Even-chance lotteries in social choice theory

This paper discusses aspects of the theory of social choice when a nonempty choice set is to be determined for each situation, which consists of a feasible set of alternatives and a preference order for each voter on the set of nonempty subsets of alternatives. The individual preference assumptions include ordering properties and averaging conditions, the latter of which are motivated by the interpretation that subset A is preferred to subset B if and only if the individual prefers an even-chance lottery over the basic alternatives in A to an even-chance lottery over the basic alternatives in B. Corresponding to this interpretation, a choice set with two or more alternatives is resolved by an even-chance lottery over these alternatives. Thus, from the traditional no-lottery social choice theory viewpoint, ties are resolved by even-chance lotteries on the tied alternatives. Compared to the approach which allows all lotteries to compete along with the basic alternatives, the present approach is a contraction which allows only even-chance lotteries.After discussing individual preference axioms, the paper examines Pareto optimality for nonempty subsets of a feasible set in a social choice context with n voters. Aspects of simple-majority comparisons in the even-chance context follow, including an analysis of single-peaked preferences. The paper concludes with an Arrowian type impossibility theorem that is designed for the even-chance setting.     

An axiomatic analysis of the Nash equilibrium concept

The purpose of this paper is to analyze axiomatically the Nash equilibrium concept. The class of games under study is a (relatively large) subclass of n-person normal form games. Solutions are correspondences which associate to each game a non empty set of strategy vectors of this game. It is shown that if a solution satisfies the axioms Independence of irrelevant alternatives (IIA) and Individual rationality (IR), then all the strategy vectors in this solution are Nash equilibria. This result holds good also if IR is replaced by Strong individual monotonicity (SIM) or Weak principle of fair compromise (WPFC).     

Power of Enforcement and Dictatorship

A new Arrovian impossibility is obtained without invoking independence of irrelevant alternatives type assumptions. The new conditions leading to the impossibility are based on the concept of power of enforcement, and specify how this power can (see A3) or cannot be expanded (see A1, A2 and A4).     

What if utility functions do not exist?

Often the preferences of decision-makers are sufficiently inconsistent so as to preclude the existence of a utility function in the classical sense. Several alternatives for dealing with this situation are discussed. One alternative, that of modifying classical demands on utility functions, is emphasized and described in the context of the theory of measurement developed in recent years by behavioral scientists. The measurement theory approach is illustrated by discussing the concept of the dimension of a partial order. Even if we cannot assign numerical utility or worth values which reflect preferences in the classical utility function sense, from the measurement theory point of view we can still learn a lot about the preferences by finding several measures of worth so that a given alternative x is preferred to an alternative y if and only if x is ranked higher than y on each of the worth scales. If such measures can be found, it follows that the preferences define a partial order, and the smallest number of such scales needed is called the dimension of the partial order. If one-dimensional preferences (those amenable to classical utility assignments) cannot be found, then the next best thing is to search for partially ordered preferences with as small a dimension as possible. Several conditions under which a partial order is two-dimensional are described.The author acknowledges the helpful comments of Joel Spencer and Ralph Strauch. He also thanks Kirby Baker and Peter Fishburn for permission to quote freely from earlier joint work on two-dimensional partial orders.     

Alternative Housing

Many types of housing for older people that do not fit into traditional categories have been proposed, and some have been activated. A number of models are discussed, including the boarding/rooming house, cooperatives, house-sharing arrangements, hotels, mobile homes, community housing, the "granny flat," group homes, and foster homes. The ways in which each housing type meets basic residential needs are considered, including needs for a familiar environment, independence, privacy, personal security, social interaction, and social support. Most alternative housing models are of low appeal, solutions that are turned to either when other alternatives are unavailable or when personal needs happen to fit a particular alternative especially well. For both reasons, it is important to understand and foster the development of such alternatives, even if the numbers served will never be really large.     

Stochastic superiority

This paper introduces a definition of stochastic superiority. One random variable is stochastically superior to another whenever it stochastically dominates the other after the risk in each random variable has been optimally reduced. Stochastic superiority is implied by stochastic dominance, but the reverse is not true. Stochastic superiority allows more pairs of random alternatives to be ranked, and efficient sets to be smaller. A very strong sufficient condition for stochastic superiority is demonstrated to also be necessary when preferences are risk averse. This condition provides a relatively easy way to conduct stochastic superiority tests. As an alternative to “almost stochastic dominance,” stochastic superiority also provides a natural solution to the “left tail problem” that arises often when comparing random alternatives.

