The topological equivalence of the pareto condition and the existence of a dictator

The paper studies two standard properties of rules for aggregating individual into social preferences: non-dictatorship and the Pareto condition. Together with the condition of independence of irrelevant alternatives, these are the three basic axioms of Arrow's social choice paradox.We prove the topological equivalence between the Pareto condition and the existence of a dictator for continuous rules. The axiom of independence of irrelevant alternatives is not required.The results use a topological framework for aggregation introduced in Chichilnisky (1980), but under different conditions. In Chichilnisky (1980) rules are anonymous and respect unanimity. Since anonymity is strictly stronger than the condition of non-dictatorship, while respect of unanimity is strictly weaker than the Pareto condition, the two sets of conditions are not comparable.     

Acyclicity,anonymity, and prefilters

We analyze the decisiveness structures associated with acyclical collective choice rules. In particular, we examine the consequences of adding anonymity to weak Pareto, thereby complementing earlier results on acyclical social choice. Both finite and countably infinite populations are considered. As established in contributions by Donald Brown and by Jeffrey Banks, acyclical social choice is closely linked to prefilters in the presence of the weak Pareto principle. We introduce the notion of a conditional prefilter and use it to generalize their results. In the finite-population case, adding anonymity implies that the collection of decisive sets is a special case of a conditional prefilter. We then identify the decisiveness structure that results from adding anonymity to the weak Pareto principle. Moving to infinite populations, we obtain the decisive set that consists of the entire population as a possibility, along with a new class of prefilters that we refer to as symmetric free Fréchet prefilters. The choice of the term Fréchet prefilter is motivated by the observation that they share a defining property with the well-known Fréchet filter—namely, that all sets in the requisite collection are such that their complement is finite.     

Decomposing random mechanisms

Random mechanisms have been used in real-life situations for reasons such as fairness. Voting and matching are two examples of such situations. We investigate whether the desirable properties of a random mechanism survive decomposition of the mechanism as a lottery over deterministic mechanisms that also hold such properties. To this end, we represent properties of mechanisms–such as ordinal strategy-proofness or individual rationality–using linear constraints. Using the theory of totally unimodular matrices from combinatorial integer programming, we show that total unimodularity is a sufficient condition for the decomposability of linear constraints on random mechanisms. As two illustrative examples we show that individual rationality is totally unimodular in general, and that strategy-proofness is totally unimodular in some individual choice models. We also introduce a second, more constructive approach to decomposition problems, and prove that feasibility, strategy-proofness, and unanimity, with and without anonymity, are decomposable in non-dictatorial single-peaked voting domains. Just importantly, we establish that strategy-proofness is not decomposable in some natural problems.     

On properties of division rules lifted by bilateral consistency

We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is “lifted” if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number of properties that are lifted, such as equal treatment of equals, resource monotonicity, composition down and composition up, and show that continuity, anonymity and self-duality are not lifted. However, each of these three properties is lifted if the rule is resource monotonic.     

Fakers becoming believers: how opinion dynamics are shaped by preference falsification,impression management and coherence heuristics

In the vast and rich literature on opinion dynamics, the role of preference falsification has generally been dismissed. Following the lead of Timur Kuran, in this paper we present one of the first multi-agent models that explores how opinion dynamics can be affected by the possible divorce between private and public opinions. It is also the first attempt to explore the role of social hierarchies in opinion dynamics conditioned by preference falsification. Our model formalizes heterogeneous evolving agents guided by a cognitively feasible set of heuristics and embedded in a social-rank-dependent structure of interactions. In social-rank-heterophilic encounters where people experience a high pressure of face-to-face interactions, unanimous support for the high social-rank preferred option emerges, while in any other scenario this option gathers majority but not unanimous support. Preference falsification has a crucial role in the emergence of unanimity, but it also creates the conditions for further private opinion actualizations that end up generating a self-sustained and sincere unanimity. When social-rank-homophilic encounters are the rule, or when group dynamics are irrelevant for opinion expression, agents never find incentives to falsify their opinions, therefore generating a social situation that resembles the general idea behind the ethnographic work of James C. Scott: true opinion expression in daily social-rank-homophilic encounters and a persistent opinion falsification in dissimilar social-rank interactions.     

