Showing papers in "Social Choice and Welfare in 2019"

Dividing bads under additive utilities

Abstract: We compare the Egalitarian rule (aka Egalitarian Equivalent) and the Competitive rule (aka Comeptitive Equilibrium with Equal Incomes) to divide bads (chores). They are both welfarist: the competitive disutility profile(s) are the critical points of their Nash product on the set of efficient feasible profiles. The C rule is Envy Free, Maskin Monotonic, and has better incentives properties than the E rule. But, unlike the E rule, it can be wildly multivalued, admits no selection continuous in the utility and endowment parameters, and is harder to compute. Thus in the division of bads, unlike that of goods, no rule normatively dominates the other.

Upward and downward bias when measuring inequality of opportunity

Abstract: We show that, when measuring inequality of opportunity with survey data, scholars face two types of biases. A well-known downward-bias, due to partial observability of cir- cumstances that affect individual outcome, and an upward bias, which is the consequence of sampling variance. The magnitude of the latter distortion depends on both the empirical strategy used and the observed sample. We suggest that, although usually neglected in em- pirical contributions, the upward bias may be significant. We propose a simple criterion to select the best specification which balances between the two sources of bias. Our method is based on cross validation and can be easily implemented to survey data. In order to show how this method can improve our understanding of the inequality of opportunity measure- ment, we provide an empirical illustration based on income data of 26 European countries. Our evidence shows that estimates of inequality of opportunity are extremely sensitive to model selection. Alternative specifications lead to significant differences in the absolute level of inequality of opportunity and to a number of substantial countries’ re-ranking. This in turn clarifies the need of an objective criterion to select the best econometric model when measuring inequality of opportunity.

Ranking objects from a preference relation over their subsets

Abstract: In many everyday situations, we need to rank individuals or single items having the possibility to observe the behavior of groups. In this paper we propose a way to get this ranking over the elements of a set X, starting from an arbitrary preference relation over the subsets of X and taking into account the information provided by this ranking over the subsets. To this purpose, we use a very common approach in the social choice framework: we single out some properties that a general solution should satisfy, and we prove that these properties characterize a unique solution. Given the generality of the approach, we believe that this paper is only a starting point for a more extended analysis. In particular, it is clear that different contexts can suggest other properties, thus identifying alternative ranking methods.

An axiomatic characterization of the Borda mean rule

Abstract: A social dichotomy function maps a collection of weak orders to a set of dichotomous weak orders. Every dichotomous weak order partitions the set of alternatives into approved alternatives and disapproved alternatives. The Borda mean rule returns all dichotomous weak orders that approve all alternatives with above-average Borda score and disapprove alternatives with below-average Borda score. We show that the Borda mean rule is the unique social dichotomy function satisfying neutrality, reinforcement, faithfulness, and the quasi-Condorcet property. Our result holds for all domains of weak orders that are sufficiently rich, including the domain of all linear orders and the domain of all weak orders.

The weighted-egalitarian Shapley values

Abstract: We propose a new class of allocation rules for cooperative games with transferable utility (TU-games), weighted-egalitarian Shapley values, where each rule in this class takes into account each player’s contributions and heterogeneity among players to determine each player’s allocation. We provide an axiomatic foundation for the rules with a given weight profile (i.e., exogenous weights) and the class of rules (i.e., endogenous weights). The axiomatization results illustrate the differences among our class of rules, the Shapley value, the egalitarian Shapley values, and the weighted Shapley values.

Random matching under priorities: stability and no envy concepts

Abstract: We consider stability concepts for random matchings where agents have preferences over objects and objects have priorities for the agents. When matchings are deterministic, the standard stability concept also captures the fairness property of no (justified) envy. When matchings can be random, there are a number of natural stability and fairness concepts that coincide with stability and no envy whenever matchings are deterministic. We formalize known stability concepts for random matchings for a general setting that allows weak preferences and weak priorities, unacceptability, and an unequal number of agents and objects. We then present a clear taxonomy of the stability concepts and identify logical relations between them. Finally, we present a transformation from the most general setting to the most restricted setting, and show how almost all our stability concepts are preserved by that transformation.

Welfare egalitarianism with other-regarding preferences

Abstract: We consider the problem of dividing a perfectly divisible good among individuals who have other-regarding preferences. Assuming no legitimate claims and purely ordinal preferences, how should society measure social welfare so as to satisfy basic principles of efficiency and fairness? In a simple model of average externalities, we characterize the class of social preferences which give full priority to the individual with the lowest egalitarian equivalent.

