Efficiency-free characterizations of the Kalai–Smorodinsky bargaining solution

Roth (1977) axiomatized the Nash (1950) bargaining solution without Pareto optimality, replacing it by strong individual rationality in Nash’s axiom list. In a subsequent work (Roth, 1979) he showed that when strong individual rationality is replaced by weak individual rationality, the only solutions that become admissible are the Nash and the disagreement solutions. In this paper I derive analogous results for the Kalai–Smorodinsky (1975) bargaining solution.     

A lemma in open sequential voting by veto

The paper is devoted to the investigation of intuitively rational choice in a hierarchical game that is a model of election by open sequential veto-voting. Casting a veto against voter’s least preferred alternative (among remaining ones) may not lead to a sophisticated equilibrium. It means that sincere choice (being intuitive) is not rational. There arises the problem of finding conditions under which a sophisticated optimal sequence of actions is intuitively rational. We prove that in the case of strict preference ordering of alternatives, there exists an intuitively rational sophisticated optimal sequence. In the sequence, each voter vetoes an alternative less preferred than the sophisticated equilibrium outcome. Thus, only intuitively rational strategies are to be considered, although complete information about voters’ preferences is still needed.     

A quantitative Arrow theorem

Arrow’s Impossibility theorem states that any constitution which satisfies independence of irrelevant alternatives (IIA) and unanimity and is not a dictator has to be non-transitive. In this paper we study quantitative versions of Arrow theorem. Consider n voters who vote independently at random, each following the uniform distribution over the six rankings of three alternatives. Arrow’s theorem implies that any constitution which satisfies IIA and unanimity and is not a dictator has a probability of at least 6^?n for a non-transitive outcome. When n is large, 6^?n is a very small probability, and the question arises if for large number of voters it is possible to avoid paradoxes with probability close to 1. Here we give a negative answer to this question by proving that for every ${\epsilon > 0}$ , there exists a ${\delta = \delta(\epsilon) > 0}$ , which depends on ${\epsilon}$ only, such that for all n, and all constitutions on three alternatives, if the constitution satisfies:

• The IIA condition.
• For every pair of alternatives a, b, the probability that the constitution ranks a above b is at least ${\epsilon}$ .
• For every voter i, the probability that the social choice function agrees with a dictatorship on i at most ${1-\epsilon}$ .

Then the probability of a non-transitive outcome is at least δ. Our results generalize to any number k ≥ 3 of alternatives and to other distributions over the alternatives. We further derive a quantitative characterization of all social choice functions satisfying the IIA condition whose outcome is transitive with probability at least 1 ? δ. Our results provide a quantitative statement of Arrow theorem and its generalizations and strengthen results of Kalai and Keller who proved quantitative Arrow theorems for k?=?3 and for balanced constitutions only, i.e., for constitutions which satisfy for every pair of alternatives a, b, that the probability that the constitution ranks a above b is exactly 1/2. The main novel technical ingredient of our proof is the use of inverse-hypercontractivity to show that if the outcome is transitive with high probability then there are no two different voters who are pivotal with for two different pairwise preferences with non-negligible probability. Another important ingredient of the proof is the application of non-linear invariance to lower bound the probability of a paradox for constitutions where all voters have small probability for being pivotal.     

Systemic decision making in AHP: a Bayesian approach

Systemic decision making is a new approach for dealing with complex multiactor decision making problems in which the actors’ individual preferences on a fixed set of alternatives are incorporated in a holistic view in accordance with the “principle of tolerance”. The new approach integrates all the preferences, even if they are encapsulated in different individual theoretical models or approaches; the only requirement is that they must be expressed as some kind of probability distribution. In this paper, assuming the analytic hierarchy process (AHP) is the multicriteria technique employed to rank alternatives, the authors present a new methodology based on a Bayesian analysis for dealing with AHP systemic decision making in a local context (a single criterion). The approach integrates the individual visions of reality into a collective one by means of a tolerance distribution, which is defined as the weighted geometric mean of the individual preferences expressed as probability distributions. A mathematical justification of this distribution, a study of its statistical properties and a Monte Carlo method for drawing samples are also provided. The paper further presents a number of decisional tools for the evaluation of the acceptance of the tolerance distribution, the construction of tolerance paths that increase representativeness and the extraction of the relevant knowledge of the subjacent multiactor decisional process from a cognitive perspective. Finally, the proposed methodology is applied to the AHP-multiplicative model with lognormal errors and a case study related to a real-life experience in local participatory budgets for the Zaragoza City Council (Spain).     

