Argumentation in Multi-issue Debates

An axiomatic modeling approach to multi-issue debates is proposed. A debate is viewed as a decision procedure consisting of two stages: (1) an “argumentation rule” determines what arguments are admissible for each party, given the “raw data”, depending on the issue or set of issues under discussion; (2) a “persuasion rule” determines the strength of the admissible arguments and selects the winning party. Persuasion rules are characterized for various alternative specifications of the argumentation rule. These characterizations capture rhetorical effects that we sometimes encounter in real-life multi-issue debates.     

Characterizing best–worst voting systems in the scoring context

An increasing body of theoretical and empirical work on discrete choice considers a choice design in which a person is asked to select both the best and the worst alternative in an available set of alternatives, in contrast to more traditional tasks, such as where the person is asked to: select the best alternative; select the worst alternative; rank the alternatives. Here we consider voting systems motivated by such “best–worst” choice; characterize a class of “best–worst” voting systems in terms of a set of axioms in the context of scoring rules; and discuss briefly possible extensions to approval–disapproval systems.     

Endogenous Voting Agendas

Existence of a “simple” pure strategy subgame perfect equilibrium is established in a model of endogenous agenda formation and sophisticated voting; upper hemicontinuity of simple equilibrium outcomes is demonstrated; and connections to the set of undominated, or “core,” alternatives are examined. In one dimension with single-peaked preferences, the simple equilibrium outcome is essentially unique and lies in the core, providing a game-theoretic foundation for the median voter theorem in terms of endogenous agenda setting. Existence of equilibrium relies on a general characterization of sophisticated voting outcomes in the presence of “majority-ties,” rather than the standard tie-breaking convention in voting subgames in favor of the alternative proposed later. The model is illustrated in a three-agent distributive politics setting, and it is shown there that the standard tie-breaking convention leads to non-existence of equilibrium.     

Choosing subsets: a size-independent probabilistic model and the quest for a social welfare ordering

“Subset voting” denotes a choice situation where one fixed set of choice alternatives (candidates, products) is offered to a group of decision makers, each of whom is requested to pick a subset containing any number of alternatives. In the context of subset voting we merge three choice paradigms, “approval voting“ from political science, the “weak utility model” from mathematical psychology, and “social welfare orderings” from social choice theory. We use a probabilistic choice model proposed by Falmagne and Regenwetter (1996) built upon the notion that each voter has a personal ranking of the alternatives and chooses a subset at the top of the ranking. Using an extension of Sen's (1966) theorem about value restriction, we provide necessary and sufficient conditions for this empirically testable choice model to yield a social welfare ordering. Furthermore, we develop a method to compute Borda scores and Condorcet winners from subset choice probabilities. The technique is illustrated on an election of the Mathematical Association of America (Brams, 1988). Received: 18 August 1995 / Accepted: 13 February 1997     

Sophisticated voting and equilibrium refinements under plurality rule

In this paper we show in the context of voting games with plurality rule that the “perfect” equilibrium concept does not appear restrictive enough, since, independently of preferences, it can exclude at most the election of only one candidate. Furthermore, some examples show that there are “perfect” equilibria that are not “proper”. However, also some “proper” outcome is eliminated by sophisticated voting, while Mertens' stable set fully satisfies such criterium, for generic plurality games. Moreover, we highlight a weakness of the simple sophisticated voting principle. Finally, we find that, for some games, sophisticated voting (and strategic stability) does not elect the Condorcet winner, neither it respects Duverger's law, even with a large number of voters. Received: 16 March 1999/Accepted: 25 September 1999     

Aggregated statistical rankings are arbitrary

In many areas of mathematics, statistics, and the social sciences, the intriguing, and somewhat unsettling, paradox occurs where the “parts” may give rise to a common decision, but the aggregate of those parts, the “whole”, gives rise to a different decision. The Kruskal-Wallis nonparametric statistical test on n samples which can be used to rank-order a list of alternatives is subject to such a Simpson-like paradox of aggregation. That is, two or more data sets each may individually support a certain ordering of the samples under Kruskal-Wallis, yet their union, or aggregate, yields a different outcome. An analysis of this phenomenon yields a computable criterion which characterizes which matrices of ranked data, when aggregated, can give rise to such a paradox. Received: 6 November 2001/Accepted: 7 March 2002     

Characterizations of two power indices for voting games with r alternatives

In the first three sections of this paper we present a set of axioms which provide a characterization of an extension of the Banzhaf index to voting games with r alternatives, such as the United Nations Security Council where a nation can vote “yes”, “no”, or “abstain”. The fourth section presents a set of axioms which characterizes a power index based on winning sets instead of pivot sets. Received: 4 April 2000/Accepted: 30 April 2001     