Relative utilitarianism under uncertainty

Abstract: In the context of uncertainty, belief-weighted relative utilitarianism consists in comparing acts according to a weighted sum of the (0, 1) -normalized subjective expected utilities they yield. The weights may change with the profile of beliefs but do not depend upon the profile of individual utilities for the outcomes. This class of social welfare functions is characterized by the Pareto principle, the sure-thing principle, a continuity condition, and an independence condition requiring that the social ranking of two acts is unaffected by the addition of an outcome that leaves everyone’s best and worst outcomes unchanged. The weights must be constant if the social ranking of constant acts is independent of individual beliefs. Anonymity then pins down plain relative utilitarianism: acts are compared according the sum of (0, 1)-normalized subjective expected utilities they generate.

Civic capital and support for the welfare state

Abstract: We model how the interplay between tax surveillance institutions and civic capital shapes taxpayers' support for welfare state. We show that, when tax surveillance is tight, rational civic-minded individuals express greater support for welfare spending than uncivic ones. We provide empirical evidence of these preferences using data from Italy, a country that has long posed a puzzle for public economists for its limited civic capital and large welfare state.

Inequality measurement with an ordinal and continuous variable

Abstract: What would be the analogue of the Lorenz quasi-ordering when the variable of interest is continuous and of a purely ordinal nature? We argue that it is possible to derive such a criterion by substituting for the Pigou-Dalton transfer used in the standard inequality literature what we refer to as a Hammond progressive transfer. According to this criterion, one distribution of utilities is considered to be less unequal than another if it is judged better by both the lexicographic extensions of the maximin and the minimax, henceforth referred to as the leximin and the antileximax, respectively. If one imposes in addition that an increase in someone’s utility makes the society better off, then one is left with the leximin, while the requirement that society welfare increases as the result of a decrease of one person’s utility gives the antileximax criterion. Incidentally, the paper provides an alternative and simple characterisation of the leximin principle widely used in the social choice and welfare literature.

Dilemma with approval and disapproval votes

Abstract: This paper looks at the issue of selecting candidates when the votes cast in ballots enable voters to approve or disapprove each candidate. More precisely, three options are offered: voters can approve, disapprove or remain neutral in regard to each candidate. We define a large family of rules that satisfy desirable properties and prove that solving a dilemma is sufficient to characterize any rule which belongs to this family. In this context a dilemma appears when candidates with only neutral votes face candidates with both supporters and opponents. On the basis of this result, we provide comparable axiomatizations of four rules including some proposed in the literature.

The measurement of welfare change

Abstract: We propose a class of measures of welfare change that are based on the generalized Gini social welfare functions. We analyze these measures in the context of a second-order dominance property that is akin to generalized Lorenz dominance as introduced by Shorrocks (Economica 50:3–17, 1983) and Kakwani (Advances in econometrics, vol 3. JAI Press, Greenwich, pp 191–213, 1984). Because we consider welfare differences rather than welfare levels, the requisite equivalence result involves affine welfare functions only, as opposed to the entire class of strictly increasing and strictly S-concave welfare indicators. Thus, our measures are associated with those members of the generalized-Gini class that are strictly increasing and strictly S-concave. Moving from second-order dominance to first-order dominance does not change this result significantly: for most intents and purposes, the generalized Ginis remain the only strictly increasing and strictly S-concave measures that are equivalent to this first-order dominance condition phrased in terms of welfare change. Our final result provides a characterization of our measures of welfare change in the spirit of Weymark’s (Math Soc Sci 1:409–430, 1981) original axiomatization of the generalized Gini welfare functions. Journal of Economic Literature Classification No.: D31.

Inequity aversion, welfare measurement and the Gini index

Abstract: Integrating individual inequity aversion (Fehr and Schmidt in Q J Econ 114:817–868, 1999) into a utilitarian social welfare function, we derive a simple welfare measure which comprises both GDP and income inequality as measured by the Gini-index.

