Showing papers in "Social Choice and Welfare in 1989"

The computational difficulty of manipulating an election

Abstract: We show how computational complexity might protect the integrity of social choice. We exhibit a voting rule that efficiently computes winners but is computationally resistant to strategic manipulation. It is NP-complete for a manipulative voter to determine how to exploit knowledge of the preferences of others. In contrast, many standard voting schemes can be manipulated with only polynomial computational effort.

Voting schemes for which it can be difficult to tell who won the election

Abstract: We show that a voting scheme suggested by Lewis Carroll can be impractical in that it can be computationally prohibitive (specifically, NP-hard) to determine whether any particular candidate has won an election. We also suggest a class of “impracticality theorems” which say that any fair voting scheme must, in the worst-case, require excessive computation to determine a winner.

Moral intuitions and economic models of distributive justice

Abstract: We argue that formal theories of justice cannot neglect the moral intuitions existing in society and illustrate this claim with empirical results. We analyse the perception of justice in a production context by starting from the surplus sharing model. Our questionnaire method is closely related to the work of Yaari and Bar-Hillel [14]. Our results suggest that differences in effort are considered to be the main justification for income differences. Our respondents strongly disagree about the remuneration of innate capabilities. It is further suggested that surplus sharing and cost sharing models cannot be treated symmetrically, because people react differently towards gains and losses.

Game Forms for Nash Implementation of General Social Choice Correspondences

Abstract: Several game forms are given for Nash implementing general social choice correspondences (SCC's) which satisfy Maskin's conditions of monotonicity and No Veto Power. The game forms have smaller strategy spaces than those used in previously studied mechanisms: the strategy for an individual consists of an alternative, two subsets (of alternatives), and a player number. For certain types of economic and political SCC's, including α-majority rule, the Walrasian, and Lindahl correspondence, the strategy space reduces to an alternative and a vector, where the number of components of the vector is at most twice the dimension of the alternative space.

Complete independence of clones in the ranked pairs rule

Abstract: The “ranked pairs” voting rule introduced in Tideman [2] is independent of clones (not materially affected by the replication of a candidate) in all but a small domain of cases. Appending a particular tie-breaking rule to the ranked pairs rule generates a rule that is completely independent of clones.

Social choice theory in the case of von Neumann-Morgenstern utilities

Abstract: Part I of this paper offers a novel result in social choice theory by extending Harsanyi's well-known utilitarian theorem into a “multi-profile” context. Harsanyi was contented with showing that if the individuals' utilities ui are von Neumann-Morgenstern, and if the given utility u of the social planner is VNM as well, then the Pareto indifference rule implies that u is affine in terms of the ui. We provide a related conclusion by considering u as functionally dependent on the ui, through a suitably restricted “social welfare functional” (u1,...,un)→u=f(u1,...,un). We claim that this result is more in accordance with contemporary social choice theory than Harsanyi's “single-profile” theorem is. Besides, harsanyi's initial proof of the latter was faulty. Part II of this paper offers an alternative argument which is intended to be both general and simple enough, contrary to the recent proofs published by Fishburn and others. It finally investigates the affine independence problem on the ui discussed by Fishburn as a corollary to harsanyi's theorem.

Normative population theory.

Abstract: Utilitarian and contractarian solutions to the problem of optimal population are examined and shown to have unacceptable implications. As argued by Parfit, for instance, utilitarianism may imply large numbers of people at a very low standard of living. An analogy is drawn between optimal population for a society and the optimal structure of an individual life. The ideal life need not maximize cardinal utility, because an individual may prefer a shorter life with less, more intense utility to a very long life with higher total utility (“Methuselah's Paradox”). The optimal population is what an individual would prefer if he had to sequentially live out each life in his choice.

Public goods, growth, and welfare

Abstract: This paper examines the possibility of immiserizing growth in an economy with a private and a pure public good. Our analysis shows that increases in resource endowments and/or technical improvements affecting the public good will be welfare-improving when the two commodities are normal and a Nash equilibrium exists. When substitution effects are strong, immiserizing growth is likely to characterize technical advances in the private good production.

Robustness of optimal majority rules over teams with changing size

Abstract: This work investigates the robustness of optimal restricted majority rules under a changing size of a decision group. Robustness is an important property of decision rules, especially when cost of adjustment to a new rule is high. This is most likely to be the case when information about the competence of the members of the decision team is not costless. One of the useful findings of this study is that optimal restricted majority rules are robust over reductions of the decision team.

