1951, has shown that the social welfare function—one of the main concepts of the new welfare economics as defined by Abram Bergson (Burk) in 1938 and clarified by Paul Samuelson in the Foundations of Economic Analysis—does not exist under reasonable conditions. Indeed, from the very start, Arrow kept asserting that his famous impossibility result has direct and devastating consequences for the Berg-son-Samuelson social welfare function, though he seemed to soften his position in the early eighties. On his side, especially from the seventies on, Samuelson remained active on this issue and continued to defend the concept he had devised with Bergson, tooth and nail, against Arrow’s attacks. The aim of this article is precisely to examine this rather strange controversy, which is almost unknown in the scientific community, even though it lasted more than fifty years and involved a conflict between two economic giants, Arrow and Samuelson, and, behind them, two distinct communities—welfare economics, which was on the wane, against the emerging social choice theory—representing two conflicting ways of dealing with mathematical tools in welfare economics and two different conceptions of social welfare.

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