Construction of voting situations concordant with ranking patterns

Decisions in Economics and Finance - Referring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set...     

Condorcet meets Bentham

We show that if the statistical distribution of utility functions in a population satisfies a certain condition, then a Condorcet winner will not only exist, but will also maximize the utilitarian social welfare function. We also show that, if people’s utility functions are generated according to certain plausible random processes, then in a large population, this condition will be satisfied with very high probability. Thus, in a large population, the utilitarian outcome will be selected by any Condorcet consistent voting rule.     

Extension of a theorem of Smale on equilibria for pure exchange economies

The methods used by Smale in his paper Global Analysis and Economics IIa, seem to be heavily dependent on the hypothesis that utility functions have no critical points. In this paper we prove that the no critical point hypothesis can be dropped and the class of regular economies, for which the equilibria are locally continuous functions of the parameters of the economy, can be extended.     

Dismantling the south-west coalition: further evidence of distributive politics in preemption legislation

Economics of Governance - The factors influencing legislative voting behavior have often been studied. This is especially true regarding antebellum federal preemption legislation. Several...     

Strategic participation and the median voter result

In a seminal paper on electoral equilibrium under majority rule, Ledyard (1984) demonstrates that strategic participation by voters results in an electoral equilibrium at the proposal that maximizes the utility of a randomly selected voter. Palfrey and Rosenthal (1985) limit the usefulness of this result by showing that strategic participation rates are miniscule in large electorates, and that the incentive to participate vanishes completely as the electorate grows without bound. The most reasonable modification of Ledyard’s approach that circumvents these criticisms is to allow for a negative cost of voting. We show that when voters can have even an arbitrarily small negative cost of voting, there is an electorate sufficiently large so that any proposal is defeated or tied by the median proposal. This observation raises questions about the existence of electoral equilibrium under strategic participation, and is relevant to the efficiency of elections.     

Equilibrium theory with unbounded consumption sets and non-ordered preferences : Part I. Non-satiation

A new condition is introduced for the existence of equilibrium for an economy where preferences need not be transitive or complete and the consumption set of each agent need not be bounded from below. The new condition allows us to extend the literature in two ways. First, the result of the paper can cover the case where the utility set for individually rational allocations may not be compact. As illustrated in Page et al. [Page Jr., F.H., Wooders, M.H., Monteiro, P.K., 2000. Inconsequential arbitrage. Journal of Mathematical Economics 34, 439–469], the no arbitrage conditions do not apply to an economy with a non-compact utility set. Second, we generalize the arbitrage-based equilibrium theory to the case of non-transitive preferences.     

Pseudocontinuous functions and existence of Nash equilibria

In topological spaces, we introduce a new class of functions (pseudocontinuous functions) and we present some characterizations and properties. In particular, we show that any preference relation endowed of utility functions is continuous if and only if any utility is pseudocontinuous. A maximum theorem is proved for such a class of functions and connections with similar results are investigated. Finally, the existence of Nash equilibria for games with pseudocontinuous payoffs is obtained.     

On the performance of voting systems in spatial voting simulations

We study the performance of voting systems in terms of minimizing the overall social disutility of making a collective choice in an univariate voting space with ideological voting and perfect information. In order to obtain a distribution of the performance indicator for each of the 12 systems chosen for this study—Baldwin’s Method, Black’s Method, The Borda Count, Bucklin’s Grand Junction System, Coombs’ Method, Dodgson’s System, Instant Run-Off Voting, Plurality, Simpson’s MinMax, Tideman’s Ranked Pairs, Schulze’s Beatpath Method, and Two-Round Majority—we simulate elections using an Agent-Based Computational approach under several different distributions for voters and candidates positioning, with up to 15 available candidates. At each iteration, voters generate complete and strict ordinal utility functions over the set of available candidates, based on which each voting system computes a winner. We define the performance of a system in terms of its capability of choosing among the available candidates the one that minimizes aggregate voter disutility. As expected, the results show an overall dominance of Condorcet completion methods over the traditional and more widely used voting systems, regardless of the distributions of voter and candidate positions.     

An existence theorem of intertemporal recursive utility in the presence of Lévy jumps

This paper presents an existence theorem for a class of backward stochastic integral equations. The main contribution is a generalization of Duffie and Epstein's [Duffie, D., Epstein, L., 1992. Stochastic differential utility, (Appendix C with Skiadas C.), Econometrica 60, 353–394.] existence theorem of intertemporal recursive utility to allow the information structure to be driven by a Lévy jump process. The existence theorem applies also for a more general class of utility functions, such as recursive utility with habit-formation, and can be used to prove the existence of an equilibrium asset price process as a unique solution to the stochastic Euler equation derived by Ma [Ma, C., 1993b. Valuation of Derivative Securities with Mixed Poisson–Brownian Information and Recursive Utility, McGill University, mimeo.].     

Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces.     

Network potentials

A network payoff function assigns a utility to all participants within a social network. In this paper we investigate network payoff functions that admit an exact network potential or an ordinal network potential. We also investigate exact and ordinal potentials of Myerson’s non-cooperative network formation game based on consent in link formation. We show that the admittance of certain of these network and game-theoretic potentials implies the existence of pairwise stable networks and the convergence of network formation processes. Our main results extend and strengthen the current insights in the literature on game theoretic approaches to social network formation. We thank Matt Jackson and Sudipta Sarangi for extensive discussions on the subject of this paper. Part of this research was done while S. Chakrabarti was at Bonn on a post-doctoral research fellowship. We thank the Department of Economics at the University of Bonn for their hospitality and financial support. Part of this research was done at the Center for Economic Research at Tilburg University, Tilburg, the Netherlands. R. P. Gilles financially supported from the Netherlands Organization for Scientific Research (NWO), grant # 46-550, is gratefully acknowledged.     