Restricted domains,arrow-social welfare functions and noncorruptible and non-manipulable social choice correspondences: The case of private alternatives

An n-person social choice problem is considered in which the alternatives are n dimensional vectors, with the ith component of such a vector being the part of the alternatives affecting individual i alone. Assuming that individuals are selfish (individual i must be indifferent between any two alternatives with the same components), that they may be indifferent among alternatives and that each individual may choose his preferences out of a different set of permissible preferences, we prove that any set of restricted domains of preferences admits an n person non-dictatorial Arrow-type social welfare function if and only if it admits a two-person Arrow-type social welfare function: we characterize all the sets of restricted domains of preferences which admit two-person Arrow-type social welfare functions (and therefore also admit n-person Arrow-type social welfare functions) and then we prove that we also characterized all the sets of restricted domains of preferences which admit nondictatorial, nonmanipulable, noncorruptible and rational social choice correspondences.     

On the difficulty of extending the coco value to games with more than two players

Kalai and Kalai (2013) presented five axioms for solutions of 2-person semi-cooperative games: games in which the basic data specifies individual strategies and payoffs, but in which the players can sign binding contracts and make utility transfers. The axioms pin down a unique solution, the coco value. I show that if one adds a mild dummy player axiom to the list, then the axioms become inconsistent when there are more than two players.     

Preseparable Extensions of Multidimensional Preferences

Throughout much of the literature in economics and political science, the notion of separability provides a mechanism for characterizing interdependence within individual preferences over multiple dimensions. In this paper, we show how preseparable extensions can be used to construct certain classes of separable and non-separable preferences. We prove several associated combinatorial results, and we note a correspondence between separable preference orders, Boolean term orders, and comparative probability relations. We also mention several open questions pertaining to preseparable extensions and separable preferences. This work was partially supported by National Science Foundation grant DMS-0451254, which funds a Research Experience for Undergraduates program at Grand Valley State University. Portions of this paper are adapted from Hodge’s doctoral dissertation [4]. The authors wish to thank the referees and editor for their helpful comments and suggestions.     

Rationality,emotion and preference change Drama-theoretic models of choice

Traditional models of “rational choice”, such as those based on Game Theory and Decision Theory tend to work on the assumption that aims/preferences can be specified prior to the decision process, and remain fixed during it. Other approaches, by contrast, stress the dynamics of preference change and problem re-formulation. In the context of conflict and cooperation analysis, we have recently attempted to bridge these two traditions by introducing drama-theoretic models. This paper reviews some theories about preference change from this standpoint, some concerning individual preferences (including the role of emotions), others introducing group and organisational dimensions. We suggest that it possible to build dynamic models of choice which use the paradoxes of rational choice to link and systematise research both on the strategic role of emotions and on the strategic use of argumentation.     

考虑横向公平偏好的项目团队成员知识共享激励研究

现有知识共享激励研究大都建立在理性经济人假设基础上,而在现实经济活动中,这一假设存在较大局限性。本文将传统个体激励和团队激励相分离的激励模式转化为整合激励模式,运用博弈模型构建了基于横向公平偏好的知识共享激励模型,并对模型进行检验与数据模拟,结果表明:项目团队成员知识共享个体激励和团队激励均衡状态下,个体激励和团队激励对成员的知识共享努力水平具有互补性。知识共享风险成本较低(高)情形下,个体激励与横向公平偏好负相关(呈倒U型关系),团队激励与横向公平偏好正相关(呈U型关系)。     

Eliciting and mapping qualitative preferences to numeric rankings in group decision making

Group work is becoming the norm in organizations. From strategy planning committees to quality management teams, organizational members are collaborating on problem solving. One area of team support that is often desired is the scoring and ranking of decision alternatives on qualitative/subjective domains, and the aggregation of individual preferences into group preferences. In this paper we present a new conceptual approach to qualitative preference elicitation and aggregation. This approach is based on well established decision analysis techniques. It significantly advances the state of the art of group decision making by addressing four common limitations: (1) the inability to deal with vagueness of human decision makers in articulating preferences; (2) difficulties in mapping qualitative evaluation to numeric estimates; (3) problems in aggregating individual preferences into meaningful group preference; and (4) the lack of simple user friendly techniques for dealing with a large number of decision alternatives. Our approach is easy to implement in stand alone personal computers and groupware. We illustrate this with a real-world problem.     

Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration

This paper considers a decentralized process in many-to-many matching problems. We show that if agents on one side of the market have substitutable preferences and those on the other side have responsive preferences, then, from an arbitrary matching, there exists a finite path of matchings such that each matching on the path is formed by satisfying a blocking individual or a blocking pair for the previous matching, and the final matching is pairwise-stable. This implies that an associated stochastic process converges to a pairwise-stable matching in finite time with probability one, if each blocking individual or pair is satisfied with a positive probability at each period along the process.     

Comonotone and coconvex rational interpolation and approximation

Comonotonicity and coconvexity are well-understood in uniform polynomial approximation and in piecewise interpolation. The covariance of a global (Hermite) rational interpolant under certain transformations, such as taking the reciprocal, is well-known, but its comonotonicity and its coconvexity are much less studied. In this paper we show how the barycentric weights in global rational (interval) interpolation can be chosen so as to guarantee the absence of unwanted poles and at the same time deliver comonotone and/or coconvex interpolants. In addition the rational (interval) interpolant is well-suited to reflect asymptotic behaviour or the like.     

