Showing papers in "Social Choice and Welfare in 2007"

Cross-country determinants of life satisfaction: exploring different determinants across groups in society

Abstract: This paper explores a wide range of cross-country determinants of life satisfaction exploiting a database of 90,000 observations in 70 countries. We distinguish four groups of aggregate variables as potential determinants of satisfaction: political, economic, institutional, and human development and culture. We use ordered probit to investigate the importance of these variables on individual life satisfaction and test the robustness of our results with Extreme Bounds Analysis. The results show that only a small number of factors, such as openness, business climate, postcommunism, the number of chambers in parliament, Christian majority, and infant mortality robustly influence life satisfaction across countries while the importance of many variables suggested in the previous literature is not confirmed. This remains largely true when the analysis splits national populations according to gender, income and political orientation also.

Arrow's theorem in judgment aggregation

Abstract: In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using “systematicity” and “independence” conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model.

A generalised model of judgment aggregation

Abstract: The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements (“if P then Q ”) as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems can be represented in it. This includes decision problems expressed in languages of standard propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems.

Equality of Opportunity versus Equality of Opportunity Sets

Abstract: We characterize two different approaches to the idea of equality of opportunity. Roemer’s social ordering is motivated by a concern to compensate for the effects of certain (non-responsibility) factors on outcomes. Van de gaer’s social ordering is concerned with the equalization of the opportunity sets to which people have access. We show how different invariance axioms open the possibility to go beyond the simple additive specification implied by both rules. This offers scope for a broader interpretation of responsibility-sensitive egalitarianism.

Contests with group-specific public-good prizes

Abstract: We examine the equilibrium effort levels of individual players and groups in contests in which n groups compete to win a group-specific public-good prize, the individual players choose their effort levels simultaneously and independently, and the probability of winning for each group depends on the groups’ effort levels. In the basic model, we show that, in each group, only the highest-valuation players expend positive effort and the rest expend zero effort; there is underinvestment in the contest for the group as a whole. Next, in the main model in which the players are budget-constrained, we show that low-valuation players free ride on high-valuation players’ contributions, not vice versa, but the free-rider problem is “alleviated” as compared with the basic model.

The Consensus Value : A New Solution Concept for Cooperative Games

Abstract: To generalize the standard solution for 2-person TU games into n-person cases, this paper introduces a recursive two-sided negotiation process to establish cooperation between all players. This leads to a new solution concept for cooperative games: the consensus value. An explicit comparison with the Shapley value is provided, also at the axiomatic level. Moreover, a class of possible generalizations of the consensus value is introduced and axiomatized with the Shapley value at one end and the equal surplus solution at the other. Finally, we discuss a non-cooperative mechanism which implements the consensus value.

The limits of epistemic democracy

Abstract: The so-called doctrinal paradox reveals that a jury that decides by majority on the truth of a set of propositions, may come to a conclusion that is at odds with a legal doctrine to which they all subscribe. The doctrinal paradox, and its subsequent generalization by List and Pettit (Econ Philos 18:89–110, 2002), reveal the logical difficulties of epistemic democracy. This paper presents several generalizations of the paradox that are formulated with the use of many-valued logic. The results show that allowing the individual or the collective judgements to be formulated in terms of degrees of beliefs does not ensure the possibility of collective epistemic decision making.

Exact results on manipulability of positional voting rules

Abstract: We consider 3-candidate elections under a general scoring rule and derive precise conditions for a given voting situation to be strategically manipulable by a given coalition of voters. We present an algorithm that makes use of these conditions to compute the minimum size M of a manipulating coalition for a given voting situation. The algorithm works for any voter preference model — here we present numerical results for IC and for IAC, for a selection of scoring rules, and for numbers of voters up to 150. A full description of the distribution of M is obtained, generalizing all previous work on the topic. The results obtained show interesting phenomena and suggest several conjectures. In particular we see that rules “between plurality and Borda” behave very differently from those “between Borda and antiplurality”.

Monotonicity in Condorcet’s Jury Theorem with dependent voters

Abstract: Condorcet’s Jury Theorem (CJT) provides a theoretical basis of public choice theory and political science. This paper provides an extension of CJT for random subcommittees consisting of dependent heterogeneous experts. Necessary and sufficient conditions for beneficial augmentation (reduction) of the size of a random subcommittee are provided. These results are applied in several dependency models.

Equal representation in two-tier voting systems

Abstract: The paper investigates how voting weights should be assigned to differently sized constituencies of an assembly. The one-person, one-vote principle is interpreted as calling for a priori equal indirect influence on decisions. The latter are elements of a one-dimensional convex policy space and may result from strategic behavior consistent with the median voter theorem. Numerous artificial constituency configurations, the EU and the US are investigated by Monte-Carlo simulations. Penrose’s square root rule, which originally applies to preference-free dichotomous decision environments and holds only under very specific conditions, comes close to ensuring equal representation. It is thus more robust than previously suggested.

