Intensity of preference and related uncertainty in non-compensatory aggregation rules

Non-compensatory aggregation rules are applied in a variety of problems such as voting theory, multi-criteria analysis, composite indicators, web ranking algorithms and so on. A major open problem is the fact that non-compensability implies the analytical cost of loosing all available information about intensity of preference, i.e. if some variables are measured on interval or ratio scales, they have to be treated as measured on an ordinal scale. Here this problem has been tackled in its most general formulation, that is when mixed measurement scales (interval, ratio and ordinal) are used and both stochastic and fuzzy uncertainties are present. Objectives of this article are first to present a comprehensive review of useful solutions already proposed in the literature and second to advance the state of the art mainly in the theoretical guarantee that weights have the meaning of importance coefficients and they can be summarized in a voting matrix. This is a key result for using non-compensatory Condorcet consistent rules. A proof on the probability of existence of ties in the voting matrix is also developed.     

A graph-theoretical approach to the aggregation of individual preference orderings

A graph-theoretical approach as first outlined by Harary et al. is developed for solving the problem of aggregating a given set of individual preference orderings provided that no individual preferential judgment is inconsistent with the collective preference ordering obtained by aggregation.

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Changes in preference

A basic framework for studies of changes in preference is introduced, and four types of changes in preference are identified.Revision by a sentence such as A is better thanB means that a preference forA overB is acquired. The result ofcontraction by A is better thanB is that the subject no longer holdsA to be better thanB. Inaddition andsubtraction, an alternative is added to, or subtracted from, respectively, the set of alternatives that are under consideration. Formal models of these four types of change are introduced, and they are shown to satisfy plausible postulates for rational changes in preferences.     

中国城市居民委员会的工作比较研究：上海与沈阳

居委会作为街道办事处“派出机构”的角色在客观上已经凌驾于“群众性自治组织”的法律定位之上。相应地,居委会工作人员在长期担当政府代理人角色的路径依赖之下,主观上已经把与社区发展息息相关的日常政务工作建构为社区内部事务。因此,社区建设的实质是基层社会治理结构的建设,它需要国家力量给基层社会的自我运作让渡出一定的空间,而要实现这一目标,关键性的基本前提是政府职能部门的基层管理和服务工作一定要到位,创造性的制度变革是顺应不同性质组织功能的要求,构建“社区建设指导委员会（政府）-社区管理委员会（社会联合体）-社区工作者（专业服务组织）-社区居委会（自治性组织）”的社区治理结构体系。     

Stochastic revealed preference and rationalizability

This article explores rationalizability issues for finite sets of observations of stochastic choice in the framework introduced by Bandyopadhyay et al. (Journal of Economic Theory, 84(1), 95–110, 1999). It is argued that a useful approach is to consider indirect preferences on budgets instead of direct preferences on commodity bundles. A new rationalizability condition for stochastic choices, “rationalizable in terms of stochastic orderings on the normalized price space” (rsop), is defined. rsop is satisfied if and only if there exists a solution to a linear feasibility problem. The existence of a solution also implies rationalizability in terms of stochastic orderings on the commodity space. Furthermore it is shown that the problem of finding sufficiency conditions for binary choice probabilities to be rationalizable bears similarities to the problem considered here.     

Revealed preference and linear utility

We study a Linear Axiom of Revealed Preference (LARP) that characterizes the consistency of a choice function with respect to a preference order satisfying the independence axiom. In addition, LARP characterizes lexicographic linear utility rationality when the choice space is a convex subset of a finite-dimensional real vector space, and LARP characterizes linear utility rationality when the choice space corresponds to a finite choice experiment.     

Prudence and extensionality in theories of preference and value

Luce's axiom governing probabilities of choice is formulated as a principle governing metalinguistic probabilities. IfX, Y, W are sets of options, and δ(X), δ(Y), δ(W) are sentences asserting that choice is made from these sets, then the axiom is $$\begin{gathered} If \pi [\delta (X)] \ne 0 and \pi [\delta (X \cap Y)] \ne 0, then \hfill \\ \pi _{\delta (X)} [\delta (Y \cap W)] = \pi _{\delta (X \cap Y)} [\delta (W)]\pi _{\delta (X)} [\delta (Y)] \hfill \\ \end{gathered} $$ where π is a probability on sentences. The axiom is then entailed by extensionality of the probability π in company with a simple condition on probabilities of truth-functions. Conditions are also given under which the probability π is uniquely represented by a probability on the sets of options. What look to be logical constraints on the metalanguage entail a normative or prudential constraint. Debreu's well-known counterinstance to the axiom as a principle governing probability of choice is examined and a novel and consistent interpretation of the axiom is proposed.     

Bare preference and interpersonal utility comparisons

From time to time it has been proposed to use just noticeable preference intervals as standard intervals upon which to base interpersonal utility comparisons. Such proposals have met with a number of difficulties due especially to the discovery that such intervals are difficult to take as representing equal differences in utility even for one individual.In this paper I suggest conditions upon individual utility functions which, if satisfied, would make such bare preference intervals useful as a basis for interpersonal utility comparisons even if the intervals are not interpreted as representing equal utility differences for any single individual.     

