Euclidean preferences

This note is devoted to the question: how restrictive is the assumption that preferences be Euclidean in d dimensions. In particular it is proven that any preference profile with I individuals and A alternatives can be represented by Euclidean utilities with d   dimensions if and only if d≥min?(I,A−1)$d\ge \min ?(I\text{,}A-1)$. The paper also describes the systems of A points which allow for the representation of any profile over A alternatives, and provides similar results when only strict preferences are considered. These findings contrast with the observation that if preferences are only required to be convex then two dimensions are always sufficient.     

Strategy-proof allocation when preferences are single-plateaued

Abstract. We consider private good economies with single-plateaued preferences. A solution selects for each preference profile a non-empty set of allocations. An agent strictly prefers a set of allocations to another set of allocations if and only if he strictly prefers any allocation in the first set to any in the second set according to his single-plateaued preference relation. We characterize the class of sequential-allotment solutions by essentially single-valuedness, Pareto-indifference, and coalitional stragety-proofness. These solutions are the Pareto-indifferent extensions of the solutions studied by Barberà et al. 1997. Received: 9 May 2000 / Accepted: 1 May 2001     

Strategy-proof fuzzy aggregation rules

We investigate the structure of fuzzy aggregation rules which, for every permissible profile of fuzzy individual preferences, specify a fuzzy social preference. We show that all fuzzy aggregation rules which are strategy-proof and satisfy a minimal range condition are dictatorial. In other words, there is an individual whose fuzzy preferences determine the entire fuzzy social ranking at every profile in the domain of the aggregation rule. To prove this theorem, we show that all fuzzy aggregation rules which are strategy-proof and satisfy the minimal range condition must also satisfy counterparts of independence of irrelevant alternatives and the Pareto criterion. There has been hardly any treatment of the manipulability problem in the literature on social choice with fuzzy preferences.     

Stochastic utility theorem

This paper analyzes individual decision making. It is assumed that an individual does not have a preference relation on the set of lotteries. Instead, the primitive of choice is a choice probability that captures the likelihood of one lottery being chosen over the other. Choice probabilities have a stochastic utility representation if they can be written as a non-decreasing function of the difference in expected utilities of the lotteries. Choice probabilities admit a stochastic utility representation if and only if they are complete, strongly transitive, continuous, independent of common consequences and interchangeable. Axioms of stochastic utility are consistent with systematic violations of betweenness and a common ratio effect but not with a common consequence effect. Special cases of stochastic utility include the Fechner model of random errors, Luce choice model and a tremble model of [Harless, D., Camerer, C., 1994. The predictive utility of generalized expected utility theories. Econometrica 62, 1251–1289].     

The Blocking Lemma for a many-to-one matching model

The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms’ preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.     

A theory of time preferences over risky outcomes

This paper provides two representation theorems for time preferences. They both cover as special cases a variety of time preference models considered in the experimental and theoretical literatures on intertemporal choice. In particular, similarity relations on time and outcomes, exponential, quasi-hyperbolic and hyperbolic discounting are special cases of the theorems. This approach identifies certain factors that are common to time preference structures which look so different.The paper builds on the recent work by Masatlioglu and Ok [Masatlioglu, Y., Ok, E., 2008. A theory of (relative) discounting. Journal of Economic Theory, in press] on Euclidean bundles and obtains similar representation theorems for the case of compact, separable and connected spaces of bundles. My work allows for the inclusion of the case in which bundles are lotteries.     

A utility representation theorem with weaker continuity condition

We prove that a mixture continuous preference relation has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but our condition on the continuity of a preference relation is strictly weaker than the usual continuity assumed by them.     

Stemmingen zonder winnaar

Summary A group of n persons has to decide on one out of k alternatives. To achieve this end each pair of alternatives is put to a vote. It is assumed that each person ranks the k alternatives according to an individual preference scale and that on every vote between two alternatives he will vote for the alternative that occurs higher on his scale. If n is odd and an alternative obtains a majority on each of the ( k - 1) occasions on which it is put to a vote, the group will decide on that alternative. If no such winning alternative exists, a paradox of voting is said to occur. For even values of n the definition of a paradox is slightly more complicated.
On the assumption that the preference scales of the n persons are obtained by n independent random drawings from the k ! permutations of the numbers 1, 2,…, k , we discuss the computation of the probability of a paradox of voting P _k,n. Values of P _3,n and P _k= lim P _k,n are given.     

Debreu-like properties of utility representations

Traditionally the codomain of a utility function is the set of real numbers. This choice has the advantage of ensuring the existence of a continuous representation but does not allow to represent many preference structures that are relevant to utility theory. Recently, some authors have started a systematic study of utility representations that are not real-valued, introducing the notion of a Debreu chain. We continue their analysis defining two Debreu-like properties, which are connected to a local continuity of a utility representation. The classes of locally Debreu and pointwise Debreu chains here introduced enlarge the class of Debreu chains. We give several examples and analyze some properties of these two classes of chains, with particular attention to lexicographic products.     

Shortlisting procedure with a limited capacity

A decision maker, who is overwhelmed by the number of available alternatives, limits her consideration. We investigate a model where a decision maker’s capacity determines whether she is overwhelmed: She considers all the available alternatives if their number does not exceed her capacity; otherwise, she applies a shortlisting procedure to reduce the number of alternatives to within her capacity. We show how to deduce the decision maker’s capacity, her preference and the alternatives that she considers from the observed behavior. Furthermore, we provide the necessary and sufficient conditions for a consideration function to be derived by the shortlisting procedure with a limited capacity.     