Elections and strategic positioning games

We formalize the interplay between expected voting behavior and strategic positioning behavior of candidates as a common agency problem in which the candidates (i.e., the principals) compete for voters (i.e., agents) via the issues they choose and the positions they take. A political situation is defined as a feasible combination of candidate positions and expected political payoffs to the candidates. Taking this approach, we are led naturally to a particular formalization of the candidates' positioning game, called a political situation game. Within the context of this game, we define the notion of farsighted stability (introduced in an abstract setting by Chwe 1994) and apply Chwe's result to obtain existence of farsightedly stable outcomes. We compute the farsightedly stable sets for several examples of political situations games, with outcomes that conform to real-world observations.Received: 18 May 2001, Accepted: 22 January 2002, JEL Classification: C7, D7, D8Myrna H. Wooders: http://www.warwick.ac.uk/fac/soc/Economics/wooders/An earlier version of this paper was completed while the first author was visiting the Department of Economics, University of Exeter. The first author gratefully acknowledges Exeter's support and hospitality. Similarly, the second author gratefully acknowledges the support and hospitality of the Centre for Operations Research and Econometrics (CORE) of the University of Louvain-la-Neuve, Belgium and of the University of Cergy-Pontoise, France. Both authors are indebted to Amrita Dhillon, John Duggan and Gilat Levy for helpful comments about references. Both authors thank an anonymous referee for helpful comments.     

Continuous representation of Von Neumann–Morgenstern preferences

This paper considers a continuous representation of preference relations satisfying Grandmont's (1972) Expected Utility Hypothesis. We equip the preferences with the topology of closed convergence, then we show the existence of a jointly continuous expected utility function and consider its uniqueness. Furthermore, we construct an embedding map of the preferences into the set of expected utility functions.     

On the structure of voting systems between two alternatives

Voting systems between two alternatives have been widely studied in the literature of Social Choice. One of the results given by Fishburn (The theory of social choice. Princeton University Press, Princeton, 1973) allows us to characterize anonymous, neutral and monotonic voting systems by means of functions satisfying adequate conditions. From among all kinds of functions, the class of affine functions is highly interesting because from them it is possible to obtain the voting systems most used in practice. In this paper we analyze the structure of the set of these functions and we show that this set is convex and its extreme points are the functions that generate the following voting systems: simple majority, absolute majority, unanimous majority and Pareto majority. Moreover, we suggest a simple method for choosing a voting system when two alternatives are under consideration.     

Spatial majority voting equilibria and the provision of public goods

This paper develops general equilibrium conditions for urban areas where a pure public good is provided at a level decided upon by majority voting. Models with a property tax and a head tax and external land ownership are analyzed, and equilibrium solutions are compared using a specific form for the utility function. Optimal cities are characterized and compared to those emerging from the majority voting equilibria. Models where aggregate land rent is divided equally among the urban residents are also developed.     

Behavioral premium principles

Decisions in Economics and Finance - We define a premium principle under the continuous cumulative prospect theory which extends the equivalent utility principle. In prospect theory, risk attitude...     

Identification and stochastic specification in Rosen's hedonic price model

The use of an explicitly specified utility function to derive the inverse demand functions in S. Rosen's hedonic price model provides considerable insight into the correct stochastic specification of the model. It turns out that except in special cases, the inverse demand equations are nonlinear in parameters and cannot be formulated conveniently as regression models. Moreover, the inverse demand functions and the hedonic price function must be estimated simultaneously to obtain consistent estimates of the parameters of these functions. A tractable estimation technique is described. It is desirable to derive the inverse demand functions from a utility specification that is not a strongly separable function of houses' attributes since strong separability implies the existence of deterministic relations among incomes, prices, and observed housing attributes that may fail to hold in applications. Finally, it is shown that the use of an explicitly specified utility function does not guarantee identification of the parameters of Rosen's model.     

Portfolio choice in the model of expected utility with a safety-first component

Decisions in Economics and Finance - The standard problem of portfolio choice between one risky and one riskless asset is analyzed in the model of expected utility with a safety-first component...     

Cardinal versus ordinal criteria in choice under risk with disconnected utility ranges

This paper provides a formal justification for the existence of subjective random components intrinsic to the outcome evaluation process of decision makers and explicitly assumed in the stochastic choice literature. We introduce the concepts of admissible error function and generalized certainty equivalent, which allow us to analyze two different criteria, a cardinal and an ordinal one, when defining suitable approximations to expected utility values. Contrary to the standard literature requirements for irrational preferences, adjustment errors arise in a natural way within our setting, their existence following directly from the disconnectedness of the range of the utility functions. Conditions for the existence of minimal errors are also studied. Our results imply that neither the cardinal nor the ordinal criterion do necessarily provide the same evaluation for two or more different prospects with the same expected utility value. As a consequence, a rational decision maker may define two different generalized certainty equivalents when presented with the same prospect in two different occasions.     

Utility maximization in a stochastic affine interest rate and CIR risk premium framework: a BSDE approach

Decisions in Economics and Finance - This paper investigates optimal investment problems in the presence of stochastic interest rates and stochastic volatility under the expected utility...