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Abstract: Abstract In this paper we propose a simple axiom which, along with the axioms of additivity (transfer) and dummy player, characterizes the Shapley value (the Shapley–Shubik power index) on the domain of TU (simple) games. The new axiom, cross invariance, demands payoff invariance on symmetric players across “quasi-symmetric games,” that is, games where excluding null players, all players are symmetric. Additionally, we demonstrate that the axiom of additivity can be replaced by a new axiom called strong monotonicity, or it can be completely dropped if a stronger version of cross invariance is employed. We also show that the weighted Shapley values can be characterized using a weighted variant of cross invariance. Efficiency is derived rather than assumed in our characterizations. This fresh perspective contributes to a deeper understanding of the Shapley value and its applicability. PubDate: 2023-11-25
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Abstract: Abstract Measuring inequality is a challenging task, particularly when data is collected in a coarse manner. This paper proposes a new approach to measuring inequality indices that considers all possible income values and avoids arbitrary statistical assumptions. Specifically, the paper suggests that two sets of income distributions should be considered when measuring inequality, one including the highest income per individual and the other including the lowest possible income per individual. These distributions are subjected to inequality index measures, and a weighted average of these two indices is taken to obtain the final inequality index. This approach provides more accurate measures of inequality while avoiding arbitrary statistical assumptions. The paper focuses on two special cases of social welfare functions, the Atkinson index and the Gini index, which are widely used in the literature on inequality. PubDate: 2023-11-16
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Abstract: Abstract We study the implications of stochastic same-sidedness (SSS) axiom in the random voting model. At a given preference profile if one agent changes her preference ordering to an adjacent one by swapping two consecutively ranked alternatives, then SSS imposes two restrictions on the lottery selected by a voting rule before and after the swap. First, the sum of probabilities of the alternatives which are ranked strictly higher than the swapped pair should remain the same. Second, the sum of probabilities assigned to the swapped pair should also remain the same. We show that every random social choice function (RSCF) that satisfies efficiency and SSS is a random dictatorship provided that there are two voters or three alternatives. For the case of more than two voters and atleast four alternatives, every RSCF that satisfies efficiency, tops-onlyness and SSS is a random dictatorship. PubDate: 2023-11-02
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Abstract: Abstract In a one-commodity economy with single-peaked preferences and individual endowments, we study different ways in which reallocation rules can be strategically distorted by affecting the set of active agents. We introduce and characterize the family of iterative reallocation rules and show that each rule in this class is withdrawal-proof and endowments-merging-proof, at least one is endowments-splitting-proof and that no such rule is pre-delivery-proof. PubDate: 2023-11-02
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Abstract: Abstract We investigate a dynamic development process which involves heterogeneous agents making location choices. In our spatial model agents differ from each other by the impact they have on the development dynamics. In equilibrium, a high impact agent, the pioneer, sacrifices some short-run benefits and chooses an underdeveloped location. The pioneer improves that location and creates incentives for other agents to choose it later in the game. We design a laboratory experiment to test various comparative statics of the model and analyze the role of pioneers as well as the effect that early investments in public goods have on long-run outcomes. Our findings are consistent with theoretical predictions — high impact subjects tend to choose pioneering more frequently than other agents. As predicted, improvements in initial conditions through early investments in public goods significantly affect the dynamics of the system and can lead to substantial welfare improvements. Moreover, learning and experimentation play a significant role in our experiments and help subjects’ behavior to match point predictions of the model. We also observe behavioral deviations such as when some low impact subjects consistently act as lesser pioneers and also choose the underdeveloped location. Such behavior can be treated as growing cooperation and linked to Pareto improvement concerns over the outcomes of previous games. PubDate: 2023-11-01
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Abstract: Abstract This study investigates a novel intervention approach to network games, in which players are delinquents whose payoffs depend on the actions of their network neighbors. The social planner aims to manipulate the delinquency costs of players, seeking to minimize the total delinquency level. We consider two intervention scenarios. First, we consider binary interventions, where the planner can either increase the cost of an offender by a fixed amount; or leave its cost unchanged. The optimal intervention problem involves maximizing a submodular function. We establish a connection between cost and structural intervention in networks. Next, we consider continuous levels of intervention, where the planner can choose how much to increase the cost of an offender. We show that the optimal intervention problem is a tractable convex optimization if the intervention function is concave. We provide a characterization of the optimal intervention which is highly related to players’ centralities in the network. We further discuss the interior solution and apply our result to nested split graphs. PubDate: 2023-11-01
