Arrow’s theorem in judgment aggregation

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.     

Judgment aggregation without full rationality

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition of rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinstein’s group identification problem. This paper was circulated in August 2006 and presented at the Yale workshop on Aggregation of Opinions, September 2006, at the Centre interuniversitaire de rechere en économie quantitative, Montreal, October 2006, and at the 1st International Workshop on Computational Social Choice, Amsterdam, December 2006. We are grateful to the participants at these occasions and the anonymous referees for comments. We also thank Ton Storcken for discussion. Elad Dokow and Ron Holzman have independently proved closely related results, which were also presented at the Yale workshop in September 2006, and circulated in the December 2006 paper (Dokow and Holzman 2006).     

A generalised model of judgment aggregation

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.     

Geometric models of consistent judgement aggregation

Given a set of propositions with unknown truth values, a ‘judgement aggregation function’ is a way to aggregate the personal truth-valuations of a group of voters into some ‘collective’ truth valuation. We introduce the class of ‘quasimajoritarian’ judgement aggregation functions, which includes majority vote, but also includes some functions which use different voting schemes to decide the truth of different propositions. We show that if the profile of individual beliefs satisfies a condition called ‘value restriction’, then the output of any quasimajoritarian function is logically consistent; this directly generalizes the recent work of Dietrich and List (Majority voting on restricted domains. Presented at SCW08; see , 2007b). We then provide two sufficient conditions for value-restriction, defined geometrically in terms of a lattice ordering or a metric structure on the set of individuals and propositions. Finally, we introduce another sufficient condition for consistent majoritarian judgement aggregation, called ‘convexity’. We show that convexity is not logically related to value-restriction.     

Behavioral evidence for framing effects in the resolution of the doctrinal paradox

The aggregation of individual sets of judgments over interconnected propositions can yield inconsistent collective sets of judgments, even when the individual sets of judgments are themselves consistent. A doctrinal paradox occurs when majority voting on a compound proposition (such as a conjunction or disjunction) yields a different result than majority voting on each of the elements of the proposition. For example, when most individuals accept proposition X; most individuals accept proposition Y ; but only a minority of individuals accept the compound proposition ‘X and Y’. Conducting two elemental votes would lead to accept X and Y , but conducting one compound vote would lead to reject X and Y . In such a situation, do people manifest a stable preference as to which voting procedure should be applied? This research reports the results of two behavioral experiments using a within-participant design, which show that procedural preferences can be upturned by framing either positively or negatively the set of judgments to be aggregated. This shift in procedural preference leads to large swings in the final collective judgment endorsed by participants.     

Propositionwise judgment aggregation: the general case

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or extended unanimity preservation. We fully characterize the agendas for which there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between, 2002), Nehring (Oligarchies in judgment aggregation: a characterization, 2006), Dietrich and List (Soc Choice Welf 29(1):19–33, 2007a) and Dokow and Holzman (J Econ Theory 145(2):495–511, 2010a).     

Aggregation of binary evaluations for truth-functional agendas

In the problem of judgment aggregation, a panel of judges has to evaluate each proposition in a given agenda as true or false, based on their individual evaluations and subject to the constraint of logical consistency. We elaborate on the relation between this and the problem of aggregating abstract binary evaluations. For the special case of truth-functional agendas we have the following main contributions: (1) a syntactical characterization of agendas for which the analogs of Arrow’s aggregation conditions force dictatorship; (2) a complete classification of all aggregators that satisfy those conditions; (3) an analysis of the effect of weakening the Pareto condition to surjectivity. This is a sequel to the paper “Aggregation of binary evaluations.” The contents of both papers were presented, under the title “An Arrovian impossibility theorem for social truth functions,” at the Second World Congress of the Game Theory Society, Marseille, July 2004. The first version of “Aggregation of binary evaluations” was completed in June 2005. That working paper was subsequently split into two parts, of which this is the second. The comments of an anonymous referee are gratefully acknowledged. Part of R. Holzman’s work was done while he was a Fellow of the Institute for Advanced Studies at the Hebrew University of Jerusalem.     

Methods for distance-based judgment aggregation

Judgment aggregation theory, which concerns the translation of individual judgments on logical propositions into consistent group judgments, has shown that group consistency generally cannot be guaranteed if each proposition is treated independently from the others. Developing the right method of abandoning independence is thus a high-priority goal. However, little work has been done in this area outside of a few simple approaches. To fill the gap, we compare four methods based on distance metrics between judgment sets. The methods generalize the premise-based and sequential priority approaches to judgment aggregation, as well as distance-based preference aggregation. They each guarantee group consistency and implement a range of distinct functions with different properties, broadening the available tools for social choice. A central result is that only one of these methods (not previously considered in the literature) satisfies three attractive properties for all reasonable metrics.     