The structure of decision schemes with cardinal preferences

This paper replacesGibbard’s (Econometrica 45:665-681, 1977) assumption of strict ordinal preferences by themore natural assumption of cardinal preferences on the set pure social alternatives and we also admit indifferences among the alternatives. By following a similar line of reasoning to the Gibbard-Satterthwaite theoremin the deterministic framework, we first show that if a decision scheme satisfies strategy proofness and unanimity, then there is an underlying probabilistic neutrality result which generates an additive coalitional power function. This result is then used to prove that a decision scheme which satisfies strategy proofness and unanimity can be represented as a weak random dictatorship. A weak random dictatorship assigns each individual a chance to be a weak dictator. An individual has weak dictatorial power if the support of the social choice lottery is always a subset of his/her maximal utility set. In contrast to Gibbard’s complete characterization of randomdictatorship, we also demonstrate with an example that strategy proofness and unanimity are sufficient but not necessary conditions for a weak random dictatorship.     

Delay,multiplicity, and non-existence of equilibrium in unanimity bargaining games

We consider a class of perfect information bargaining games with unanimity acceptance rule. The proposer and the order of responding players are determined by the state that evolves stochastically over time. The probability distribution of the state in the next period is determined jointly by the current state and the identity of the player who rejected the current proposal. This protocol encompasses a vast number of special cases studied in the literature. We show that subgame perfect equilibria in pure stationary strategies need not exist. When such equilibria do exist, they may exhibit delay. Limit equilibria as the players become infinitely patient need not be unique.     

The unanimity rule and extremely asymmetric committees

This paper analyzes how to allocate experts into committees that use the unanimity rule to make decisions. We show that an optimal allocation of experts is extremely asymmetric. To reach the optimal allocation, therefore, one needs only to rank the experts in terms of their abilities and then allocate adjacent experts such that an expert’s ability tends to vary inversely with the size of his committee. In the special case of three-member committees, we show that the optimal allocation maximizes the sum of the products of the experts’ skills in each committee.     

Alliances and negotiations: an incomplete information example

We study a bargaining game between an individual and an ‘alliance’ in the sense of Manzini and Mariotti (J Econ Theory 121:128–41, 2005), in which the opponent of the alliance is incompletely informed about the relative strengths of its members. The best equilibrium outcome for the alliance under a unanimity rule is not attainable with a non-unanimity rule. However, unlike in the complete information model, less than optimal outcomes and delays may occur with positive probability even under unanimity, depending on the prior beliefs and the preferences of the agents. We are grateful to a careful referee for comments. We wish to thank Clara Ponsati for useful comments.     

Capital structure,investment unanimity,and public goods: the case for social responsibility

This paper examines the concepts of optimal capital structure and investment in an economy where government’s role is the provision of a public good. That public good is financed through current tax revenues and the sale of government securities. Absent such complications, traditional finance theory has established the equivalence among (competitive) value maximization, unanimity, and Pareto optimality. In the setting of this paper, however, the market value of government securities is not determined by the value of public good production, and the correspondence between value maximization, Parto optimality, and unanimity will not generally hold without significant restrictions on the tax structure. Otherwise, value maximization is neither an optimal nor unanimously supported objective for the firm.     

Anonymity and continuous social choice

Continuity of social choice is reformulated in terms of the quotient topology on profiles of individual preferences induced by the equivalence class corresponding to anonymity. It is shown that Chichilnisky's impossibility continues to hold.     

May’s theorem in an infinite setting

We generalize May’s theorem to an infinite setting, preserving the elementary character of the original theorem. We define voting scenarios and generalized voting scenarios, and prove appropriate versions of May’s theorem. The case of generalized voting scenarios specialized to a countably infinite set of voters and the collections of all coalitions that have asymptotic density, shows that majority rule is the only aggregation rule that satisfies neutrality, irrelevance of null coalitions, anonymity, and positive responsiveness.     

Social distance,heterogeneity and social interactions

A crucial ingredient in social interaction models is the structure of peer groups, which link individuals with similar characteristics. We propose and study a dynamic binary choice model with social interactions in which heterogeneity of peer group effects is modeled introducing diversity in individual characteristics and linking pairwise influences to a social distance between individuals. Our framework allows for mimetic as well as anti-mimetic interactions and a heterogeneous structure of peer groups across individuals. Dynamic equilibria are studied in the limit when the number of agents is large. We show that the model exhibits multiple equilibria resulting from conflicts between various group pressures the individuals are subjected to. We study in particular the correlation in the population at equilibrium between the characteristics of the agents and their decisions: this quantity has an interesting empirical interpretation and solves a simple analytical equation when the number of agents is large. Finally we discuss the empirical content of the model and present a consistent estimator for the parameter describing which is consistent for any typical population regardless of the structure of individual characteristics.     