Fair cake-cutting among families

Abstract: We study the fair division of a continuous resource, such as a land-estate or a time-interval, among pre-specified groups of agents, such as families. Each family is given a piece of the resource and this piece is used simultaneously by all family members, while different members may have different value functions. Three ways to assess the fairness of such a division are examined. (a) Average Fairness means that each family’s share is fair according to the “family value function”, defined as the arithmetic mean of the value functions of the family members. (b) Unanimous Fairness means that all members in all families feel that their family’s share is fair according to their personal value function. (c) Democratic Fairness means that in each family, at least a fixed fraction (e.g. a half) of the members feel that their family’s share is fair. We compare these criteria based on the number of connected components in the resulting division and on their compatibility with Pareto-efficiency.

Constitutionally consistent voting rules over single-peaked domains

Abstract: Constitutional consistency requires that the voting rule produce the same outcome at any vote profile as the one it produces at its induced vote profile for any given set of voting rules (or constitution) consisting of the voting rule itself. We consider this type of consistency in two voting models with single-peaked preferences, one with a finite set of alternatives and the other, when the set of alternatives is the interval [0, 1]. We show that cumulative-threshold rules are the only unanimous, anonymous and constitutionally consistent voting rules. These rules assign monotone decreasing (increasing) thresholds to each alternative and pick the minimum (maximum) alternative from the range of the vote profile that receives more cumulative votes (votes received by all the alternatives smaller (or greater) than itself) than the threshold assigned to it. This class of rules consists of the min, max and median rules. The addition of continuity leads to the characterization of k-median rules in the interval voting model.

Strategy-proof aggregation rules and single peakedness in bounded distributive lattices

Abstract: It is shown that, under a very comprehensive notion of single peakedness, an aggregation rule on a bounded distributive lattice is strategy-proof on any rich domain of single peaked total preorders if and only if it admits one of three distinct and mutually equivalent representations by lattice-polynomials, namely whenever it can be represented as a generalized weak consensus rule, a generalized weak sponsorship rule , or an iterated medianrule. The equivalence of individual and coalitional strategy-proofness that is known to hold for single peaked domains in bounded linearly ordered sets and in finite trees typically fails in such an extended setting. A related impossibility result concerning non-trivial anonymous and coalitionally strategy-proof aggregation rules is also obtained.

Relationally equal treatment of equals and affine combinations of values for TU games

Abstract: We axiomatize the set of affine combinations between the Shapley value, the equal surplus division value, and the equal division value in cooperative games with transferable utilities. The set is characterized by efficiency, linearity, the balanced contributions property for equal contributors and outsiders, and the differential null player out property. The balanced contributions property for equal contributors and outsiders requires the balance of contributions between two players who contribute the same amount to the grand coalition and whose singleton coalitions earn the same worth. The differential null player out property requires that an elimination of a null player affects the other players identically. These two relational axioms are obtained by investigating Myerson’s (Int J Game Theory 9:169–182, 1980) balanced contributions property and Derks and Haller’s (Int Game Theory Rev 1:301–314, 1999) null player out property, respectively, from the perspective of a principle of Aristotle’s distributive justice, whereby “equals should be treated equally”.

Strategyproof judgment aggregation under partial information

Abstract: We introduce a model of judgment aggregation in which individuals do not necessarily have full information regarding the judgments held by their peers. This intuitively limits an individual’s ability to strategically manipulate the aggregation process. Our results confirm this basic intuition. Specifically, we show that known impossibility results concerning the existence of reasonable strategyproof judgment aggregation rules break down once we abandon the classical assumption of full information. For instance, the simple plurality rule is strategyproof in case individuals do not have any information about their peers, while the well-known premise-based rule can be rendered strategyproof by withholding only a negligible amount of information.

How Should Payment Services be Taxed

Abstract: This paper considers the design of taxes on real money balances and bank payment services, when realistically, the household can use either cash or a bank payment account for the purchase of different varieties of goods. These taxes, plus a consumption tax, fund a government revenue requirement. We find that generally, real money balances and bank transaction fees should be taxed, and at different rates, i.e. the tax system should not leave the choice of payment services undistorted. For a wide class of time transactions cost technologies, including the Baumol-Tobin case, fees should be taxed at a lower rate than real money balances, and the tax on real money balances should be positive. However, it is possible that fees should be subsidized. The rate of tax on fees has no simple relationship to the optimal consumption tax, and can be higher or lower. A Corlett-Hague type intuition for these results is also developed, which relies on the concept of a virtual time endowment.