Sincere voting in models of legislative elections

Abstract: An assumption of sincere voting for one's most preferred candidate is frequently invoked in models of electoral competition in which the elected legislature consists of more than a single candidate or party. Voters, however, have preferences over policy outcomes--which are determined by the ex post elected legislature--and not over candidates per se. This observation provokes the following question. For what methods of translating election results into legislative policy outcomes is sincere voting rational in the legislative election? This paper provides the answer. One of the principal implications is that for sincerity to be rational, there necessarily exists a candidate for office whose electoral platform is the final legislative outcome, whether or not that candidate is elected to the legislature.

Wilson's theorem for economic environments and continuous social preferences

Abstract: Wilson's generalization of Arrow's impossibility theorem has been proved for the realm of private goods and economic preferences by Border and by Bordes and Le Breton. However, their proofs require the exclusion of the zero vector from the commodity space. This paper assumes continuity of social preference to obtain the impossibility theorem for the entire allocation space, even if the society is infinite. A simple corollary reveals that there is some individual who is assigned the zero consumption vector at every social optimum whenever the social welfare function is nonnull and nonimposed, and satisfies Arrow's independence axiom and continuity and transitivity of social preference.

The Structure of Neutral Monotonic Social Functions

Abstract: In this paper, we show that neutral monotonic social functions and their specializations to social decision functions, quasi-transitive social decision functions, and social welfare functions can be uniquely represented as a collection of overlapping simple games, each of which is defined on a nonempty set of concerned individuals. Moreover, each simple game satisfies certain intersection conditions depending on the number of social alternatives; the number of individuals belonging to the concerned set under consideration; and the collective rationaly assumption.

Arrow's theorem for economic environments and effective social preferences

Abstract: Arrow's impossibility theorem has been proved for the realm of private goods and economic preferences by Border and by Bordes and Le Breton. However, their proofs require the exclusion of the zero vector from the commodity space. This paper proves the impossibility theorem for the entire allocation space and the classical domain of economic preferences by adding effectiveness to Arrow's hypothesis. Social preference is effective if every nonempty compact set contains at least one socially optimal allocation.

Individual irrationality and social welfare

Abstract: Individual preferences inconsistent with personal welfare caused neither by ignorance nor by a positive consideration for the welfare of others are defined as (welfare) irrational. Sources of irrationality (rigid adherence to moral principles, excessive fear of danger, excessive tempetation of pleasure, revenge, inertia, ‘faulty telescopic faculty’, the fallacy of diminishing marginal utility of utility, etc.) are discussed. An evolutionary explanation of irrationality is suggested and some implications for individual decision and social policy indicated.

Fairness, the Veil of Ignorance and Social Choice

Abstract: A point of departure for this study is the recognition that various individuals may have different opinions about the exact form a social welfare function should have. To obtain some kind of amalgamation of differing individual social preferences, a modified version of the Rawlsian veil of ignorance is used and a definition of social efficiency suggested and analysed. A socially efficient state is defined by means of endogenous and individual veils of ignorance and, in addition, the Pareto principle. Efficiency may be described as a situation where individuals with similar social preferences constitute “subsocieties” in an optimal manner. Furthermore, a state is fair if it is (socially) efficient and “equitable”. An extension of the concept of fairness, called weak fairness, is also suggested. The analysis in this study does not presuppose any objective interpersonally comparable measure of utility.

Hurka's Gamble and Methuselah's Paradox: a response to Cowen on normative population theory

Abstract: The principle of total utility in population choice is seriously challenged by Hurka's Gamble and Methuselah's Paradox (and the associated Lewis-Cowen Theory). This paper defends the principle of total utility by attempting to resolve these apparent paradoxes by an opposite gamble and some other explanations.

Political geography and interest-group power

Abstract: The relationship between the distribution of an interest group's members (i.e., voters) across legislative districts and the group's ability to influence government policy is not well understood. We propose a simple model of interest groups and legislative decisionmaking to characterize this relationship formally, and analyze the model for the case of three competing interest groups. We find that an interest group's expected power is maximized when its members are evently divided across (m+1)/2 of the m districts, except when the group is somewhat small, in which case its expected power is maximized when it is evenly divided across all m districts. Expected power decreases sharply as a group's members become concentrated in fewer than (m+1)/2 districts.