互联网虚假信息研究概述

由于互联网的普遍性、匿名性以及竞争的激烈性,越来越多的网络用户通过虚假信息以混淆视听、恶意诋毁竞争对手和蓄意扰乱社会秩序。本文通过论述互联网虚假信息的研究现状,结合相关研究理论和方法,探索互联网虚假信息的研究方向。     

Wicksell's Unaminity Rule

A bstract    This paper identifies the extent to which James Buchanan's interpretation of Knut Wicksell's unanimity rule, as spelled out in the second essay in Finanztheoretische Untersuchungen (1896), has come to dominate the public economics literature despite competing with the interpretation offered by Richard Musgrave. A brief summary of the differing interpretations is offered. Citation analysis is used to examine the frequency with which Wicksell is cited and by whom. The sociology of the economics profession and avenues for the dissemination of ideas are examined to understand the dominance of Buchanan's particular interpretation and application of the unanimity rule.     

The Social Cost of Cheap Pseudonyms

We consider the problems of societal norms for cooperation and reputation when it is possible to obtain cheap pseudonyms, something that is becoming quite common in a wide variety of interactions on the Internet. This introduces opportunities to misbehave without paying reputational consequences. A large degree of cooperation can still emerge, through a convention in which newcomers "pay their dues" by accepting poor treatment from players who have established positive reputations. One might hope for an open society where newcomers are treated well, but there is an inherent social cost in making the spread of reputations optional. We prove that no equilibrium can sustain significantly more cooperation than the dues-paying equilibrium in a repeated random matching game with a large number of players in which players have finite lives and the ability to change their identities, and there is a small but nonvanishing probability of mistakes. Although one could remove the inefficiency of mistreating newcomers by disallowing anonymity, this is not practical or desirable in a wide variety of transactions. We discuss the use of entry fees, which permits newcomers to be trusted but excludes some players with low payoffs, thus introducing a different inefficiency. We also discuss the use of free but unreplaceable pseudonyms, and describe a mechanism that implements them using standard encryption techniques, which could be practically implemented in electronic transactions.     

Optimal Social Design: Estimating a Social Welfare Function from Questionnaire Data

A social design x evokes a response y from a set of individuals. The value of the design is expressed in terms of a social welfare function which is derived from Arrow’s formulation of social choice. Making certain simplifying assumptions the social welfare function can be expressed in terms of individuals’ ideal designs. A method for estimating the social welfare function from quite limited empirical evidence is developed. The method is applied to an educational case study. There was considerable variation in individuals’ ideal designs. The components of the social welfare were estimated: the welfare ideal, the population sensitivity, the population variation, the deviation from the ideal and the welfare ceiling. Methodological problems are discussed.     

Privacy Is Precious: On the Attempt to Lift Anonymity on the Internet to Increase Revenue

We investigate the effect of a reduction of anonymity on consumers' purchase decisions (whether to buy, and if so how much to pay) at an online music store with Pay‐What‐You‐Want (PWYW)‐like pricing and in an Internet experiment mimicking the real world situation. Revealing the customer's name, e‐mail, and payment to the artist (seller) led to insignificantly higher payments, although it drastically reduced the number of customers purchasing. Overall, the regime led to a revenue loss of 25%. In the online experiment, revenue drops by 35%. These results suggest that the positive effect of reduced anonymity, previously established for donation or public goods contexts, does not extend to a consumption environment. Instead, the substantial opt‐out of customers is likely to be motivated by concerns about privacy.     

On Two Existing Approaches to Statistical Analysis of Social Media Data

Using social media data for statistical analysis of general population faces commonly two basic obstacles: firstly, social media data are collected for different objects than the population units of interest; secondly, the relevant measures are typically not available directly but need to be extracted by algorithms or machine learning techniques. In this paper, we examine and summarise two existing approaches to statistical analysis based on social media data, which can be discerned in the literature. In the first approach, analysis is applied to the social media data that are organised around the objects directly observed in the data; in the second one, a different analysis is applied to a constructed pseudo survey dataset, aimed to transform the observed social media data to a set of units from the target population. We elaborate systematically the relevant data quality frameworks, exemplify their applications and highlight some typical challenges associated with social media data.