Money or morality: fairness ideals in unstructured bargaining

Abstract: We augment the Nash bargaining solution by fairness ideals in order to predict the outcomes of unstructured bargaining after the individual production of a joint surplus. If production depends on individual effort, talent, and luck, fairness ideals might be based on the accountability principle. In a lab experiment with real production and unstructured bargaining, we investigate subjects’ fairness ideals, their bargaining behaviour, and the outcomes of the bargaining process. As impartial spectators, about 75% of the subjects hold meritocratic or libertarian fairness ideals. However, these ideals do not affect their bargaining behaviour which is strongly opportunistic. Therefore the fairness-augmented Nash solution with opportunistic fairness ideals predicts the bargaining outcome best.

The space of all proportional voting systems and the most majoritarian among them

Abstract: We present an alternative voting system that aims at bridging the gap between proportional representative systems and majoritarian electoral systems. The system lets people vote for multiple party-lists, but then assigns each ballot paper to a single party. This opens a whole range of possible parliaments, all proportionally representative. We show theoretically that this space is convex. Then among the possible parliaments we present an algorithm to produce the most majoritarian result. We then test the system and compare the results with a pure proportional and a majoritarian voting system showing how the results are comparable with the majoritarian system. Then we simulate the system and show how it tends to produce parties of exponentially decreasing size with always a first, major party with about half of the seats. Finally we describe how the system can be used in the context of a parliament made up of two separate houses.

Egalitarianism, utilitarianism, and the Nash bargaining solution

Abstract: A bargaining solution satisfies egalitarian–utilitarian monotonicity (EUM) if the following holds under feasible-set-expansion: a decrease in the value of the Rawlsian (resp. utilitarian) objective is accompanied by an increase in the value of the utilitarian (resp. Rawlsian) objective. A bargaining solution is welfarist if it maximizes a symmetric and strictly concave social welfare function. Every 2-person welfarist solution satisfies EUM, but for $$n\ge 3$$ every n-person welfarist solution violates it. In the presence of other standard axioms, EUM characterizes the Nash solution in the 2-person case, but leads to impossibility in the n-person case.

Implementation without expected utility: ex-post verifiability

Abstract: This study investigates implementation of a social choice function with complete information, where we impose various restrictions such as boundedness, permission of only small transfers, and uniqueness of iterative dominance in strict terms. We assume that the state is ex-post verifiable after the determination of allocation. We show that with three or more players, any social choice function is uniquely and exactly implementable in iterative dominance. Importantly, this study does not assume either expected utility or quasi-linearity, even if we utilize the stochastic method of mechanism design explored by Abreu and Matsushima (Econometrica 60:993–1008, 1992a; Econometrica 60:1439–1442, 1992b; J Econ Theory 64(1):1–19, 1994). We further show that even with incomplete information, and even with two players, any ex-post incentive compatible social choice function is uniquely and exactly implementable in iterative dominance.

Aggregation of Bayesian preferences: unanimity vs monotonicity

Abstract: This article reconsiders the issue of Bayesian aggregation by pointing at a conflict that may arise between two logically independent dominance criteria, Pareto dominance and statewise dominance, that are commonly imposed on social preferences. We propose a weaker dominance axiom that restricts statewise dominance to Pareto dominant alternatives and Pareto dominance to statewise dominant alternatives. The associated aggregation rule is a convex combination of two components., the first being a weighted sum of the individuals' subjective expected utility (SEU) functional, the second being a social SEU functional, with associated social utility function and social belief. Such representation establishes the existence of a trade off between adherence to the Pareto principle and compliance with statewise dominance. We then investigate what are the consequences of adding to our assumptions either of the two dominance criteria in their full force and obtain that each of them is equivalent to discarding the other, unless there is essentially a common prior probability.

Conformity and truthful voting under different voting rules

Abstract: We induce conformity in a binary-decision voting game in which one of the options require certain support (majority, supermajority or unanimity) to be the adopted decision. We consider heterogenous types of voters in that each of them prefer a different outcome in the voting game. We demonstrate theoretically that truthful voting is the unique equilibrium without conformity for each possible voting rule. Introducing conformity enlarges the set of equilibria, which includes voting profiles in which agents do not necessarily vote for their preferred option. If we account for the presence of non-conformist honest voters that vote truthfully for their preferred option, truthful voting is more pervasive for conformist voters in equilibrium. In our setting, the effects of conformity and honest voters on the likelihood of voting truthfully depend on the voting rule that determines whether or not voters are in a decisive group to implement one of the decisions. We provide empirical support for our theoretical predictions by means of a laboratory experiment. Our findings indeed suggest an interplay between the voting rule and the willingness to conform.