Pressure Group Size and the Politics of Income Redistribution

Abstract: Numerous authors have argued that small groups with concentrated interests have an advantage over larger groups with more diffuse interests. We argue that the reverse situation is more likely. In addition, we extend the one candidate analysis to situations where there are two contestants for any one legislative seat.

A Quantitative Theory of Preferences" Some Results on Transition Functions*

Abstract: We investigate a general theory of combining individual preferences into collective choice. The preferences are treated quantitatively, by means of preference functions ϱ(a,b), where 0≦ϱ(a,b)≦∞ expresses the degree of preference of a to b. A transition function is a function Ω(x,y) which computes ϱ(a,c) from ϱ(a,b) and ϱ(b,c), namely ϱ(a,c)=Ω(ϱ(a,b),ϱ(b,c)). We prove that given certain (reasonable) conditions on how individual preferences are aggregated, there is only one transition function that satisfies these conditions, namely the function Ω(x,y)=x·y (“multiplication of odds”). We also formulate a property of transition functions called invariance, and prove that there is no invariant transition function; this “impossibility theorem” shows limitations of the quantitative method.

Core implementation via dynamic game forms

Abstract: Implementation of a social choice correspondence (SCC) involves finding a decentralized choice mechanism for which the solution is a manifestation of the SCC. We examine whether dynamic game forms with corelike solutions are feasible candidates for implementation. When the solution is the α-, β-, or “intermediate”-cores respectively, such feasibility is found to require a choice structure which embeds a sequential dictatorship, in turn implying the SCC has a partial dictator. Implementation via the strong equilibrium set is found feasible iff society consists of a single citizen. Tapering the range of “permissible” utility profiles to include only von Neumann-Morgenstern utilities does little to rectify these impossibility results. Effectivity functions are used as analytical tools and several new effectivity function concepts are introduced.

Equilibrium and efficiency with property rights and local consumption externalities

Abstract: There is no mechanism that guarantees existence and Pareto optimality of equilibrium in all situations if each individual has limited property rights and a utility function that depends upon his neighbour's consumption. This is true under virtually any assumption about coalition formation. Therefore, Sen's paradox of the Paretian liberal is confirmed in an economic exchange setting with limited externalitities, and Coase's conjecture on the efficiency of bargaining with complete information is denied.

Policies over time and pareto optimality

Abstract: This paper is concerned with sequences of policies that occur over time in voting models and planning procedures. The framework for our analysis includes assumptions that are satisfied by models in the corresponding literatures, together with other standard assumptions for microeconomic analysis that involve time. The starting point for our analyses is the prespective that results from combining the following (widely held) views: 1) certain voting models and planning procedures can be interpreted as being “non-tatonnement” or “sequential” processes (where each policy in the sequence that is generated is actually experienced by voters or consumers) and 2) an alternative being Pareto optimal in any given period (“temporal Pareto optimality”) is the appropriate efficiency criterion only if the alternative is the final outcome from a tatonnement process-and that, otherwise, one should examine the efficiency of the entire path (using “intertemporal Pareto optimality”). Our first observation about the planning literature is that is has (by and large) neglected the efficiency criterion that is appropriate for the discrete-time procedures that can be interpreted as “non-tatonnement” or “sequential” processes-and that, what's more, such trajectories will (in general) fail to meet this criterion. Our second observation identifies some results that can be used to establish that some of these trajectories will at least be “ultimately” intertemporally Pareto optimal. In our discussion of voting theory, we review Buchanan's opposition to requiring (social) choice consistency for voting procedures-and his argument for this position on (Pareto) efficiency grounds. We then consider voting procedures that can be interpreted as “non-tatonnement” or “sequential” processes and arrive at the conclusion that, in these cases, (i) majority rule cycles are intertemporally Pareto inefficient and (ii) achieving intertemporal Pareto optimality requires choice consistency. We then go on to show that related observations apply to Kramer's normative conclusions about his dynamical model of political equilibrium — and identify some further references where similar observations apply. In the final part of our discussion of voting models, we arrive at the further conclusion that, in the most relevant cases, a trajectory that stays in the temporal Pareto set is not necessarily more desirable (on efficiency grounds) than one that doesn't.

Convexity of integer veto and Elimination Procedures

Abstract: Elimination Procedures generated by marginal contribution in an integer veto function implement through sincere (respectively sincere and sophisticated) behavior the core correspondence of the veto function if the latter is convex (respectively additive). Moreover a partial converse of this result is proved. A characterization of a subclass of convex (respectively additive) veto functions is thus obtained.