Note on preference and axioms of choice

Annals of the Institute of Statistical Mathematics -     

Optimal portfolio, consumption and retirement decision under a preference change

We investigate an optimal portfolio, consumption and retirement decision problem in which an economic agent can determine the discretionary stopping time as a retirement time with constant labor wage and disutility. We allow the preference of the agent to be changed before and after retirement. It is assumed that the agent's coefficient of relative risk aversion becomes higher after retirement. Under a constant relative risk aversion (CRRA) utility function, we obtain the optimal policies in closed-forms using martingale methods and variational inequality methods. We give some numerical results of the optimal policies. We also consider the relation between the level of disutility and the labor wage with the optimal retirement wealth level.     

Optimal investment,consumption and timing of annuity purchase under a preference change

In this paper, we study the optimal investment and consumption strategies for a retired individual who has the opportunity of choosing a discretionary stopping time to purchase an annuity. We assume that the individual receives a fixed annuity income and changes his/her preference after paying a fixed cost for annuitization. By using the martingale method and the variational inequality method, we tackle this problem and obtain the optimal strategies and the value function explicitly for the case of constant force of mortality and constant relative risk aversion (CRRA) utility function.     

Enabling e-transactions with multi-attribute preference models

This paper describes potential applications of multi-attribute preference models (MAPM) in e-commerce and offers some guidelines for their implementation. MAPM are methodologies for modeling complex preferences that depend on more than one attribute or criterion, and include multi-attribute utility theory, conjoint analysis, and the Analytic Hierarchy Process. There are numerous examples of applications in e-commerce that would benefit from the acquisition of information regarding the preferences of a consumer, a customer, an advice seeker, or a decision maker. Here, the focus is on applications of MAPM models in B2C and B2B websites, where preferences of consumers are assessed for the purpose of identifying products or services that closely match their needs.     

Multiattribute preference models with reference points

In the context of multiple attribute decision making, preference models making use of reference points in an ordinal way have recently been introduced in the literature. This text proposes an axiomatic analysis of such models, with a particular emphasis on the case in which there is only one reference point. Our analysis uses a general conjoint measurement model resting on the study of traces induced on attributes by the preference relation and using conditions guaranteeing that these traces are complete. Models using reference points are shown to be a particular case of this general model. The number of reference points is linked to the number of equivalence classes distinguished by the traces. When there is only one reference point, the induced traces are quite rough, distinguishing at most two distinct equivalence classes. We study the relation between the model using a single reference point and other preference models proposed in the literature, most notably models based on concordance and models based on a discrete Sugeno integral.     

Evaluation of choice set generation algorithms for route choice models

This paper discusses choice set generation and route choice model estimation for large-scale urban networks. Evaluating the effectiveness of Advanced Traveler Information Systems (ATIS) requires accurate models of how drivers choose routes based on their awareness of the roadway network and their perceptions of travel time. Many of the route choice models presented in the literature pay little attention to empirical estimation and validation procedures. In this paper, a route choice data set collected in Boston is described and the ability of several different route generation algorithms to produce paths similar to those observed in the survey is analyzed. The paper also presents estimation results of some route choice models recently developed using the data set collected.     

Sensitivity analysis for choice problems with partial preference relations

In this paper we consider choice problems under the assumption that the preferences of the decision maker are expressed in the form of a parametric partial weak order without assuming the existence of any value function. We investigate both the sensitivity (stability) of each non-dominated solution with respect to the changes of parameters of this order, and the sensitivity of the set of non-dominated solutions as a whole to similar changes. We show that this type of sensitivity analysis can be performed by employing techniques of linear programming.     

Three new models for preference voting and aggregation

Preference voting and aggregation require the determination of the weights associated with different ranking places. This paper proposes three new models to assess the weights. Two of them are linear programming (LP) models which determine a common set of weights for all the candidates considered and the other is a nonlinear programming (NLP) model that determines the most favourable weights for each candidate. The proposed models are examined with two numerical examples and it is shown that the proposed models cannot only choose a winner, but also give a full ranking of all the candidates.     