Using the Borda rule for ranking sets of objects

Abstract: We analyze the problem of ranking sets of objects based on a ranking over the single objects. In recent years various papers used the sum of individual scores for the objects, in particular Borda scores, to make such comparisons. The advantage of this approach lies in providing a complete ranking of sets of objects and therefore can be seen as an alternative to other methods based on best and/or worst objects. The paper contributes in two ways. On the one hand, we highlight certain drawbacks that arise when using Borda scores in such comparisons. On the other hand, we provide two characterization results for Borda-sum rankings, one for the restricted setting of sets of equal cardinality and one for the general setting which allows for comparisons of sets of unequal cardinality.

Are estimates of intergenerational mobility biased by non-response? Evidence from the Netherlands

Abstract: Intergenerational mobility is often studied using survey data. In such settings, selective unit or item non-response may bias estimates. Linking Dutch survey data to administrative income data allows us to examine whether selective responses bias the estimated relationship between parental income and children's mathematics and language test scores in grades 6 and 9. We find that the estimates of these relationships are biased downward due to parental unit non-response, while they are biased upwards due to item non-response. In the analyses of both unit and item non-response, the point estimates for language and mathematics test scores point in the same direction but only one of the two relationships is significant. These findings suggest that estimates of intergenerational mobility based on survey data need to be interpreted with caution because they may be biased by selective non-response. The direction of such bias is difficult to predict a priori. Bias due to unit and item non-response may work in opposing directions and may differ across outcomes.

Congruence relations on a choice space

Abstract: A choice space is a finite set of alternatives endowed with a map associating to each menu a nonempty subset of selected items. A congruence on a choice space is an equivalence relation that preserves its structure. Intuitively, two alternatives are congruent if the agent is indifferent between them, and, in addition, her choice is influenced by them in exactly the same way. We give an axiomatic characterization of the notion of congruence in terms of three natural conditions: binary fungibility, common destiny, and repetition irrelevance. Further, we show that any congruence satisfies the following desirable properties: (hereditariness) it induces a well-defined choice on the quotient set of equivalence classes; (reflectivity) the primitive behavior can be always retrieved from the quotient choice, regardless of any feature of rationality; (consistency) all basic axioms of choice consistency are preserved back and forth by passing to the quotient. We also prove that the family of all congruences on a choice space forms a lattice under set-inclusion, having equality as a minimum, and a unique maximum, called revealed indiscernibility. The latter relation can be seen as a limit form of revealed similarity as the agent’s rationality increases.

Truth-tracking judgment aggregation over interconnected issues

Abstract: This paper analyzes the problem of aggregating individual judgments over two interconnected issues. Voters share a common preference which is state-dependent, but they hold private information about what the state might be. I assume strategic voting in a Bayesian voting game setting and I want to determine voting rules which induce an efficient Bayesian Nash equilibrium in truthful strategies, hence lead to collective judgments that efficiently incorporate all private information. Interconnectedness may lead to private information that is inconsistent with the state, which leads to the impossibility of efficient information aggregation. Once I introduce the possibility of abstention, the negative conclusion no longer prevails and there is always a voting rule which aggregates information efficiently. I obtain a similar positive result when I rule out the possibility of inconsistent private information. I analyze the situations in which such rules exist whenever necessary, as well as the nature of these rules.

Evidence reading mechanisms

Abstract: In an environment with privately informed agents who can produce evidence, we study implementation of a social choice function by reading mechanisms: mechanisms that simply apply the social choice function to a consistent interpretation of the evidence. We provide sufficient conditions on the social choice function and the evidence structure for ex post implementability by such mechanisms. If the first-best policy of a mechanism designer satisfies this condition, then its implementation by a reading mechanism does not require commitment. We show that with rich evidence structures, (1) a function that is implementable with transfers is also implementable with evidence but no transfer, (2) under private value, the efficient allocation is implementable with budget balanced and individually rational transfers, and (3) in single-object auction and bilateral trade environments with interdependent values, the efficient allocation is implementable with budget balanced and individually rational transfers.