     

It Takes a Village to Deliver and Test Child and Family-Focused Services

OBJECTIVES: The purpose of this article is to highlight the benefits of collaboration in child focused mental health services research. METHOD: Three unique research projects are described. These projects address the mental health needs of vulnerable, urban, minority children and their families. In each one, service delivery was codesigned, interventions were co-delivered and a team of stakeholders collaboratively tested the impact of each one. RESULTS: The results indicate that the three interventions designed, delivered, and tested are associated with reductions in youth mental health symptoms. CONCLUSION: These interventions are feasible alternatives to traditional individualized outpatient treatment.     

Better May be Worse: Some Monotonicity Results and Paradoxes in Discrete Choice Under Uncertainty

It is not unusual in real-life that one has to choose among finitely many alternatives when the merit of each alternative is not perfectly known. Instead of observing the actual utilities of the alternatives at hand, one typically observes more or less precise signals that are positively correlated with these utilities. In addition, the decision-maker may, at some cost or disutility of effort, choose to increase the precision of these signals, for example by way of a careful study or the hiring of expertise. We here develop a model of such decision problems. We begin by showing that a version of the monotone likelihood-ratio property is sufficient, and also essentially necessary, for the optimality of the heuristic decision rule to always choose the alternative with the highest signal. Second, we show that it is not always advantageous to face alternatives with higher utilities, a non-monotonicity result that holds even if the decision-maker optimally chooses the signal precision. We finally establish an operational first-order condition for the optimal precision level in a canonical class of decision-problems, and we show that the optimal precision level may be discontinuous in the precision cost.     

Finite Alternating-Move Arbitration Schemes and the Equal Area Solution

We start by considering the Alternate Strike (AS) scheme, a real-life arbitration scheme where two parties select an arbitrator by alternately crossing off at each round one name from a given panel of arbitrators. We find out that the AS scheme is not invariant to “bad” alternatives. We then consider another alternating-move scheme, the Voting by Alternating Offers and Vetoes (VAOV) scheme, which is invariant to bad alternatives. We fully characterize the subgame perfect equilibrium outcome sets of these above two schemes in terms of the rankings of the parties over the alternatives only. We also identify some of the typical equilibria of these above two schemes. We then analyze two additional alternating-move schemes in which players’ current proposals have to either honor or enhance their previous proposals. We show that the first scheme’s equilibrium outcome set coincides with that of the AS scheme, and the equilibrium outcome set of the second scheme coincides with that of the VAOV scheme. Finally, it turns out that all schemes’ equilibrium outcome sets converge to the Equal Area solution’s outcome of cooperative bargaining problem, if the alternatives are distributed uniformly over the comprehensive utility possibility set and as the number of alternatives tends to infinity. Journal of Economic Literature Classification Number: C72.     

Binary Relations: Finite Characterizations and Computational Complexity

A characterization of a property of binary relations is of finite type if it is stated in terms of ordered T-tuples of alternatives for some positive integer T. The concept was introduced informally by Knoblauch (2005). We give a clear, complete definition below. We prove that a characterization of finite type can be used to determine in polynomial time whether a binary relation over a finite set has the property characterized. We also prove a simple but useful nonexistence theorem and apply it to three examples.      

Stochastic evolution of rationality

Following up on previous results by Falmagne, this paper investigates possible mechanisms explaining how preference relations are created and how they evolve over time. We postulate a preference relation which is initially empty and becomes increasingly intricate under the influence of a random environment delivering discrete tokens of information concerning the alternatives. The framework is that of a class of real-time stochastic processes having interlinked Markov and Poisson components. Specifically, the occurence of the tokens is governed by a Poisson process, while the succession of preference relations is a Markov process. In an example case, the preference relations are the various possible semiorders on the set of alternatives. Asymptotic results are obtained in the form of the limit probabilities of any semiorder. The arguments extend to a much more general situation including interval orders, biorders and partial orders. The results provide (up to a small number of parameters) complete quantitative predictions for panel data of a standard type, in which the same sample of subjects has been asked to compare the alternatives a number of times.     

The Budget-Voting Paradox

The budget-voting paradox states that, when social alternatives are proper subsets of a finite set of decisions, choosing decision-wise according to the majority rule may select an alternative that is covered in the majority tournament among alternatives. Individual preferences are defined on single decisions, and are extended to preferences over the alternative set by means of a preference extension rule. We prove the existence of the paradox for any rank-based, monotone, and independent extension rule.      

Digraph Competitions and Cooperative Games

Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided in terms of game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed.     

