Similarity-based mistakes in choice

We characterize the following choice procedure. The decision maker is endowed with two binary relations over alternatives, a preference and a similarity. In every choice problem she includes in her choice set all alternatives which are similar to the best feasible alternative. Hence she can, by mistake, choose an inferior option because it is similar to the best. We characterize this boundedly rational behavior by suitably weakening the rationalizability axiom of Arrow (1959). We also characterize a variation where the decision maker chooses alternatives on the basis of their similarities to attractive yet infeasible options. We show that similarity-based mistakes of either kind lead to cyclical behavior. Finally, we reinterpret our procedure as a method for choosing a bundle given a set of individual items, in which the decision maker combines the best feasible item with those that complement it.     

Crisp monetary acts in multiple-priors models of decision under ambiguity

In axiomatic models of decision under ambiguity using a set of priors, a clear distinction can be made between acts which are affected by ambiguity and those which are not: the crisp acts. In these multiple-priors models, the decision maker is indifferent between holding a constant act or holding a non constant crisp act with the same expected utility, if it exists. In financial settings, we show that this indifference, together with the standard definition of monetary acts in the Anscombe–Aumann framework, implies that the investor ignores the variance of some assets, a behavior which conflicts with the assumption on which modern portfolio theory has been built. In this paper we establish the geometrical and topological properties of the set of priors that rule out the existence of non constant crisp acts. These properties in turn restrict what can possibly be an unambiguous financial asset.     

Expected utility theory with non-commutative probability theory

In this paper, we extend von Neumann and Morgenstern’s expected utility approach to a non-commutative probability theory. We introduce a new representation of the decision maker’s set of events which extends the canonical representation. We reformulate von Neumann and Morgenstern’s approach to modeling decision maker behavior by non-commutative probability theory. We introduce a set of preference axioms similar to von Neumann and Morgenstern’s axioms, and show that they lead to a generalization of the expected utility theorem. Our generalization allows for decision makers to make an intuitive distinction between representations of a set of events. We find that this methodology enables several paradoxes and inconsistencies in traditional expected utility theory (e.g., Allais paradox, etc.) to be solved or better understood.     

Evaluation of supplier capability and performance: A method for supply base reduction

Development of partnership with suppliers is widely recognised today as a potent tool for supply chain improvement. To develop an effective partnership, it is necessary to have a small supply base and an effort to reduce the supply base to a manageable level. Despite its overwhelming importance, models of supply base reduction are rare. Supplier sorting methods, used for pre-selection of suppliers and sometimes seen as methods for supply base reduction, have limitations ranging from (1) requirement of an exhaustive database of historical information (case-based reasoning), (2) inability to predefine the number of elements in a cluster (cluster analysis) and (3) inability to identify suppliers who are both highly capable as well as high performers (data envelopment analysis). In the present work, we develop a systematic framework for carrying out the supply base reduction process. The study assumes two important dimensions of suppliers—performance and capability. Performance of a supplier represents short-term effects on the achievement of supply chain objectives while supplier capability indicates long-term effects. Many of the performance and capability factors are imprecise in nature. In order to account for the imprecision involved in numerous subjective characteristics of suppliers, we use fuzzy set approach to measure the imprecision of these factors and rank a potential list of suppliers against their performance and capability. We then display their ranks in a ‘capability–performance matrix’ that helps a decision maker arrange the suppliers in decreasing order of preference. The desired numbers of suppliers are finally selected on the basis of this ordered list. The suggested framework will be of immense help to the practising managers in reducing the supply base—a prerequisite for building a strong supplier partnership and developing an effective supply chain.     

Ellsberg’s two-color experiment,portfolio inertia and ambiguity

Results in this paper relate the observation of an interval of prices at which a decision maker (DM) strictly prefers to hold a zero position on an asset (termed “portfolio inertia”) to the DM’s perception of the underlying payoff relevant events as ambiguous, as the term is defined in [Econometrica 69 (2001) 265]. The connection between portfolio inertia and ambiguity is established without invoking a parametric preference form, such as the Choquet expected utility or the max–min multiple priors model. This allows us to draw an observable distinction between portfolio inertia that may arise purely due to first-order risk aversion type effects, such as those which could arise even if preferences were probabilistically sophisticated, and portfolio inertia that involves ambiguity perceptions.     