Is the inf-convolution of law-invariant preferences law-invariant?

We analyze the question of whether the inf-convolution of law-invariant risk functionals (preferences) is still law-invariant. In other words, we try to understand whether the representative economic agent (after risk redistribution) only cares about the distribution of the total risk, assuming all individual agents do so. Although the answer to the above question seems to be affirmative for many examples of commonly used risk functionals in the literature, the situation becomes delicate without assuming specific forms and properties of the individual functionals. We illustrate with examples the surprising fact that the answer to the main question is generally negative, even in an atomless probability space. Furthermore, we establish a few very weak conditions under which the answer becomes positive. These conditions do not require any specific forms or convexity of the risk functionals, and they are the richness of the underlying probability space, and monotonicity or continuity of one of the risk functionals. We provide several examples and counter-examples to discuss the subtlety of the question on law-invariance.     

Duality,area-considerations,and the Kalai–Smorodinsky solution

We introduce a new solution concept for $2$-person bargaining problems, which can be considered as the dual of the Equal-Area solution (EA) (see Anbarc? and Bigelow (1994)). Hence, we call it the Dual Equal-Area solution (DEA). We show that the point selected by the Kalai–Smorodinsky solution (see Kalai and Smorodinsky (1975)) lies in between those that are selected by EA and DEA. We formulate an axiom–area-based fairness–and offer three characterizations of the Kalai–Smorodinsky solution in which this axiom plays a central role.     

Multicriteria choice based on criteria importance methods with uncertain preference information

Multicriteria choice methods are developed by applying methods of criteria importance theory with uncertain information on criteria importance and with preferences varying along their scale. Formulas are given for computing importance coefficients and importance scale estimates that are “characteristic” representatives of the feasible set of these parameters. In the discrete case, an alternative with the highest probability of being optimal (for a uniform distribution of parameter value probabilities) can be used as the best one. It is shown how such alternatives can be found using the Monte Carlo method.     

A distributed social choice protocol for combinatorial domains

In this paper, we study the problem of collective decision-making over combinatorial domains, where the set of possible alternatives is a Cartesian product of (finite) domain values for each of a given set of variables, and these variables are not preferentially independent. Due to the large alternative space, most common rules for social choice cannot be directly applied to compute a winner. In this paper, we introduce a distributed protocol for collective decision-making in combinatorial domains, which enjoys the following desirable properties: (i) the final decision chosen is guaranteed to be a Smith member; (ii) it enables distributed decision-making and works under incomplete information settings, i.e., the agents are not required to reveal their preferences explicitly; (iii) it significantly reduces the amount of dominance testings (individual outcome comparisons) that each agent needs to conduct, as well as the number of pairwise comparisons; (iv) it is sufficiently general and does not restrict the choice of preference representation languages.     

Where do preferences come from?

Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Preferences are usually assumed to be fixed and exogenously given. Building on related work on reasons and rational choice (Dietrich and List, Nous, forthcoming), we describe a framework for conceptualizing preference formation and preference change. In our model, an agent’s preferences are based on certain ‘motivationally salient’ properties of the alternatives over which the preferences are held. Preferences may change as new properties of the alternatives become salient or previously salient properties cease to be salient. Our approach captures endogenous preferences in various contexts and helps to illuminate the distinction between formal and substantive concepts of rationality, as well as the role of perception in rational choice.     

复有理型插值一致逼近函数及其导数

本文研究在单位圆周{|z| =1}上一致逼近函数f(z)及其导数,利用Hermite插值中的基函数建立复有理型插值,并证明它们在{|z| =1}上分别一致收敛于f(z)或f′(z) ,给出了收敛速度.     

A collective choice method based on individual preferences relational systems (p.r.s.)

In group decision-making literature, several procedures are proposed in order to establish a collective preference from the different individual ones. The majority of these procedures, however, reveal that the individual preferences are always expressed in total pre-orders (or ranking). Indeed, until now very few have considered individual preferences which are expressed in partial pre-orders or, more generally, in preferences relational systems (p.r.s.). Moreover, many of these procedures generate collective preferences which are expressed in total pre-orders (ranking decision-making problematic). The efforts reported in the literature to develop procedures which treat other decision-making problematics—such as choice problematic—remain insufficient. In this paper, we propose a method which would determine from individual p.r.s. at least one collective subset containing the “best” alternatives. Each of these collective subsets results from the exploitation—according to the choice problematic—of a collective p.r.s. obtained from the aggregation of the individual p.r.s. Furthermore, each collective p.r.s. has two main characteristics: (i) it is at a minimum distance from all individual p.r.s. and (ii) it takes into account the members’ relative importance.