Majority Voting and Social Choice

Craven, John

doi:10.2307/2296783

Cited by 30 publications

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“…Craven (1971), Brown (forthcoming) and Ferejohn and Grether (1974) each exhibit several conditions which are sufficient to prevent social preference cycles in certain classes of voting procedures which choose among a fixed number of alternatives. Each of these papers examines only conditions precluding cycles for all preference profiles.…”

Section: Variable Majority Rulementioning

confidence: 99%

“…cyclic) majority preference relations without straying too far from simple majority rule and thereby losing its desirable normative characteristics. Craven (1971), Schwartz (1972), Brown (forthcoming), Ferejohn and Grether (1974) and Young (1977), for example, have investigated such procedures. Virtually nothing is known about the 668 REVIEW OF ECONOMIC STUDIES properties of these decision rules, except for Bordes ' (1976) recent characterization of the transitive closure of majority rule.…”

Section: R Introductionmentioning

confidence: 99%

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On Variable Majority Rule and Kramer's Dynamic Competitive Process

Blair

1979

The Review of Economic Studies

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r. INTRODUCTIONThis paper defines and characterizes axiomatically two rational voting procedures which are variants of simple majority rule. The rules are closely related and coincide when individual indifference is excluded. Some of the conditions used are then discussed and related to similar properties that have been studied in the social choice literature.It has long been known that a majority winner in a field of three or more candidates need not exist in general unless the preferences of the electorate display some degree of similarity. Sen and Pattanaik (1969) derived a set of necessary and sufficient conditions for a majority preference relation to be well behaved. Kramer (1973) studied these conditions in the context of quasi-concave differentiable preferences over a multidimensional Euclidean choice space, the natural setting for most economic decision models, and showed that they were extremely restrictive. Even the most modest diversity in preferences causes a violation of all the Sen-Pattanaik conditions in B". At least two reactions are possible to Kramer's important theorem. One response is to deny its relevance to actual political systems; few collectivities in fact make decisions by pairwise comparisons of all feasible alternatives using direct majority rule. Building on the work of Downs (1956), much effort has been devoted to the analysis of spatial models in which the electorate votes only on alternatives advocated by a small number of parties or candidates. But the existence of equilibria in these models has until recently been equally problematic (see Riker and Ordeshook (1972) for an overview of spatial models).In another paper Kramer (1977) has recently developed a model in this tradition which is the most general structure yet examined in which majority voting is at all well behaved. The model is a dynamic one in which two parties are assumed to compete for votes in a series of elections over time. The parties choose as platforms points in a multidimensional policy space with the objective of maximizing the number of votes the party receives in the next election. Each voter chooses his most preferred party according to his spherical indifference map. Kramer shows that the sequence of successively-enacted policies tends to converge to a relatively small subset of the feasible policy alternatives. It is of considerable interest to know what normative properties are exhibited by this decision process. The social preference relation which the competing parties implicitly maximize is the second of the rules to be axiomatized in this paper.There is a second possible response to the difficulties posed by the restrictiveness of the Sen-Pattanaik conditions in economic models. One might look for ways to " repair" defective (i.e. cyclic) majority preference relations without straying too far from simple majority rule and thereby losing its desirable normative characteristics. Craven (1971), Schwartz (1972, Brown (forthcoming), Ferejohn and Grether (1974) and Young (1977), for example, have investig...

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Section: Variable Majority Rulementioning

confidence: 99%

Section: R Introductionmentioning

confidence: 99%

On Variable Majority Rule and Kramer's Dynamic Competitive Process

Blair

1979

The Review of Economic Studies

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“…A number of studies have been concerned with the propensity of simple voting systems to elect the Condorcet winner when there is one [Paris (1975), Ludwin (1976), Chamberlin and Cohen (1968), Gehrlein (1981d) and Fishburn and Gehdein (1982)]. Craven (1971)and Rosenthal (1975) consider variations of majority rule which attempt to reduce the probability of Condorcet's paradox. The current study concerns itself with the simplest of all questions about Condorcet's paradox, specifically, "How likely is the paradox to occur?…”

Section: Introductionmentioning

confidence: 99%

Condorcet's paradox

Gehrlein

1983

Theor Decis

176

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162WILLIAM V. GEHRLEIN ns a = 1. In this example A > sB, B > sC and C> sA where A > sB denotes group simple majority preference for A over B. As a result, we find that there is no alternative capable of defeating all other candidates on the basis of pairwise simple majority elections. If n~ = 1, n: 3 = 1, n~ = 1, we find that A is the Condorcet winner or simple majority winner since A > sC and A > sB.

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“…Consider, for exam ple, proportional voting rul es. Craven (1971) shows that for the choice set to be nonempty over a finite alte rnative set with any more than a few al terna tives in it, a voting proportion close to unanimity is required, Greenberg (1979) makes a similar showing for CCE subset al ternative se ts with more than a few dimensions. But proportional voting rules requiring proportions significantly greater than one-half often wil l not be decisive, Tw o alterna tives preferred to all others by everyone may "tie" as social choices because voters are ne arly equally divided between them, For proportional voting rules, decisiveness therefore may be obtaine d only at the cost of the 'po ssibility of having an empty choice set, Another problem with impo sing decisiveness on the underlying social choice correspondence s is that extremely ne gative resul ts ensue, Theo1<:'1 3.4 in Sen (1983) as well as resul ts in Maskin (1979) and Da sgupta, Hammond and Maskin (1979) indica te that decisive social choice correspondences are impl ementable by strong Nash equilibria .Q.!…”

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confidence: 96%

Full Nash implementation of neutral social functions

Strnad

1987

Journal of Mathematical Economics

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Majority Voting and Social Choice

Cited by 30 publications

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On Variable Majority Rule and Kramer's Dynamic Competitive Process

On Variable Majority Rule and Kramer's Dynamic Competitive Process

Condorcet's paradox

Full Nash implementation of neutral social functions

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