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.     

When conflict induces the expression of incomplete preferences

Multicriteria conflict arises in pairwise comparisons, where each alternative outperforms the other one on some criterion, which imposes a trade-off. Comparing two alternatives can be difficult if their respective advantages are of high magnitude (the attribute spread is large). In this paper, we investigate to which extent conflict in a comparison situation can lead decision makers to express incomplete preferences, that is, to refuse to compare the two alternatives, or to be unable to compare them with confidence. We report on an experiment in which subjects expressed preferences on pairs of alternatives involving varying conflicts. Results show that depending on whether the participants are allowed to express incomplete preferences or not, attribute spread has a different effect: a large attribute spread increases the frequency of incomparability statements, when available, while it increases the use of indifference statements when only indifference and preference answers are permitted. These results lead us to derive some implications for preference elicitation methods involving comparison tasks.     

The Value of Preference Information in Agency Relationships

Standard models of agency theory often assume that the principal has complete information about the preferences of the agent. This paper starts from the assumption of incomplete information on the agent&2018;s preferences and models a situation where the principal can obtain additional preference information before concluding a contract with the agent. We introduce the concept of a Value of Preference Information (VPI), which describes the benefits to the principal from obtaining such information. This information can be obtained either before or after the principal knows the precise structure of the decision problems which will be delegated to the agent. Analytic and simulation techniques are used to study factors influencing the VPI in these two situations.     

An integrated model-based interactive approach to FMAGDM with incomplete preference information

Incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations are very useful to express decision makers’ incomplete preferences over attributes or alternatives in the process of decision making under fuzzy environments. The aim of this paper is to investigate fuzzy multiple attribute group decision making problems where the attribute values are represented in intuitionistic fuzzy numbers and the information on attribute weights is provided by decision makers by means of one or some of the different preference structures, including weak ranking, strict ranking, difference ranking, multiple ranking, interval numbers, incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations. We transform all individual intuitionistic fuzzy decision matrices into the interval decision matrices and construct their expected decision matrices, and then aggregate all these expected decision matrices into a collective one. We establish an integrated model by unifying the collective decision matrix and all the given different structures of incomplete weight preference information, and develop an integrated model-based approach to interacting with the decision makers so as to adjust all the inconsistent incomplete fuzzy preference relations, inconsistent incomplete linguistic preference relations and inconsistent incomplete multiplicative preference relations into the ones with acceptable consistency. The developed approach can derive the attribute weights and the ranking of the alternatives directly from the integrated model, and thus it has the following prominent characteristics: (1) it does not need to construct the complete fuzzy preference relations, complete linguistic preference relations and complete multiplicative preference relations from the incomplete fuzzy preference relations, incomplete linguistic preference relations and incomplete multiplicative preference relations, respectively; (2) it does not need to unify the different structures of incomplete preferences, and thus can simplify the calculation and avoid distorting the given preference information; and (3) it can sufficiently reflect and adjust the subjective desirability of decision makers in the process of interaction. A practical example is also provided to illustrate the developed approach.     

Interactive group decision-making procedure using weak strength of preference

In the paper, we present an interactive decision procedure for aggregating group members’ preferences which are specified in incomplete ways. A group consensus under incomplete information is not usually reached at a single step since less-specific preferences on attribute weights and performance scores make a clear selection of best alternative more difficult. To circumvent these difficulties, a measure, indicating the strength of preference between alternatives, is derived to help each of decision makers change his/her preference structure. To make preference changes based on the measure effective, we present a solution method to convert an intractable nonlinear programme into a linear one.     

Multiple criteria linear programming model for portfolio selection

The portfolio selection problem is usually considered as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model the risk is measured with variance, thus generating a quadratic programming model. The Markowitz model is frequently criticized as not consistent with axiomatic models of preferences for choice under risk. Models consistent with the preference axioms are based on the relation of stochastic dominance or on expected utility theory. The former is quite easy to implement for pairwise comparisons of given portfolios whereas it does not offer any computational tool to analyze the portfolio selection problem. The latter, when used for the portfolio selection problem, is restrictive in modeling preferences of investors. In this paper, a multiple criteria linear programming model of the portfolio selection problem is developed. The model is based on the preference axioms for choice under risk. Nevertheless, it allows one to employ the standard multiple criteria procedures to analyze the portfolio selection problem. It is shown that the classical mean-risk approaches resulting in linear programming models correspond to specific solution techniques applied to our multiple criteria model. This revised version was published online in June 2006 with corrections to the Cover Date.     

