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In recent years, a number or authors have identified conditions on individual preference orders that imply transitive majorities or which imply that at least one alternative is not beaten by any other alternative under simple majority comparison. Within the context of a three-alternative situation, this paper summarizes these contributions and proves several new results that complete an analysis of sets of individual preference orders that guarantee a simple-majority winner among the three alternatives. Along with guarantees and odd-guaratees for sets of strict partial orders authors of this article consider the guaratees notions when all orders are required to be weak orders. Four definitions will be used to identify restrictions on individual preference orders taht will be used in the analysis. The article further presents numerical presentation of the research topic.

Under the assumption of single peaked preferences, the majority rule equilibrium considered as a correspondence from the voters' preference peaks is shown to be continuous. We also complement the work of Fishburn, who first presented a general location theorem for majority rule equilibriums, by dropping the assumptions that the alternative set is finite and that voters' preferences are strict partial orders. [ABSTRACT FROM AUTHOR]

Presents a paradox in social choice theory whose solution requires the abandonment of even acyclicity. Voter preferences in social choice theory; Assumption of citizens' intransitive weak preference, strong Pareto principle and ternary acyclicity; Factors forcing the abandonment of social acyclicity.

Let n stimuli be linearly ordered by a physical attribute. Consider an individual's 'more than' relation based on perceived attribute values. Assuming that the individual's relation agrees with the linear order and is an interval order, the paper examines the extent to which ordered pairs in the linear order but not in the interval order (due to nondetection of 'small' differences) can be correctly identified on the basis of the interval order alone. Different methods of constructing strict weak orders from interval orders are compared by the degree of agreement with the underlying linear order. [ABSTRACT FROM AUTHOR]

The article shows that the conflict involving collective rationality goes much deeper than one might suppose on the basis of the impossibility theorems that focus on binary social choices. In effect, it is proved that generalized versions of the principal conditions used by researchers A. Mas-Colell and H. Sonnenschein are incompatible. The results are based on social choices from subsets of in alternatives rather than on social choices from subsets of two alternatives. It will be assumed throughout that the number n of voters is finite. To weaken one of the typical structural conditions slightly we shall assume later that all voters have linear preference orders on X, and, given this, adopt a universal domain condition which says that all n-tuples of linear preference orders on X are admissible or potential voter preference profiles. The article builds up to binary-choice impossibility theorems with special emphasis on notions of collective rationality. The collective-rationality idea along with other conditions to apply are generalized to m-alternative subsets of X, and states the new impossibility theorem. Proofs are given with conclusions in the final section.

This paper presents a survey of results in preference theory with intransitive indifference and discusses them for the areas of basic preference theory, consumer preference, additive utility, qualitative probability, expected utility, and social choice. [ABSTRACT FROM AUTHOR]

An iterative method is proposed for constructing a weak order from a partial order on a set of stimuli that is based on individual pairwise comparison data. The method generalizes Duncan Luce's construction of the weak order induced by a semiorder. Various aspects of the iterative procedure are discussed, including its rationale, the number of iterations required to obtain a weak order, and the extent to which the data support additions to the initial partial order as a function of the number of iterations performed before the additions occur. [ABSTRACT FROM AUTHOR]

a−b≺* c−d is taken to mean that 'your' degree of preference for a over b is less than 'your' degree of preference for c over d. Various properties of the strength-of-preference comparison relation ≺* are examined along with properties of simple preferences defined from ≺*. The investigation recognizes an individual's limited ability to make 'precise' judgments. Several utility theorems relating a−b ≺* c−d to u(a)−u(b)

This paper argues that social choice from among more than two feasible alternatives should not be based on social choice from two-alternative subsets. It considers in some detail the case where one alternative ties or beats every other alternative on the basis of simple majorities, and raises the question of whether such an alternative should be chosen. A condition of 'stochastic unanimity', introduced in this context, is shown to be incompatible with the simple majority rule when it can apply. This new condition plus a consideration of ties leads into a brief discussion of the use of individual expected utility in social choice theory. [ABSTRACT FROM AUTHOR]