Weakest collective rationality and the Nash bargaining solution

We propose a new axiom, weakest collective rationality (WCR) which is weaker than both weak Pareto optimality (WPO) in Nash’s (Econometrica 18:155–162, 1950) original characterization and strong individual rationality (SIR) in Roth’s (Math Oper Res 2:64–65, 1977) characterization of the Nash bargaining solution. We then characterize the Nash solution by symmetry (SYM), scale invariance (SI), independence of irrelevant alternatives (IIA) and our weakest collective rationality (WCR) axiom.     

Collective,universal, and joint rationality

Rationality’s extension from individuals to groups yields collective rationality. Just as individuals should be rational, groups should be collectively rational. This paper briefly presents collective rationality and then compares it to universal rationality and joint rationality. Universal rationality is the rationality of all members of a group. It directs individualistic evaluation of a collective act. Joint rationality is the rationality of each individual’s part in a collective act given the collective act’s realization. Game theory uses it to characterize solutions to games. Collective rationality is not the same as either universal or joint rationality. However, in certain ideal conditions collective rationality agrees with universal rationality, and in other ideal conditions it agrees with joint rationality. Distinguishing the three types of evaluation and explaining their relations contributes to a general theory of rationality.     

The limits of epistemic democracy

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.     

Framing Public Discussion of Gay Civil Unions

Although the framing of public opinion has often been conceptualizedas a collective and social process, experimental studies offraming have typically examined only individual, psychologicalresponses to alternative message frames. In this research weemploy for the first time group conversations as the unit ofanalysis (following Gamson 1992) in an experimental study offraming effects. Two hundred and thirty-five American citizensin 50 groups (17 homo-geneously conservative groups, 15 homogeneouslyliberal groups, and 18 heterogeneous groups) discussed whetheror not gay and lesbian partnerships should be legally recognized.Groups were randomly assigned to one of two framing conditions(a "homosexual marriage/special rights" frame or a "civil union/equalrights" frame). Results indicated framing effects that were,in all cases, contingent on the ideological leanings of thegroup. The "marriage" frame tended to polarize group discussionsalong ideological lines. Both liberal and conservative groupsappeared to find their opponents’ frame more provocative,responding to them with a larger number of statements and expressinggreater ambivalence than when reacting to more hospitable frames.     

Consistency between tastes and values: A universalization approach

The object of this paper is to propose a consistency test for an individual involved in collective choice process. Collective choice processes considered in the paper are those that transform individuals ‘tastes’– which reflect the self-interested view point of the individuals – into (social) ranking of alternatives. In addition to her tastes, an individual has values about the way by which collective decision should be made. We distinguish two categories of such values. First, there are end-values that restrict the class of social rankings that the individual considers ethically acceptable. Second there are aggregation-values that specify the way by which the social ranking should depend upon the individuals tastes. The consistency test stands on an hypothetical operation of universalization of the individual tastes to everyone. Five illustrations of the potential usefulness of our approach for interpreting social choice theory and welfare economics are proposed. These illustrations deal with utilitarian aggregation in the presence of income inequality aversion, the so-called ‘ethics of responsibility’ and the aggregation of individual ranking of opportunity sets based on their freedom of choice. A discussion of the relevance of the consistency test for addressing the problem of ‘laundering’ individual preferences is also provided. Received: 25 June 1998/Accepted: 16 March 1999     

Collective violence as social control

Collective violence is often social control: self-help by a group. It typically defines and responds to conduct as deviant. When unilateral and nongovernmental, it appears in four major forms—lynching, rioting, vigilantism, and terrorism—each distinguished by its system of liability (individual or collective) and degree of organization (higher or lower). Following Donald Black's paradigm of pure sociology, the central assumption is that collective violence varies with its location and direction in social space—the conflict structure. I offer ten propositions that predict and explain the likelihood and severity of collective violence in general and the four forms of collective violence in particular. Conflict structures with a high degree of relational distance, cultural distance, functional independence, and inequality between the adversaries are associated with collective violence in general. Each of the four forms depends on the degree of social polarization between the parties as well as the continuity of the deviant behavior to which the violence responds. Earlier versions of this paper were presented at the Annual Meeting of the American Sociological Association, Pittsburgh, Pennsylvania, August 1992, and the Centennial Congress of the International Institute of Sociology, University of Paris (Sorbonne), Paris, June 1993.     

Individuals as authors of human rights: not only addressees

I propose human rights as self-authored through a personality structure of “assertive selfhood.” To that end I identify three features of self-authorship: emergent through collective political action; as a critical stance; and borne by non-idiosyncratic norms. So conceived, human rights require a field of recognition as a social structure supportive of claims to assertive selfhood. I show that the capacity to self-grant depends critically on the participant’s personality structure as well as on the structure of some of the social institutions he or she inhabits. But like any political vision, the project for self-granted human rights has distinct limits, above all with respect to the many inequalities among potential self-authors.     