Social choice and the indexing dilemma

Abstract: This paper distinguishes an index ordering and a social ordering function as a simple way to formalize the indexing problem in the social choice framework. Two main conclusions are derived. First, the alleged dilemma between welfarism and perfectionism is shown to involve a third possibility, exemplified by the fairness approach to social choice. Second, the idea that an individual is better off than another whenever he has more (goods, functionings, etc.) in all dimensions, which is known to enter in conflict with the Pareto principle, can be partly salvaged by adopting the fairness approach.

The value of opportunities over time when preferences are unstable

Abstract: Most work on measuring opportunity is directed at ranking opportunity sets. This paper addresses the more general issue of assessing the opportunity provided by multi-period decision problems, focusing on the dynamic inconsistencies that can occur if agent’s preferences are unstable. A principle is proposed by which a dominance relation among outcomes iteratively induces a dominance relation among multi-period problems. This principle implies that opportunities to make sequences of individually reasonable actions have positive value, even if, because of dynamic inconsistency, those sequences lead to unambiguous loss. Opportunities which allow an agent to constrain herself are shown to have zero value.

Enlargement and the balance of power: an experimental study

Abstract: Theoretical analysis suggests that enlargement of a voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the existing voters may actually gain, a phenomenon known as the paradox of new members. We test for this effect using laboratory experiments. Participants propose and vote on how to divide a budget according to weighted majority voting rules, and we measure the voting power of a player by his average payoff in the experiment. By comparing voting power across voting bodies of varying size, we find empirical support for the paradox of new members.

‘One and a Half Dimensional’ Preferences and Majority Rule

Abstract: I examine a model of majority rule in which alternatives are described by two characteristics: (1) their position in a standard, left-right dimension, and (2) their position in a good-bad dimension, over which voters have identical preferences. I show that when voters’ preferences are single-peaked and concave over the first dimension, majority rule is transitive, and the majority’s preferences are identical to the median voter’s. Thus, Black’s (The theory of committees and elections, 1958) theorem extends to such a “one and a half” dimensional framework. Meanwhile, another well-known result of majority rule, Downs’ (An economic theory of democracy, 1957) electoral competition model, does not extend to the framework. The condition that preferences can be represented in a one-and-a-half-dimensional framework is strictly weaker than the condition that preferences be single-peaked and symmetric. The condition is strictly stronger than the condition that preferences be order-restricted, as defined by Rothstein (Soc Choice Welf 7:331–342;1990).

Welfarist evaluations of decision rules for boards of representatives

Abstract: We consider a decision board with representatives who vote on proposals on behalf of their constituencies. We look for decision rules that realize utilitarian and (welfarist) egalitarian ideals. We set up a simple model and obtain roughly the following results. If the interests of people from the same constituency are uncorrelated, then a weighted rule with square root weights does best in terms of both ideals. If there are perfect correlations, then the utilitarian ideal requires proportional weights, whereas the egalitarian ideal requires equal weights. We investigate correlations that are in between these extremes and provide analytic arguments to connect our results to Barbera and Jackson (J Polit Econ 114(2):317–339, 2006) and to Banzhaf voting power.

Coercion, Contract and the Limits of the Market

Abstract: It is a widely accepted principle of economics that if two or more adults voluntarily agree to a contract or an exchange that has no negative fall-out on others, then the government should not stop such a contract. This is often called the ‘principle of free contract’ (PFC). There is a body of writing in economics which upholds the PFC. Yet this ubiquitous principle is ill-defined and full of ambiguities. For instance, since it refers to voluntary choice, its proper use presumes an understanding of what is ‘voluntary’ and, therefore, also, of what is coercive. What is ironic is that, while philosophers and legal scholars have debated and analyzed these concepts and the validity of the principle of free contract, there is very little discussion of these in economics, even though so much of economics is founded on this principle. This has caused a lot of policy confusion. The aim of this paper is to construct general rules for when we may violate the PFC. The argument is constructed within the Paretian framework. Hence, the violation of the PFC is not justified by appeal to deontological ethics or non-welfarist criteria. This is not an easy task since the principle of free contract is often viewed as a rule that is a derivative of the Pareto principle.