A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making

In decision making problems, there may be the cases where the decision makers express their judgements by using preference relations with incomplete information. Then one of the key issues is how to estimate the missing preference values. In this paper, we introduce an incomplete interval multiplicative preference relation and give the definitions of consistent and acceptable incomplete ones, respectively. Based on the consistency property of interval multiplicative preference relations, a goal programming model is proposed to complement the acceptable incomplete one. A new algorithm of obtaining the priority vector from incomplete interval multiplicative preference relations is given. The goal programming model is further applied to group decision-making (GDM) where the experts evaluate their preferences as acceptable incomplete interval multiplicative preference relations. An interval weighted geometric averaging (IWGA) operator is proposed to aggregate individual preference relations into a social one. Furthermore, the social interval multiplicative preference relation owns acceptable consistency when every individual one is acceptably consistent. Two numerical examples are carried out to show the efficiency of the proposed goal programming model and the algorithms.     

The arbitrage pricing theorem with incomplete preferences

This paper proves existence of equilibrium and the arbitrage pricing theorem for an asset exchange economy, where individuals' preferences may be incomplete or intransitive. This extends existing results to more general preferences. We also prove the arbitrage pricing theorem for a theory of choice under uncertainty by Bewley [Bewley, T. F. (2002), Knightian decision theory: part I, Decisions in Economics and Finance 25, 79–110.]. These preferences model Knightian uncertainty by preferences which may be incomplete but satisfy independence.     

A rational random behaviour model of choice

In this paper, a multinomial-Dirichlet-geometric model of consumer brand choice is developed. This individual-level stochastic choice model is derived as an extension of Theil's theory of rational random behaviour. These behavioural assumptions permit modelling of changes in likelihood of purchase as consumers are confronted with environmental factors whose occurrence and exact nature could not be anticipated at the planning stage of a shopping trip. Moreover, the model allows for uncertainties about future events which might affect actual choice to be built into the choice process alongside a traditional choice model which reflects preferences and/or utilities (and potential uncertainties surrounding them). Empirical results using consumer diary purchase panel data indicate a strong superiority of the model developed compared with previous models which assume stationary preference vectors.     

Is politics power or policy oriented? A comparative analysis of dynamic access models in policy networks*

We will show that these base models and some intermediate ones result in fundamentally different network structures and predicted outcomes. Moreover, we will show that the policy driven models do fundamentally better than the power driven models.

In policy networks actors use access relations to influence preferences of other actors. Establishment and shifts of access relations and their consequences for outcomes of decisions are the main focal points in this paper. Unlike most policy network studies, we therefore do not take the network and its relations as given and constant. Instead we device computer simulation models to account for the dynamics in policy networks. We compare different models and investigate the resulting network structures and predicted outcomes of decisions. The choice among the alternative models is made by their correspondence with empirical network structures and actual outcomes of decisions.

In our models, we assume that all relevant actors aim at policy outcomes as close as possible to their own preferences. Policy outcomes are determined by the preferences of the final decision makers at the moment of the vote. In general, only a small fraction of the actors takes part in the final vote. Most actors have therefore to rely on access relations for directly or indirectly shaping the preferences of the final decision makers. For this purpose actors make access requests to other actors. An access relation is assumed to be established if such a request is accepted by the other actor.

Access relations require time and resources. Actors are therefore assumed to be restricted in the number of access requests they can make and the number of requests they can accept Moreover, due to incomplete information and simultaneous actions by other actors, actors have to make simplifying assumptions in the selection of their “best” requests and learn by experience.

We device two base models that correspond to two basic views on the nature of political processes. In the first view politics is seen as power driven. Corresponding to this view, actors aim at access relations with the most powerful actors in the field. They estimate their likelihood of success by comparing their own resources with those of the target actors. Power also determines the order in which actors accept requests. In the second view, policy matters and actors roughly estimate the effects access relations might have on the outcome of decisions. Actors select requests to “bolster” their own preference as much as possible.     

不完全偏好下随机选择问题中的极大元定理

提出了不完全偏好的概念.在不完全偏好意义下获得了随机选择问题中的极大元定理和其它一些定理,统一和推广了许多已知结果.     