The assessment of the expected value of information in the binary decision model

The expected value of information represents the maximum amount the decision maker should spend on inquiry before making a decision. This amount depends upon the accuracy of the information. In many cases of inquiry, prior objective knowledge of the accuracy is not available. This paper presents and compares two methods of subjectively assessing the value of imperfect information in the binary decision model. In the first method, the decision maker provides a likelihood function for the inquiry and hence the probabilities of error. The second method is the preposterior approach, in which the decision maker provides the prior distribution for the posterior probability.     

Hazard rate,stochastic choice and consideration sets

Manzini and Mariotti (2014) define the menu-independent random consideration set rule, where the decision maker considers each alternative with a menu-independent probability known as the attention function. We relax the assumption of menu-independence and allow for any restriction to be imposed on the attention function. We show that there is an equivalence between the attention function and the hazard rate. This equivalence is used to characterize the menu dependent random consideration set rules that correspond to (i) specific conditions on the probability rule, and (ii) different stochastic choice models from the literature.     

Adjusting inconsistency through learning in group decision-making, and its application to China's MBA recruiting interview

In group decision-making, because of limitations on individual knowledge and information bases, or because of the existing decision rule, an individual decision maker may not be capable of evaluating selected alternatives. Such circumstances can lead to inconsistencies across group decision matrices. These inconsistencies are difficult to remedy under existing approaches. Based on Rough Set Theory, we thus propose a new approach that integrates two types of learning techniques. It first applies a machine-learning procedure that extracts possible alternatives from other decision makers that are currently not included in a given decision maker's alternative set. It then applies a group knowledge-learning model to determine corresponding attribute values of those newly learned alternatives in meeting a group's consistency requirement. Efficacy of the approach is illustrated by its application to China's MBA recruiting interview.     

A model of stochastic choice from lists

We study stochastic choice from lists. All lists present the same set of alternatives albeit in different orders. Faced with a list, the decision maker makes her choice in two stages. In the first stage she searches through the list till she sees $k$ alternatives. In the second stage she chooses from the alternatives she has seen. Both $k$ and the choice rule governing her second stage behavior are random. We show that the underlying primitives of our model are revealed by the decision maker’s choice frequencies from lists. We characterize the model and two of its special cases. In the first special case the decision maker deterministically chooses the best observed alternative according to a given preference. In the second, the decision maker maximizes random preferences.     

Weakened WARP and top-cycle choice rules

We propose the following weakened version of WARP: if the decision maker selects an alternative x and rejects another alternative y in some context, he cannot select y and reject x in another context. This axiom is consistent with cyclic choices. It is necessary and sufficient for the choice from every subset A of a (finite) universal set X to coincide with the weak upper-contour set of the transitive closure of some fixed complete relation at some alternative in A. Adding further simple axioms forces the choice from each subset to coincide with the top cycle (in that subset) of some fixed tournament over the universal set.     

An approach to the display and analysis of multiobjective problems

In all operations research applications, the problem of implementation rests on the information conveyed to the decision maker. The presentation of results is a critical link in the success of a project. An ineffective transfer of information will reduce the chance of decision maker acceptance. This final step in the analysis is particularly difficult in multiobjective analyses, where the amount of relevent information increases with each performance measure.This paper will describe an alternative to the typical graphical approach to multiobjective display, which is adaptable to any number of objectives. A real world example is given and some theoretical insights are developed.     

A representation of decision by analogy

We give a representation of analogical reasoning in choice under uncertainty. A decision maker is faced with two decision problems, a familiar and a novel one. It is shown that, under assumptions that capture the salience of alignable differences in choice, the decision maker can be construed as choosing between acts in the novel decision problem as if drawing all likelihood information from a multi-valued correspondence between states of the world in the familiar domain and states of the world in the novel domain. The latter is interpreted as an analogy between the two decision problems, and the fuzziness of the analogy is related to revealed ambiguity in the novel decision problem.     

Timing of information in agency problems with hidden actions

This paper endogenizes in a standard hidden action model the point in time when a risk neutral and wealth constrained agent and the principal observe the realization of an additional signal: before the agent’s effort choice (ex ante information) or after (ex post information). In a decision problem, ex ante information does (weakly) better than ex post information because the decision maker can tailor efforts to the information. We show that this is not the case for incentive problems: a negative incentive effect arises under ex ante information that prevails even though the principal tailors the agent’s effort to the information.     