Generic difference of expected vote share and probability of victory maximization in simple plurality elections with probabilistic voters

Abstract: In this paper I examine single member, simple plurality elections with n ≥ 3 probabilistic voters and show that the maximization of expected vote share and maximization of probability of victory are “generically different” in a specific sense. More specifically, I first describe finite shyness (Anderson and Zame in Adv Theor Econ 1:1–62, 2000), a notion of genericity for infinite dimensional spaces. Using this notion, I show that, for any policy \(x^{*}\) in the interior of the policy space and any candidate j, the set of n-dimensional profiles of twice continuously differentiable probabilistic voting functions for which \(x^{*}\) simultaneously satisfies the first and second order conditions for maximization of j’s probability of victory and j’s expected vote share at \(x^{*}\) is finitely shy with respect to the set of n-dimensional profiles of twice continuously differentiable probabilistic voting functions for which \(x^{*}\) satisfies the first and second order conditions for maximization of j’s expected vote share.

Psychology Implies Paternalism? Bounded Rationality may Reduce the Rationale to Regulate Risk-Taking

Abstract: Behavioral economists increasingly argue that violations of rationality axioms provide a new rationale for paternalism – to “de-bias” individuals who exhibit errors, biases and other allegedly pathological psychological regularities associated with Tversky and Kahneman’s (in Science 185:1124–1131, 1974) heuristics-and-biases program. The argument is flawed, however, in neglecting to distinguish aggregate from individual rationality. The aggregate consequences of departures from normative decision-making axioms may be Pareto-inferior or superior. Without a well-specified theory of aggregation, individual-level biases do not necessarily imply losses in efficiency. This paper considers the problem of using a social-welfare function to decide whether to regulate risk-taking behavior in a population whose individual-level behavior may or may not be consistent with expected utility maximization. According to the social-welfare objective, unregulated aggregate risk distributions resulting from non-maximizing behavior are often more acceptable (i.e., lead to a weaker rationale for paternalism) than population distributions generated by behavior that conforms to the standard axioms. Thus, psychological theories that depart from axiomatic decision-making norms do not necessarily strengthen the case for paternalism, and conformity with such norms is generally not an appropriate policy-making objective in itself.

Bargaining over a finite set of alternatives

Abstract: We analyze bilateral bargaining over a finite set of alternatives. We look for "good" ordinal solutions to such problems and show that Unanimity Compromise and Rational Compromise are the only bargaining rules that sat- isfy a basic set of properties. We then extend our analysis to admit problems with countably infinite alternatives. We show that, on this class, no bargain- ing rule choosing finite subsets of alternatives can be neutral. When rephrased in the utility framework of Nash (1950), this implies that there is no ordinal bargaining rule that is finite-valued.

Lorenz Dominance and Non-welfaristic Redistribution

Abstract: Our concern is for income inequalities that may result from non-welfaristic redistribution schemes. We show that for large classes of income functions Lorenz dominance results can be found in the comparison of two egalitarian equivalent mechanisms. Comparisons of different conditionally egalitarian mechanisms only yield poverty dominance results. In general, no egalitarian equivalent mechanism can be Lorenz dominated by a conditionally egalitarian mechanism. Our analysis stresses the need for accurate empirical estimates of the pre-tax income function and of the distributions of responsibility and compensation characteristics.

First and second best voting rules in committees

Abstract: A committee of people with common preferences but different abilities in identifying the best alternative (e.g., a jury) votes in order to decide between two alternatives. The first best voting rule is a weighted voting rule that takes the different individual competences into account, and is therefore not anonymous, i.e., the voters’ identities matter. Under this rule, it is rational for the committee members to vote according to their true opinions, or informatively. This is not necessarily true for an anonymous voting rule, under which members may have an incentive to vote non-informatively. Thus, strategic, sophisticated voters may vary their voting strategies according to the voting rule rather than naively voting informatively. This paper shows that the identity of the best anonymous and monotone (i.e., quota) voting rule does not depend on whether the committee members are strategic or naive or whether some are strategic and some are naive. One such rule, called the second best rule, affords the highest expected utility in all cases. “Wasn’t he sweet?” said Yossarian. “Maybe they should give him three votes.” Joseph Heller,

On the voting power of an alliance and the subsequent power of its members

Abstract: Even, and in fact chiefly, if two or more players in a voting game have on a binary issue independent opinions, they may have interest to form a single voting alliance giving an average gain of influence for all of them. Here, assuming the usual independence of votes, we first study the alliance voting power and obtain new results in the so-called asymptotic limit for which the number of players is large enough and the alliance weight remains a small fraction of the total of the weights. Then, we propose to replace the voting game inside the alliance by a random game which allows new possibilities. The validity of the asymptotic limit and the possibility of new alliances are examined by considering the decision process in the Council of Ministers of the European Union.