On rankings and top choices in random utility models with dependent utilities

Different aggregate preference orders based on rankings and top choices have been defined in the literature to describe preferences among items in a fixed set of alternatives. A useful tool in this framework is constituted by random utility models, where the utility of each alternative, or object, is represented by a random variable, indexed by the object, which, for example, can capture the variability of preferences over a population. Applications are derived in diverse research fields, including computer science, management science and reliability. Recently, some stochastic ordering conditions have been provided for comparing alternatives by means of some aggregate preference orders in the case of independent random utility variables by Joe (Math Soc Sci 43:391–404, 2002). In this paper we provide new conditions, based on some joint stochastic orderings, for aggregate preference orders among the alternatives in the case of dependent random utilities. We also provide some examples of application in different research fields.      

Breaking the curse of dimensionality in nonparametric testing

For tests based on nonparametric methods, power crucially depends on the dimension of the conditioning variables, and specifically decreases with this dimension. This is known as the “curse of dimensionality”. We propose a new general approach to nonparametric testing in high dimensional settings and we show how to implement it when testing for a parametric regression. The resulting test behaves against directional local alternatives almost as if the dimension of the regressors was one. It is also almost optimal against classes of one-dimensional alternatives for a suitable choice of the smoothing parameter. The test performs well in small samples compared to several other tests.     

Nash implementing social choice rules with restricted ranges

We consider Nash implementation of social choice rules with restricted ranges, i.e., where some of the available alternatives are chosen at no preference profile. We show that the appropriate adaptation of Maskin monotonicity to this context depends on the range of the mechanisms: the wider is this range, the weaker is the monotonicity condition to be used. As a result, mechanisms employing outcome functions which allow for out-of-range alternatives at off-equilibrium messages can Nash implement social choice rules which fail to be Nash implementable by mechanisms whose ranges are restricted to the range of the social choice rule to be implemented. The Walrasian social choice correspondence is a particular instance of this. Moreover, social choice rules which are not Maskin monotonic can be “monotonized” by the addition of artificial out-of-range alternatives—a point we illustrate through Solomon’s Dilemma.     

Revealed preference theory on the choice of lotteries

The choice behavior of a decision-maker is said to be consistent with expected utility maximization if there exists a utility function defined on the set of prizes such that the decision-maker chooses lotteries with the highest expected utility. We present a revealed preference characterization of choice behavior that is consistent with expected utility maximization. A necessary and sufficient condition for expected utility maximization is that there does not exist a way to compound lotteries such that the probability distribution over the final prizes generated by the chosen lotteries of each observation is equal to that generated by the rejected lotteries of each observation. Our result is quite general and can be applied to any compact set of prizes and any choice correspondence.     

Reduction-consistency in collective choice problems

We consider the problem of choosing a subset of a feasible set over which each agent has a strict preference. We propose an invariance property, reduction-consistency, of choice rules and study its implications. The property is a natural expression for the problems of a general principle of consistency having been studied extensively in resource allocation problems. We show that no scoring rule satisfies reduction-consistency, and base a characterization of the top rule on the property. We also investigate the minimal extension of a rule needed to recover reduction-consistency, and identify the minimal extensions of several rules including the Borda and plurality rules.     

Two versions of the tragedy of the commons

The commons are a one input-one output production process with increasing marginal cost. In the everage return game, each agent chooses his input contribution and total output is shared in proportion to individual contributions. In the average cost game, each agent chooses his output share and total input cost is shared in proportion to individual demands. The tragedy is that the non cooperative equilibrium results in inefficient overutilization of the technology. We prove formally the tragedy when individual preferences are convex and both goods are normal. This result has not been proved previously on such a general preference domain. We also show that overutilization is less severe in the average cost game than in the average return game.     

Random aggregation without the Pareto principle

Barberà-Sonnenschein (J Econ Theory 18:244–254, 1978) have shown that any binary and Paretian random social choice function can be associated with a mapping which associates a real number with each coalition of individuals. This function gives, for each coalition, the power that this group has in imposing on society, their common preference relation on a pair of alternatives. The aim of this paper is to extend this result, showing that the Pareto criterion is not a necessary condition for the existence of such a coalitional power function.     

Stratified network mapping decision making technique based decision support framework for R&D budget allocation in South Korea

In this research work, we proposed and developed a stratified network mapping (SNM) decision making method and used it to improve the industry–university specialization in R&D in each region selected in this study. The proposed method considers the influence of criteria on and their priority in alternatives performance evaluation process. By analyzing the influence of these criteria on decision-making, we can easily improve the performance of alternatives. The SNM gives a clear understanding of each alternatives performance efficiency level. It explores possible and inefficient states and high-level influence states in inefficient states. Narrowly using multi-criteria decision-making methods to rank alternatives does not improve the performance of alternatives. The proposed method helps rank alternatives and improve the performance level of alternatives in each state. We analyzed the R&D investment of central and local governments of South Korea. It is an attempt to invigorate and facilitate R&D collaboration using a decision support model. We analyzed industry–academia research networks and enhanced the efficiency of the research.     

A multiple criteria decision model for analyzing and choosing among different development patterns for the Helsinki cargo harbor

This paper describes a real application of a multicriteria approach to choosing among different options for developing the Helsinki harbor. In addition to the environmental impact assessment procedure, an analysis of the alternatives using the SMAA-method (Stochastic Multiobjective Acceptability Analysis) is carried out. The method applied here has been developed for situations in which the use of decision-makers’ preference information is not possible. Instead, the problem is described by typical weight vectors leading to each solution, taking into account the evident uncertainty embedded in the criteria values.