A fuzzy ranking method with range reduction techniques

For ranking alternatives based on pairwise comparisons, current analytic hierarchy process (AHP) methods are difficult to use to generate useful information to assist decision makers in specifying their preferences. This study proposes a novel method incorporating fuzzy preferences and range reduction techniques. Modified from the concept of data envelopment analysis (DEA), the proposed approach is not only capable of treating incomplete preference matrices but also provides reasonable ranges to help decision makers to rank decision alternatives confidently.     

Continuity, completeness and the definition of weak preferences

This note explores the connections between continuity and completeness under alternative conceptions of preference relations. For non-trivial preorders, it shows that, unlike the standard definitions, the weak preference relation defined in Galaabaatar and Karni (2010) allows for incomplete preferences while maintaining all the continuity properties of complete preference relations. It also makes it possible to distinguish indifference between alternatives from non-comparability of alternatives. If the preference relations are complete, this definition agrees with the customary definitions.     

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.     

On some ordinal models for decision making under uncertainty

In the field of Artificial Intelligence many models for decision making under uncertainty have been proposed that deviate from the traditional models used in Decision Theory, i.e. the Subjective Expected Utility (SEU) model and its many variants. These models aim at obtaining simple decision rules that can be implemented by efficient algorithms while based on inputs that are less rich than what is required in traditional models. One of these models, called the likely dominance (LD) model, consists in declaring that an act is preferred to another as soon as the set of states on which the first act gives a better outcome than the second act is judged more likely than the set of states on which the second act is preferable. The LD model is at much variance with the SEU model. Indeed, it has a definite ordinal flavor and it may lead to preference relations between acts that are not transitive. This paper proposes a general model for decision making under uncertainty tolerating intransitive and/or incomplete preferences that will contain both the SEU and the LD models as particular cases. Within the framework of this general model, we propose a characterization of the preference relations that can be obtained with the LD model. This characterization shows that the main distinctive feature of such relations lies in the very poor relation comparing preference differences that they induce on the set of outcomes. We wish to thank two anonymous referees for their helpful comments on an earlier draft of this text. The usual caveat applies.     

On neutrality of preferences on acts with respect to use of proxy outcomes

Construing acts as functions on a set of states to the set of lotteries on ultimate outcomes, this partly expository paper cautions that, in non-Savage choice theories, the popular technique of replacing multiattributed ultimate outcomes by equally desirable and crisper proxies may misguide the choice of act, in that preferences between the induced proxy acts may not mirror preferences between their original counterparts. When this pathology cannot occur, preferences and the associated choice theory are said to beneutral as regards proxy substitution. Sufficient conditions for neutrality include Monotone Dominance, Transitivity, and a restricted form of Linearity. The Linearity property can be circumvented by direct assignment of proxy certainty equivalents to outcome lotteries rather than to ultimate outcomes; then preferences are said to besemineutral if the corresponding proxy acts mirror preferences between their original counterparts. Relationships of these problem transformations are noted and certain normative choice theories are examined as to neutrality of preference with respect to use of arbitrary proxies.     

A consistency and consensus-based method to group decision making with interval linguistic preference relations

Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers’ preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure.     

Household risk aversion and portfolio choices

In practice, stock investment is one of the most important decisions made by households. The primary goal of this paper is to explain family investment decisions under the assumptions of household member’s preferences and efficient risk sharing based on the collective household model. In particular, by examining the absolute (relative) risk aversion of the household welfare function, we demonstrate how household’s portfolio allocation in stocks changes with family wealth. We examine two types of preference heterogeneity between family members: parameter heterogeneity and functional form heterogeneity. This study offers an alternative explanation of household portfolio choice corresponding with the observation that wealthier households tend to hold greater share of their wealth in risky assets. Specifically, if two decision-makers have standard constant relative risk aversion preference with different relative risk aversions in a household, family’s relative risk aversion decreases as household wealth increases (decreasing relative risk aversion).     

基于COWA算子的不同类型残缺判断矩阵集结方法

本文研究了决策信息以残缺不确定判断矩阵形式给出的群体决策问题。将残缺不确定区间互反判断矩阵转化为残缺不确定区间互补判断矩阵。基于COWA算子,定义了期望值函数,把残缺不确定区间互反判断矩阵转化成残缺实判断矩阵进行排序,减少了决策信息的丢失。利用IOWA算子来集结群体判断矩阵。最后通过算例说明了该方法的可行性和有效性。