The majoritarian compromise is majoritarian-optimal and subgame-perfect implementable

It is shown that the Majoritarian Compromise of Sertel (1986) is subgame-perfect implementable on the domain of strict preference profiles, although it fails to be Maskin-monotonic and is hence not implementable in Nash equilibrium. The Majoritarian Compromise is Pareto-optimal and obeys SNIP (strong no imposition power), i.e. never chooses a strict majority's worst candidate. In fact, it is “majoritarian approving” i.e. it always picks “what's good for a majority” (alternatives which some majority regards as among the better “effective” half of the available alternatives). Thus, being Pareto-optimal and majoritarian approving, it is majoritarian-optimal. Finally, the Majoritarian Compromise is measured against various criteria, such as consistency and Condorcet-consistency. Received: 31 January 1995/Accepted: 22 July 1998     

On strategy-proof social choice under categorization

I consider social choice problems such that (i) the set of alternatives can be partitioned into categories based on a prominent and objective feature and (ii) agents have strict preferences over the alternatives. Main results are characterizations of the structure of the strategy-proof social choice functions. I prove that each social choice function is strategy-proof if and only if it is decomposable into “small” strategy-proof social choice functions; one of them chooses one category and each of the others chooses one alternative from a category.     

General Representation of Epistemically Optimal Procedures

Assuming that votes are independent, the epistemically optimal procedure in a binary collective choice problem is known to be a weighted supermajority rule with weights given by personal log likelihood ratios. It is shown here that an analogous result holds in a much more general model. Firstly, the result follows from a more basic principle than expected-utility maximisation, namely from an axiom (“Epistemic Monotonicity”) which requires neither utilities nor prior probabilities of the ‘correctness’ of alternatives. Secondly, a person’s input need not be a vote for an alternative; it may be any type of input, for instance a subjective degree of belief or probability of the correctness of one of the alternatives. The case of a profile of subjective degrees of belief is particularly appealing, since no parameters such as competence parameters need to be known here.     

A simple procedure for finding equitable allocations of indivisible goods

The paper investigates how far a particular procedure, called the “descending demand procedure,” can take us in finding equitable allocations of indivisible goods. Both interpersonal and intrapersonal criteria of equitability are considered. It is shown that the procedure generally fares well on an interpersonal criterion of “balancedness”; specifically, the resulting allocations are Pareto-optimal and maximize the well-being of the worst-off individual. As a criterion of intrapersonal equitability, the property of envy-freeness is considered. To accommodate envy-freeness, a modification of the basic procedure is suggested. With two individuals, the modified procedure is shown to select the envy-free allocations that are balanced, i.e. the allocations that maximize the well-being of the worse-off individual among all envy-free allocations. Received: 3 March 2000/Accepted: 27 November 2000     

Strategy-proofness and efficiency in a simple production economy

We consider an economy with two agents, “firm” and “worker.” The firm owns a technology which transforms a single input into a single output and the worker owns a limited amount of input good, for example, leisure. The firm is interested in profit measured in terms of output and the worker's preferences are defined over the input-output space. Manipulability comes not only from a lack of information about the (worker's) preferences but also about the technology. With a possibility for manipulation, can we still obtain efficient allocations? We show that there is no allocation mechanism which is Pareto efficient, strategy-proof, and non-dictatorial. Received: 30 March 1998/Accepted: 06 July 1999     

Top-Pair and Top-Triple Monotonicity

We say that a social choice function (SCF) satisfies Top-k Monotonicity if the following holds. Suppose the outcome of the SCF at a preference profile is one of the top k-ranked alternatives for voter i. Let the set of these k alternatives be denoted by B. Suppose that i’s preference ordering changes in such a way that the set of first k-ranked alternatives remains the set B. Then the outcome at the new profile must belong to B. This definition of monotonicity arises naturally from considerations of set “improvements” and is weaker than the axioms of strong positive association and Maskin Monotonicity. Our main results are that if there are two voters then a SCF satisfies unanimity and Top-2 or Top-pair Monotonicity if and only if it is dictatorial. If there are more than two voters, then Top-pair Monotonicity must be replaced by Top-3 Monotonicity (or Top-triple Monotonicity) for the analogous result. Our results demonstrate that connection between dictatorship and “improvement” axioms is stronger than that suggested by the Muller–Satterthwaite result (Muller and Satterthwaite in J Econ Theory 14:412–418, 1977) and the Gibbard–Sattherthwaite theorem.     