A quantitative discursive dilemma

The typical judgment aggregation problem in economics and other fields is the following: a group of people has to judge/estimate the value of an uncertain variable y, which is a function of k other variables, i.e., y = D(x ₁, . . . , x _k ). We analyze when it is possible for the group to arrive at collective judgements on the variables that respect D. We consider aggregators that fulfill Arrow’s IIA-condition and neutrality. We show how possibility and impossibility depend on the functional form of D, and generalize Pettit’s (2001) binary discursive dilemma to quantitative judgements.     

Dividing Justly in Bargaining Problems with Claims

Theoretical research on claims problems has concentrated on normative properties and axiomatizations of solution concepts. We complement these analyses by empirical evidence on the predictability of three classical solution concepts in a bankruptcy problem. We examine both people’s impartial normative evaluations as well as their actual negotiation behavior in a bargaining with claims environment. We measure people’s judgments on the normative attractiveness of solution concepts with the help of a survey and also observe actual agreements in a bargaining experiment with real money at stake. We find that the proportional solution is the normatively most attractive rule, whereas actual negotiation agreements are closest to the ‘constrained equal-award’ solution.     

The probability of inconsistencies in complex collective decisions

Many groups make decisions over multiple interconnected propositions. The doctrinal paradox or discursive dilemma shows that propositionwise majority voting can generate inconsistent collective sets of judgments, even when individual sets of judgments are all consistent. I develop a simple model for determining the probability of the paradox, given various assumptions about the probability distribution of individual sets of judgments, including impartial culture and impartial anonymous culture assumptions. I prove several convergence results, identifying when the probability of the paradox converges to 1, and when it converges to 0, as the number of individuals increases. Drawing on the Condorcet jury theorem and work by Bovens and Rabinowicz (2001, 2003), I use the model to assess the truth-tracking performance of two decision procedures, the premise- and conclusion-based procedures. I compare the present results with existing results on the probability of Condorcets paradox. I suggest that the doctrinal paradox is likely to occur under plausible conditions.The author wishes to express his gratitude to Luc Bovens, Matthew Braham, Steven Brams, Bruce Chapman, Philip Pettit, Wlodek Rabinowicz and two anonymous reviewers for helpful comments or discussion. A previous version of this paper was presented at the 2002 Annual Meeting of the European Public Choice Society, Belgirate, Lago Maggiore, Italy, April 2002, and at the Sixth International Meeting of the Society for Social Choice and Welfare, held at the California Institute of Technology, Pasadena, California, July 2002.     

Privacy,technology, and conflict: Emerging issues and action in workplace privacy

IV. Conclusion Growing employee awareness of the degree to which their personal privacy is compromised in the workplace, particularly with regards to information/telecommunicatton-system use and work monitoring, has created an organizational and political climate that may yield significant restrictions on employee monitoring and on how employers maintain and distribute employees’ personal information. While both federal and state governments have generally deferred to the right of the employer-as-owner to set conditions of employment that may include intrusions into employee privacy (Grodin, 1991), a number of statutory restrictions have been promulgated or proposed that will significantly expand employee privacy rights in the workplace. Additionally, it is probable that unions will aggressively assert employee privacy rights within the context of collective bargaining, potentially using employee dissatisfaction with privacy intrusions as a basis for organizing nonunion firms.     

Developing the new socialist Czechoslovak state: abortion,eugenics, and the politics of choice between 1945 and 1962

ABSTRACT

The author analyzes the political and medical discourses surrounding the legalization of abortion in Czechoslovakia in the 1950s and the establishment of the institution of abortion commissions to approve women’s demands. Through a genealogical intersectional lens, she explores the continuity of this rationality, which started to fear the degeneration of the collective more than its depopulation. As the Cold War commenced, for the first time in history Czechoslovak women obtained reproductive rights, particularly when a pregnancy was recognized as a threat to women’s and children’s health. Drawing on biopolitical theories and other critical feminist scholarship that have problematized the liberal underpinnings of choice and autonomy, the author demonstrates how eugenics trespassed from expert circles into politics, and, with the help of planned parenthood, recreated a complex system of socio-biological classes, determining who should reproduce and whose life was worth living, and worth protecting. The text defies the classic totalitarian thesis that divides peoples and society into two types, the totalitarian subject and its liberal counterpart. The author argues that, regardless of the political system, abortion rights operate as a regulatory strategy of power aimed at maintaining a certain population optimum by re-defining women’s responsibilities to deliver a healthy child into a healthy environment.