The role of processing-by-attribute noncompensatory choice models

Research work on modeling consumer multiple choice problems using logit, regression, and probit is gaining more attention. However, in their work, Russ (1971), Tversky (1972), Newell and Simon (1972), Tversky and Sattath (1979), and Gensch and Svestka (1979; 1984) indicate that for many problems, choice behavior appears to be context dependent and hierarchical. With this specific issue in mind, this paper discusses a mathematical model which estimates threshold tolerances, eliminates nonchosen alternatives, provides choice probabilities and finally offers diagnostic information regarding the key attributes that are responsible for making a final decision. The use of other individual specific models such as: lexicographic, conjunctive, etc., have been briefly explicated.     

On substitutability and complementarity in discrete choice models

In this paper, we propose the concepts of substitutability and complementarity in discrete choice models. These concepts concern whether the choice probability of one alternative in a choice model increases or decreases with the utility of another alternative, and they play important roles in capturing certain practical choice patterns, such as the halo effect. We study conditions on discrete choice models that will lead to substitutability and complementarity. We also present ways of constructing choice models that exhibit complementary property.     

Effective choice operations on constructive and positive models

Translated fromAlgebra i Logika, Vol. 32, No. 1, pp. 45–53, January–February, 1993.     

Wisdom, Knowledge and Rationality

After surveying the strengths and weaknesses of several well-known approaches to wisdom, I argue for a new theory of wisdom that focuses on being epistemically, practically, and morally rational. My theory of wisdom, The Deep Rationality Theory of Wisdom, claims that a wise person is a person who is rational and who is deeply committed to increasing his or her level of rationality. This theory is a departure from theories of wisdom that demand practical and/or theoretical knowledge. The Deep Rationality Theory salvages all that is attractive, and avoids all that is problematic, about theories of wisdom that require wise people to be knowledgeable.     

Entropy,spatial interaction models and discrete choice analysis: Static and dynamic analogies

This paper aims at analysing the existence of a formal correspondence between spatial interaction models emanating from entropy theory and micro-economic discrete choice theory (in particular, multinomial logit models.). After a concise review of the literature on this issue, the emphasis is placed on an interpretation of formal analogies between both classes of models in a dynamic context. A simple dynamic spatial interaction model—based on optimal control theory—is proposed, and it is shown that the results confirm also the existence of a formal analogy between (macro) dynamic interaction models and (micro) choice models. Similar results are also derived for Alonso's general theory of movement in a spatial system.     

Some comments on preference order dynamic programming models

A simple deterministic dynamic programming model is used as a general framework for the analysis of stochastic versions of three classical optimization problems: knapsack, traveling salesperson, and assembly line balancing problems. It is shown that this model can provide an alternative to the preference order models proposed for these problems. Counterexample to the optimality of the preference order models are presented.     

Distance-based and ad hoc consensus models in ordinal preference ranking

This paper examines the problem of aggregating ordinal preferences on a set of alternatives into a consensus. This problem has been the subject of study for more than two centuries and many procedures have been developed to create a compromise or consensus.We examine a variety of structures for preference specification, and in each case review the related models for deriving a consensus. Two classes of consensus models are discussed, namely ad hoc methods, evolving primarily from parliamentary settings over the past 200 years, and distance or axiomatic-based methods. We demonstrate the levels of complexity of the various distance-based models by presenting the related mathematical programming formulations for them. We also present conditions for equivalence, that is, for yielding the same consensus ranking for some of the methods. Finally, we discuss various extensions of the basic ordinal ranking structures, paying specific attention to partial ranking, voting member weighted consensus, ranking with intensity of preference, and rank correlation methods, as alternative approaches to deriving a consensus. Suggestions for future research directions are given.     

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.