Youth Allowances: Incentive & Reform

Australia's income support arrangements have come under increasing scrutiny lately reflecting a growing concern about high levels of youth unemployment and about low levels of full-time education participation. This paper aims to explore the relationship between education participation and financial incentives and to assess as a possible direction for future reform, the concept of a single and universal youth allowance. The paper begins by outlining the major forms of income support available to young people and illustrates some of the complexities in the youth income support structure. The evidence on the importance of financial factors conflicts, particularly between economists and non-economists. This is in part explained by the different conceptual frameworks used. Other possible reasons are canvassed as to why studies have so far not thrown much light on the role of financial factors in the education participation decision. The paper also outlines specific directions of distortion contained in current payment relativities. Several difficulties with the proposal for a single youth allowance as a means of increasing education participation are discussed and alternatives briefly outlined. The concluding section of the paper summarises the issues relevant to the future debate on youth income support and identifies areas for further research.     

“Locals” and “Cosmopolitans”

An analysis is provided of the results of a study of the scholarly productivity of Russian doctors of science in the middle generation who work within the Russian Academy of Sciences system. We show that the scholars’ achievements on the international versus domestic Russian arenas are not only different, but are also only weakly related. This gives reason to conclude that the competencies and social capital of scholars that facilitate their achievements inside the country and abroad are different, and sometimes even alternatives to each other. We also reveal that scholarly citation indexes are insufficient to evaluate domestic Russian achievements by scholars, while the evaluation of their international achievements is much more accurate.     

The uncovered set in spatial voting games

In a majority rule voting game, the uncovered set is the set of alternatives each of which can defeat every other alternative in the space either directly or indirectly at one remove. Research has suggested that outcomes under most reasonable agenda processes (both sincere and sophisticated) will be confined to the uncovered set. Most research on the uncovered set has been done in the context of voting games with a finite number of alternatives and relatively little is known about the properties of the uncovered set in spatial voting games.We examine the geometry of the uncovered set in spatial voting games and the geometry of two important subsets of the uncovered set, the Banks set and the Schattschneider set. In particular, we find both general upper and lower limits on the size of the uncovered set, and we give the exact bounds of the uncovered set for situations with three voters. For situations with three voters, we show that the Banks set is identical to the uncovered set.     

The inferred referendum — A rule for committee decisions

We present a new method of social choice. The result of our method coincides with that of majority voting when it does not produce an intransitivity among the alternatives under consideration. When majority voting would produce an intransitivity, our method orders the alternatives in the same way as the transitive constituency would whom the committee members are most likely to represent. Analysis of the application of our method to three alternatives shows that (a) the resulting order depends only on the committee members' votes between pairs of alternatives (b) the resulting order is less in conflict with Sen's Property than the orders provided by other schemes (c) when majority voting provides an intransitivity, the hypothesis that, in fact, the committee's constituency is as we assume it to be is almost as likely as the hypothesis that it precisely mirrors the committee.     

Model for the distribution process of attitudes in a two-party-system

This article considers a social system where a political decision is to be made. Only two alternatives are permitted: YES or NO. Within the total population A there are two groups, one (X) campaigns for a YES decision, the other one (Y) argues for a NO decision. It is assumed that every individual within the total population has the same opportunities in the field of communications. The question to be answered is as follows: How are the opinions within the total population A distributed after a certain length of time. In our model we use a quantitative concept: The ‘Influence of Opinion in a Two-Party-System’. It is assumed that the relative influence of a group of people having a certain opinion is the stronger, the faster they are able to publicize their decision within the total population A. This and other assumptions (axioms) are formulated more precisely in the following discussion.     

‘q-Pareto-Scalar’ Two-Stage Extremization Model and its Reducibility to One-Stage Model

A two-stage sequential choice model is studied, the first stage being defined by q-Pareto multicriterial choice rule, and the second stage being defined by scalar extremization model. In this model, at the first stage the q-Pareto rule choses alternatives which are not only undominated in terms of Pareto comparison, but also includes into choice the alternatives which are dominated by no more than q alternatives. Since the choice set of the first-stage usually contains too many elements, obtained set is used as a presentation for the second stage constructed by a scalar extremization model. The properties of the model are studied as well as its representability to one-stage scalar extremization model.     

Positionalist voting functions

Positionalist voting functions are those social choice functions where the positions of the alternatives in the voter's preference orders crucially influence the social ordering of the alternatives. An important subclass consists of those voting functions where numbers are assigned to the alternatives in the preference orders and the social ordering is computed from these numbers. Such voting functions are called representable. Various well-known conditions for voting functions are introduced and it is investigated which representable voting functions satisfy these conditions. It is shown that no representable voting function satisfies the Condorcet criterion. This condition and Arrow's independence condition, which are typical non-positionalist conditions, are shown to be incompatible. The Borda function, which is a well-known positionalist voting function, is studied extensively, conditions uniquely characterizing it are given and some modifications of the function are investigated.My thanks are due to professor Bengt Hansson for encouragement and several helpful suggestions.