Existence of a coalitionally strategyproof social choice function: A constructive proof

This paper gives a concrete example of a nondictatorial, coalitionally strategyproof social choice function for countably infinite societies. The function is defined for those profiles such that for each alternative, the coalition that prefers it the most is “describable.” The “describable” coalitions are assumed to form a countable Boolean algebra. The paper discusses oligarchical characteristics of the function, employing a specific interpretation of an infinite society. The discussion clarifies within a single framework a connection between the negative result (the Gibbard-Satterthwaite theorem) for finite societies and the positive result for infinite ones. Received: 10 August 1998/Accepted: 29 February 2000     

Conflicts between activist research and academic success: Participatory research and alternative strategies

The article compares participatory research and alternative activist approaches, based on the literature on participatory research and interviews with nine successful sociologists who use alternative approaches. Participatory research, distinguished by high control over research by community members, equalizes power within the research process, but often retards academic publication and career advancement. The interviews show that successful academics retain control over their research, experience mild to severe conflicts with departments, and develop various strategies for combining activism and career success. All types of activist research are more effective in challenging inequality if they involve activist community organizations. Her research has focused on family, gender, and feminist and participatory methods. Recent publications includeLove in America, “Feminist Science,” and “Participatory Research” with Cathleen Armstead. Her current participatory research project explores “Family and Community Caring” in a Mexican-American community. Address for correspondence: Francesca M. Cancian, University of CA, Dept. of Sociology, Irvine, CA 92717.     

Dictatorial domains in preference aggregation

We call a domain of preference orderings “dictatorial” if there exists no Arrovian (Pareto optimal, IIA and non-dictatorial) social welfare function defined over that domain. In a finite world of alternatives where indifferences are ruled out, we identify a condition which implies the dictatoriality of a domain. This condition, to which we refer as “being essentially saturated”, is fairly weak. In fact, independent of the number of alternatives, there exists an essentially saturated (hence dictatorial) domain which consists of precisely six orderings. Moreover, this domain exhibits the superdictatoriality property, i.e., every superdomain of it is also dictatorial. Thus, given m alternatives, the ratio of the size of a superdictatorial domain to the size of the full domain may be as small as 6/m!, converging to zero as m increases.     

Identifying X-Consumers Using Causal Recipes: “Whales” and “Jumbo Shrimps” Casino Gamblers

X-consumers are the extremely frequent (top 2–3%) users who typically consume 25% of a product category. This article shows how to use fuzzy-set qualitative comparative analysis (QCA) to provide “causal recipes” sufficient for profiling X-consumers accurately. The study extends Dik Twedt’s “heavy-half” product users for building theory and strategies to nurture or control X-behavior. The study here applies QCA to offer configurations that are sufficient in identifying “whales” and “jumbo shrimps” among X-casino gamblers. The findings support the principle that not all X-consumers are alike. The theory and method are applicable for identifying the degree of consistency and coverage of alternative X-consumers among users of all product-service category and brands.     

Parent and Peer Attachment in Minority Males at High Risk for Delinquency

Juvenile delinquency and high risk behaviors have been linked to disturbances in attachment. The present study examined parent and peer attachment in 67 African American males and 97 Latinos (ages 12–17, M = 14.7 ± 1.3) attending an alternative school. The Inventory of Parent and Peer Attachment was used to identify 3 attachment style groups: “Isolated,” “Disconnected,” and “Connected.” Controlling for age, attachment group membership predicted differences in delinquent behaviors, as did ethnicity. Further, on the Youth Self-Report of the Child Behavior Checklist, attachment group membership predicted differences in both the Internalizing and Externalizing Scales. Implications for interventions with each identified attachment group are discussed.     

Constitutions, voting and democracy: A review

This review of William Riker's work suggests that his interest in rational choice theory was based on his desire to understand profound constitutional transformation in U.S. political history. Although he argued that “anything can happen in politics,” his use of the notion of heresthetic allowed him to focus on key contingent events. Indeed his later work added depth to his inductive generalizations on the nature of “federal bargains” and coalition formation.  Recent work by Austen-Smith and Banks, Merrill and Grofman, and Lijphart is also discussed in the light of Riker's earlier ideas on voting and democracy. Received: 25 February 2000/Accepted: 16 March 2000     

On the manipulation of social choice correspondences

Duggan and Schwartz (Soc Choice and Welfare 17: 85–93, 2000) have proposed a generalization of the Gibbard–Satterthwaite Theorem to multivalued social choice rules. They show that only dictatorial rules are strategy-proof and satisfy citizens sovereignty and residual resoluteness. Citizens sovereignty requires that each alternative is chosen at some preference profile. Residual resoluteness compels the election to be single-valued when the preferences of the voters are “similar”. We propose an alternative proof to the Duggan and Schwartz’s Theorem. Our proof highlights the crucial role of residual resoluteness. In addition, we prove that every strategy-proof and onto social choice correspondence concentrates the social decision power in the hands of an arbitrary group of voters. Finally, we show that this result still holds in a more general framework in which voters report their preferences over sets of alternatives.