Indecisiveness aversion and preference for commitment

We present an axiomatic model of preferences over menus that is motivated by three assumptions. First, the decision maker is uncertain ex ante (i.e., at the time of choosing a menu) about her ex post (i.e., at the time of choosing an option within her chosen menu) preferences over options, and she anticipates that this subjective uncertainty will not resolve before the ex post stage. Second, she is averse to ex post indecisiveness (i.e., to having to choose between options that she cannot rank with certainty). Third, when evaluating a menu she discards options that are dominated (i.e., inferior to another option whatever her ex post preferences may be) and restricts attention to the undominated ones. Under these assumptions, the decision maker has a preference for commitment in the sense of preferring menus with fewer undominated alternatives. We derive a representation in which the decision maker’s uncertainty about her ex post preferences is captured by means of a subjective state space, which in turn determines which options are undominated in a given menu, and in which the decision maker fears, whenever indecisive, to choose an option that will turn out to be the worst (undominated) one according to the realization of her ex post preferences.     

On the significance of the prior of a correct decision in committees

The current note clarifies why, in committees, the prior probability of a correct collective choice might be of particular significance and possibly should sometimes even be the sole appropriate basis for making the collective decision. In particular, we present sufficient conditions for the superiority of a rule based solely on the prior relative to the simple majority rule, even when the decisional skills of the committee members are assumed to be homogeneous.     

Preference aggregation and statistical estimation

This paper deals with various connections that are found to exist between statistical estimation methods for decision-making and rules of group choice in the social choice area. Initially the aggregation of individual opinions is formulated as a pattern recognition problem; firstly it is shown that individual preferences lead to a natural representation in terms of binary patterns. Then we proceed to show how the search for a group preference pattern can be conducted by classifying the input preference patterns into various pattern classes and using the resulting classification boundaries to define the area of mutual agreement over some of the available alternatives. This leads to a decision-theoretic problem which consists in defining a decision rule (for classification) that is least likely to lead to misrecognition of arbitrary preference patterns. A maximum likelihood solution is obtained and compared with some well-known rules of group decision-making. Other solutions are also possible, on the basis of different optimality criteria, and their social choice interpretation is suggested. Finally, a method using Coleman's linear model for attributes is applied to yield group decision rules by feature weighting of election issues.     

Complementary relations in the theory of preference

(1) This paper uses the following binary relations: > (is preferred to); ⩽ (is not preferred to); < (is less preferred than); ~ (is indifferent to). (2) Savage used primitive ⩾, postulated to be connected and transitive onA (the set of acts), to define the others: [x ~ y ⇔ (x ⩽ y and y ⩽ x)]; [y < x ⇔ notx ⩽ y]; [x > y ⇔ y < x]. Independently of the axioms, this definition implies that ⩽ and > are complementary relations onA: [x < y ⇔ notx > y]. (3) Pratt, Raiffa and Schlaifer used primitive ⩽, postulated to be transitive onL (the set of lotteries), to define the others with a different expression for <: [x < y ⇔ (x ⩽ y and noty ⩽ x)]. Thus, ⩽ and > are not necessarily complementary onL; since ⩽ is not postulated to be connected onL, but connected ⩽ is necessary and sufficient for such complementarity. Since the restriction of ⩽ to the subsetA ofL is connected, ⩽ and > are complementary onA. (4) Fishburn used primitive < onA to define the others with different expression for ~ and ⩽: [x ~ y ⇔ (notx < y and noty < x)]; [x ⩽ y ⇔ (x < y orx ~ y)]. His version of Savage's theory then assumed that < is asymmetric and negatively transitive onA. Thus, ⩽ and > are complementary, since asymmetric < is necessary and sufficient for such complementarity. (5) This analysis provides a new proof that the same list of elementary properties of binary relations onA applies to all three theories: ⩽ is connected, transitive, weakly connected, reflexive, and negatively transitive; while both < and > are asymmetric, negatively transitive, antisymmetric, irreflexive, and transitive; but only ~ is symmetric.     

Genetic screening technology: ethical issues in access to tests by employers and health insurance committees

Whereas the introduction of new technologies previously has raised the ethical question of who ought to have access to a new procedure or device, genetic testing technology raises the new ethical question of to whom access to a new technology ought to be limited. In this article we discuss the implications of employers and private health insurance companies having access to genetic testing technology. Although there may be legitimate business interests in allowing employers and insurers to conduct genetic screening, there are other valid societal interests in regulating or limiting the use of this technology by third parties. Public policy developed in the area of new genetic technology must reflect such interests.     

Set and revealed preference axioms for multi-valued choice

Theory and Decision - We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We...     

Risk-taking activities and heterogeneity of job-risk tradeoffs

Using data from a large national sample, this article examines how individual differences in risk attitudes affect wage-risk tradeoffs. Smoking and seat belt use are used as proxies for individual willingness to bear risk. Workers who by their behavior indicate a high value of safety-e.g., nonsmokers and seat belt wearers-receive a higher compensating differential per unit of job risk than do workers who engage in either one of the risky behaviors. For the overall sample, the implicit value of a lost workday injury is $79,632. This value ranges from $54,878 for smokers who do not wear a seat belt, to $102,552 for nonsmokers who wear a seat belt.     

Cooperation and preference by peers in early childhood: A longitudinal study

Children who are more proficient in cooperation with peers tend to be more preferred. To date, the development of peer cooperation has been studied mainly in two research traditions, one focusing on action coordination and the other focusing on interaction quality. Both aspects of cooperation are relevant for children's peer relations, but it is unclear whether both aspects of children's earliest cooperation skills predict their later preference by peers after the transition into organized social groups in school. In this study, we assessed coordination proficiency and interaction quality of 181 Dutch children longitudinally from 2 to 4 years of age. No relation between early action coordination and later preference by peers at school was found. However, especially in girls more affiliative and fewer antagonistic behaviors at the age of two predicted likeability among classmates at school at the age of four. The findings shine new light on the earliest foundations of children's peer evaluations.