Risk aversion for variational and multiple-prior preferences

The objective of this paper is to identify variational preferences and multiple-prior (maxmin) expected utility functions that exhibit aversion to risk under some probability measure from among the priors. Risk aversion has profound implications on agents’ choices and on market prices and allocations. Our approach to risk aversion relies on the theory of mean-independent risk of Werner (2009). We identify necessary and sufficient conditions for risk aversion of convex variational preferences and concave multiple-prior expected utilities. The conditions are stability of the cost function and of the set of probability priors, respectively, with respect to a probability measure. The two stability properties are new concepts. We show that cost functions defined by the relative entropy distance or other divergence distances have that property. Set of priors defined as cores of convex distortions of probability measures or neighborhoods in divergence distances have that property, too.     

On Bayesian analysis and computation for functions with monotonicity and curvature restrictions

Our goal is inference for shape-restricted functions. Our functional form consists of finite linear combinations of basis functions. Prior elicitation is difficult due to the irregular shape of the parameter space. We show how to elicit priors that are flexible, theoretically consistent, and proper. We demonstrate that uniform priors over coefficients imply priors over economically relevant quantities that are quite informative and give an example of a non-uniform prior that addresses this issue. We introduce simulation methods that meet challenges posed by the shape of the parameter space. We analyze data from a consumer demand experiment.     

Context dependent beliefs

This paper examines a model where the set of available outcomes from which a decision maker must choose alters his perception of uncertainty. Specifically, this paper proposes a set of axioms such that each menu induces a subjective belief over an objective state space. The decision maker’s preferences are dependent on the realization of the state. The resulting representation is analogous to state-dependent expected utility within each menu; the beliefs are menu dependent and the utility index is not. Under the interpretation that a menu acts as an informative signal regarding the true state, the paper examines the behavioral restrictions that coincide with different signal structures: elemental (where each element of a menu is a conditionally independent signal) and partitional (where the induced beliefs form a partition of the state space).     

Throwing good money after bad

An “investment bubble” is a period of “excessive, and predictably unprofitable, investment” (DeMarzo et al. in J Financ Econ 85:737–754, 2007). Such bubbles most often accompany the arrival of some new technology, such as the tech stock boom and bust of the late 1990s and early 2000s. We provide a rational explanation for investment bubbles based on the dynamics of learning in highly uncertain environments. Objective information about the earnings potential of a new technology gives rise to a set of priors or a belief function. A generalised form of Bayes’ rule is used to update this set of priors using earnings data from the new economy. In each period, agents—who are heterogeneous in their tolerance for ambiguity—make optimal occupational choices, with wages in the new economy set to clear the labour market. A preponderance of bad news about the new technology may nevertheless give rise to increasing firm formation around this technology, at least initially. To a frequentist outside observer, the pattern of adoption appears as an investment bubble.     

Shortlisting procedure with a limited capacity

A decision maker, who is overwhelmed by the number of available alternatives, limits her consideration. We investigate a model where a decision maker’s capacity determines whether she is overwhelmed: She considers all the available alternatives if their number does not exceed her capacity; otherwise, she applies a shortlisting procedure to reduce the number of alternatives to within her capacity. We show how to deduce the decision maker’s capacity, her preference and the alternatives that she considers from the observed behavior. Furthermore, we provide the necessary and sufficient conditions for a consideration function to be derived by the shortlisting procedure with a limited capacity.     

Incomplete markets, ambiguity, and irreversible investment

The problem of irreversible investment with idiosyncratic risk is studied by interpreting market incompleteness as a source of ambiguity over the appropriate no-arbitrage discount factor. The maxmin utility over multiple priors framework is used to model and solve the irreversible investment problem. Multiple priors are modeled using the notion of κ‐ignorance. This set-up is used to analyze finitely lived options. For infinitely lived options the notion of constant κ‐ignorance is introduced. For these sets of density generators the corresponding optimal stopping problem is solved for general (in-)finite horizon optimal stopping problems driven by geometric Brownian motion. It is argued that an increase in the set of priors delays investment, whereas an increase in the degree of market completeness can have a non-monotonic effect on investment.