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Abstract: Abstract Matching platforms not only mediate matches but also work as information gatekeepers. When users with private tastes use such a platform to find a partner, the platform asks them to provide match-relevant information; subsequently, it aggregates and distributes the collected data back to each user to facilitate the effective coordination of matches. This study aims to examine how such a platform can design its information flow to make users form matches in a way that is desirable for the platform. I characterize a form of two-way communication that employs both verifiable and non-verifiable messages; then, I delineate the conditions under which a platform can (cannot) achieve its ex-post optimal matching outcome. On a platform that achieves such an outcome, users would fully reveal their private tastes, but the platform would return personalized and only filtered information back to each user in the form of a “recommendation.” I identify three key factors that enable such communication, namely (1) the distance between the distribution of tastes of each side; (2) the uncertainty measure of each distribution; and (3) the population size. As applications, I first study the markets with costly verifiable information and propose a sufficient condition that achieves the optimal matching outcome. Then, I study a two-way communication protocol with non-verifiable messages and demonstrate that communication strictly improves efficiency under any circumstances. PubDate: 2023-11-01
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Abstract: Abstract Widely accepted theories in modern cosmology say that spacetime is probably infinite. This raises the question how to define a social welfare order (SWO) for an infinite population of people dispersed throughout time and space. Any such SWO should be Lorentz invariant: it should yield the same value independent of the position and velocity of the social observer. I define and axiomatically characterize spatiotemporal Cesàro average utilitarian SWOs as a solution to this problem. PubDate: 2023-11-01
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Abstract: Abstract In their seminal paper, Kakwani and Lambert (Eur J Polit Econ 14:369–380, 1998) state three Axioms an equitable tax system should respect. By proposing a measurement system based on re-ranking indexes of taxes, tax rates and post-tax incomes, they show how to evaluate the negative influences that Axiom violations exert on the redistributive effect of a tax. By considering each element of a real-world personal income tax, i.e. deductions and tax credits as well as statutory tax rates, in this study we take a theoretical step further by decomposing the magnitude of the three Axiom violations produced by all these tax elements. We propose two complementary strategies. The first one is a ‘stepwise’ decomposition computing the effect of each element of the tax on the redistributive effect when they are sequentially applied; the second strategy is an ‘overall and simultaneous’ decomposition always evaluating the effect of small changes in deductions, tax rates and tax credits with respect to the pre-tax income distribution, once all the three tax instruments have been simultaneously applied. These strategies can be more suitable and effective in measuring the loss of the redistributive effect produced by each tax element because of axiom violations. We also show that they can give different information on the existing inequities of the tax. We finally emphasize the goodness of our approach by applying it to a real world personal income tax. PubDate: 2023-11-01
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Abstract: Abstract Due to the imperfect ability of individuals to discriminate between sufficiently similar alternatives, individual indifferences may fail to be transitive. I prove two impossibility theorems for social choice under indifference intransitivity, using axioms that are strictly weaker than Strong Pareto and that have been endorsed (sometimes jointly) in prior work on social choice under indifference intransitivity. The key axiom is Consistency, which states that if bundles are held constant for all but one individual, then society’s preferences must align with those of that individual. Theorem 1 combines Consistency with Indifference Agglomeration, which states that society must be indifferent to combined changes in the bundles of two individuals if it is indifferent to the same changes happening to each individual separately. Theorem 2 combines Consistency with Weak Majority Preference, which states that society must prefer whatever the majority prefers if no one has a preference to the contrary. Given that indifference intransitivity is a necessary condition for the just-noticeable difference (JND) approach to interpersonal utility comparisons, a key implication of the theorems is that any attempt use the JND approach to derive societal preferences must violate at least one of these three axioms. PubDate: 2023-11-01
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Abstract: Abstract Preferences often change—even in short time intervals—due to either the mere passage of time (present-biased preferences) or changes in visceral or environmental conditions (state-dependent preferences). On the basis of empirical findings concerning state-dependent preferences, we critically discuss the “Aristotelian” view of unitary decision makers in economics. We illustrate that the conceptualization of preferences as “present-biased” as opposed to “state-dependent” has very different normative implications for which preferences should be considered “rational.” Empirically, however, the two concepts are very difficult to distinguish. The economist can justify any paternalistic intervention if she can conceptualize changing preferences so flexibly, and she can easily become a benevolent despot. We therefore urge for a more careful “Heraclitean” view of decision-making that accepts that a person may consist of multiple selves. PubDate: 2023-11-01
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Abstract: Abstract We analyze multiple-beliefs based efficiency measures in economies with risk and disagreement, including belief neutral efficiency and inefficiency, incomplete knowledge efficiency, efficiency based on unanimity, and utility aggregators that minimize Bergson welfare functions over multiple beliefs. We provide equivalence results under technical conditions that are satisfied in several work-horse economies, including the exchange economy and a standard economy with a linear production technology. We also provide several examples for which these measures differ. Our results show that the further away one gets from the standard exchange economy, the more the different multiple-beliefs based measures differ in the allocations they identify as efficient, in general. Consequently, the more important the choice of efficiency measure becomes. PubDate: 2023-11-01
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Abstract: Abstract This paper studies the allocation of voting weights in a committee representing groups of different sizes. We introduce a partial ordering of weight allocations based on stochastic comparison of social welfare. We show that when the number of groups is sufficiently large, this ordering asymptotically coincides with the total ordering induced by the cosine proportionality between the weights and the group sizes. A corollary is that a class of expectation-form objective functions, including expected welfare, the mean majority deficit and the probability of inversions, are asymptotically monotone in the cosine proportionality. PubDate: 2023-11-01