Cost sharing in a job scheduling problem

Abstract: A set of jobs need to be served by a server which can serve only one job at a time. Every job has a processing time and incurs cost due to waiting (linear in its waiting time). The jobs share their costs using monetary transfers. We provide an axiomatic characterization of the Shapley value solution for this problem.

Reaching a consensus

Abstract: This paper explores some aspects of the relation between aggregation and deliberation as ways of achieving a consensus amongst a group of indviduals on some set of issues. I argue firstly that the framing of an aggregation problem itself generates information about the judgements of others that individuals are rationally obliged to take into account. And secondly that the constraints which aggregation theories typically place on consensual or collective judgements need not be consistent with the outcomes of rational deliberative processes driven by individuals’ attempts to update on this information. The paper focuses on the particular case of allocation problems, for which there are established results both in aggregation theory and deliberation theory, to make this claim.

An axiomatization of the Nash bargaining solution

Abstract: I prove that ‘Disagreement Point Convexity’ and ‘Midpoint Domination’ characterize the Nash bargaining solution on the class of two-player bargaining problems and on the class of smooth bargaining problems. I propose an example to show that these two axioms do not characterize the Nash bargaining solution on the class of bargaining problems with more than two players. I prove that the other solutions that satisfy these two properties are not lower hemi-continuous. These different results refine the analysis of Chun (Econ Lett 34:311–316, 1990). I also highlight a rather unexpected link with the result of Dagan et al. (Soc Choice Welfare 19:811–823, 2002).

Intersecting Lorenz Curves, the Degree of Downside Inequality Aversion, and Tax Reforms

Abstract: This paper clarifies the conceptual distinction of downside inequality aversion (or transfer sensitivity) as a normative criterion for judging income distributions from the Pigou-Dalton principle of transfers. We show that when the Lorenz curves of two income distributions intersect, how the change from one distribution to the other is judged by an inequality index exhibiting downside inequality aversion often depends on the relative strengths of its downside inequality aversion and inequality aversion. For additive inequality indices or their monotonic transformations, a measure characterizing the strength of an index’s downside inequality aversion against its inequality aversion is shown to determine the ranking by the index of two distributions whose Lorenz curves cross once. The precise condition under which the same result generalizes to the case of multiple-crossing Lorenz curves is also identified. The results are particularly useful in understanding the distributional impact of tax reforms.

Citizen candidates under uncertainty

Abstract: In this paper I add uncertainty about the total vote count to a “citizen candidate” model of representative democracy I show that in a society with a large electorate, where the outcome of the election is uncertain and where winning candidates receive a large reward from holding office, there will be a two-candidate equilibrium and no equilibria with a single candidate

A systematic approach to the construction of non-empty choice sets

Abstract: Suppose a strict preference relation fails to possess maximal elements, so that a choice is not clearly defined. I propose to delete particular instances of strict preferences until the resulting relation satisfies one of a number of known regularity properties (transitivity, acyclicity, or negative transitivity), and to unify the choices generated by different orders of deletion. Removal of strict preferences until the subrelation is transitive yields a new solution with close connections to the “uncovered set” from the political science literature and the literature on tournaments. Weakening transitivity to acyclicity yields a new solution nested between the strong and weak top cycle sets. When the original preference relation admits no indifferences, this solution coincides with the familiar top cycle set. The set of alternatives generated by the restriction of negative transitivity is equivalent to the weak top cycle set.

Condorcet Cycles? A Model of Intertemporal Voting*

Abstract: An intertemporal voting model is examined where, at each date, there is a pairwise majority vote between the existing chosen state and some other state, chosen randomly. Intertemporal voting simpli…es the strategic issues and the agenda setting is as unrestricted as possible. The possibility of cycles is examined, both in the intertemporal extension to the Condorcet paradox and in more general examples. The set of possibilities is rich, as is demonstrated by an exhaustive study of a three person, three state world. Equilibrium in pure strategies may fail to exist but a weakening of the equilibrium concept to admit probabilistic voting allows a general existence result to be proved. The analysis leads to the development of a dominant state which extends the notion of a Condorcet winner.

Political election on legal retirement age

Abstract: In the context of the current debate surrounding the reform of pension systems, this paper analyzes the political economy of the legal retirement age. Using a life-cycle model in which individuals differ by age and by wage, we analyze the outcome of a majority voting process on the legal retirement age in a Pay-As-You-Go pension system. The results show that the older an individual is, the closer her optimal retirement age is to the status quo age. That is, the status quo retirement age acts as a magnet. Additionally, we find that the preferred legal retirement age of most of the working population increases when the pension system is more redistributive. We also observe a positive relationship between the preferred legal retirement age and the status quo age.