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Abstract: Abstract We examine the impact of Suzumura’s (Economica 43:381–390, 1976) consistency property when applied in the context of collective choice rules that are independent of irrelevant alternatives, neutral, and monotonic. An earlier contribution by Blau and Deb (Econometrica 45:871–879, 1977) establishes the existence of a vetoer if the collective relation is required to be complete and acyclical. The purpose of this paper is to explore the possibilities that result if completeness and acyclicity are dropped and Suzumura consistency is imposed instead. A conceptually similar but logically independent version of the combined axiom that requires the collective decision mechanism to be independent, neutral, and monotonic is employed. In the case of a finite population, we obtain an alternative impossibility theorem if a collective choice rule is assumed to be non-degenerate and a modified no veto requirement is imposed instead of Blau and Deb’s (1977) condition. If the population is countably infinite, the impossibility can be avoided but it resurfaces if our new no veto property is extended to a coalitional variant. PubDate: 2023-11-01
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Abstract: Abstract It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, the hallmark of cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology. PubDate: 2023-10-27
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Abstract: Abstract Different voting rules are commonly used to settle collective decisions. A promising way to assess voting rules, for which little is known, is to compare the expressive utility that voters derive from voting with each rule. In this paper, we first propose a simple ordinal model of expressive voting that allows us to compare voting rules in terms of the expressive utility that voters can derive from voting (their expressive power). Our model provides a novel testable implication according to which expected turnout increases with expressive power. We then ran an online experiment testing this implication in a controlled environment. We find that if voters are made aware of alternative voting rules, turnout is higher in voting rules with higher expressive power. Our results also show that higher expressive power is associated with a better representation of voters’ actual preferences and, according to our model, higher expressive utility. This suggests that the expressive power of voting rules is a relevant criterion when choosing between voting rules for economic and political decisions. PubDate: 2023-10-10
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Abstract: Abstract This paper models the welfare consequences of social fragmentation arising from technological advance. We start from the premise that technological progress falls primarily on market-traded commodities rather than prosocial relationships, since the latter intrinsically require the expenditure of time and thus are less amenable to productivity increases. Since prosocial relationships require individuals to identify with others in their social group whereas marketable commodities are commonly the objects of social status comparisons, a tradeoff arises between in-group affiliation and inter-group status comparisons. People consequently narrow the bounds of their social groups, reducing their prosocial relationships and extending their status-seeking activities. As prosocial relationships generate positive externalities whereas status-seeking activities generate negative preference externalities, technological advance may lead to a particular type of “decoupling” of social welfare from material prosperity. Once the share of status goods in total production exceeds a crucial threshold, technological advance is shown to be welfare-reducing. PubDate: 2023-10-04
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Abstract: Abstract A principal has n homogeneous objects to allocate to \(I> n\) agents. The principal can allocate at most one good to an agent, and each agent values the good. Agents have private information about the principal’s payoff of allocating the goods. There are no monetary transfers, but the principal may check any agent’s value at a cost. In this setting, we propose a direct mechanism, called the n-ascending mechanism, which balances the benefit of efficient allocation and the cost of checking agents. While such a mechanism itself is not obviously strategy-proof, we show that its outcome is easily implementable by an extensive game which has an equilibrium in obviously dominant strategies. When \(n = 2,\) we show that the 2-ascending mechanism is essentially the unique optimal mechanism that maximizes the principal’s expected net payoff. PubDate: 2023-10-01
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Abstract: Abstract Social dilemmas such as greenhouse gas emission reduction are often characterized by heterogeneity in benefits from solving the dilemma. How should leadership of group members be organized in such a setting' We implement a laboratory public goods experiment with heterogeneous marginal per capita returns from the public good and leading by example that is either implemented exogenously or by self-selection. Our results suggest that both ways of implementing leadership only have small effects on contributions to the public good. Self-selected leaders—in particular self-selected low-benefit leaders—tend to set better examples than imposed leaders, but they are also exploited more strongly by followers. Leaders seem to need additional instruments to be more effective when benefits are heterogeneous. PubDate: 2023-10-01
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Abstract: Abstract This study examines the mechanism design problem for public goods provision in a large economy with n independent agents. We propose a class of dominant-strategy incentive compatible and ex-post individually rational mechanisms, which we call the adjusted mean-thresholding (AMT) mechanisms. We show that when the cost of provision grows slower than the \(\sqrt{n}\) -rate, the AMT mechanisms are both eventually ex-ante budget balanced and asymptotically efficient. When the cost grows faster than the \(\sqrt{n}\) -rate, in contrast, we show that any incentive compatible, individually rational, and eventually ex-ante budget balanced mechanism must have provision probability converging to zero and hence cannot be asymptotically efficient. The AMT mechanisms have a simple form and are more informationally robust when compared to, for example, the second-best mechanism. This is because the construction of an AMT mechanism depends only on the first moment of the valuation distribution. PubDate: 2023-10-01
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