The price for information about probabilities and its relation with risk and ambiguity

In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker??s risk and ambiguity attitudes affect the reservation price for ambiguity resolution. These effects are analyzed for different levels of ambiguity of the act. Operating instructions for the elicitation of the reservation price for ambiguity resolution in an experimental setting are provided at the end of the article.     

Dynamic consistency in extensive form decision problems

In a stimulating paper, Piccione and Rubinstein (1997) argued how a decision maker could undertake dynamically inconsistent choices when, in an extensive form decision problem, she has a particular type of imperfect recall named absentmindedness. Such memory limitation obtains whenever information sets include decision histories along the same decision path. Starting from work focusing on the absentminded driver example, and independently developed by Segal (2000) and Dimitri (1999), the main theorem of this article provides a general result of dynamically consistent choices, valid for a large class of finite extensive form decision problems without nature.      

Are beliefs a matter of taste? A case for objective imprecise information

We argue, in the spirit of some of Jean-Yves Jaffray’s work, that explicitly incorporating the information, however imprecise, available to the decision maker is relevant, feasible, and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally that it is crucial when attempting to identify and measure the decision maker’s attitude toward imprecise information.     

A possibilistic hierarchical model for behaviour under uncertainty

Hierarchical models are commonly used for modelling uncertainty. They arise whenever there is a `correct' or `ideal' uncertainty model but the modeller is uncertain about what it is. Hierarchical models which involve probability distributions are widely used in Bayesian inference. Alternative models which involve possibility distributions have been proposed by several authors, but these models do not have a clear operational meaning. This paper describes a new hierarchical model which is mathematically equivalent to some of the earlier, possibilistic models and also has a simple behavioural interpretation, in terms of betting rates concerning whether or not a decision maker will agree to buy or sell a risky investment for a specified price. We give a representation theorem which shows that any consistent model of this kind can be interpreted as a model for uncertainty about the behaviour of a Bayesian decision maker. We describe how the model can be used to generate buying and selling prices and to make decisions.     

Strategic communication with reporting costs

A decision maker relies on information of parties affected by her decision. These parties try to influence her decision by selective disclosure of facts. As is well known from the literature, competition between the informed parties constrains their ability to manipulate information. We depart from this literature by introducing a cost to communicate. Our parties trade off their reporting cost against the effect on the decision. Some information is never revealed. In contrast to setups without communication costs, our decision maker can benefit by ex ante committing to an ex post suboptimal decision rule. Moreover, committing ex ante not to listen to one of the parties may also be beneficial for the decision maker.

     

A note on the information content of a consistent pairwise comparison judgment matrix of an AHP decision maker

A decision maker using the Analytic Hierarchy Process (AHP) could be consistent, and still provide no information in the resulting vector of priorities. An extreme example would be a pairwise comparison judgment matrix filled with 1s which is totally consistent under the various definitions of consistency, but has provided no information about the prioritization of alternatives resulting from the decision maker's judgments. In this paper, the quality of a consistent decision maker's judgments using the Analytic Hierarchy Process is placed in the context of the entropy of the resulting vector of priorities. Indeed, it is the purpose of this paper to provide a formal definition of this notion ofentropy of a priority vector, and to provide a framework for a quantitative measurement of the information content of consistent pairwise comparison judgment matrices of a decision maker who is using the Analytic Hierarchy Process. We will prove that the entropy of the vector of priorities for consistent matrices follows a normal distribution and discuss some general considerations of this result.     

Expanding state space and extension of beliefs

This article provides a simple decision theoretic model in which elements of the world successively enter the decision maker??s scope and the state space expands over time, which is intended to be the closest correspondence to the standard subjective expected utility theory. We propose a dynamic consistency condition that after any expansion of the scope, the preference ranking should remain unchanged over acts to which the expansion is irrelevant. Together with other natural axioms, it characterizes a model in which the decision maker??s belief extends over time in order that the marginal distribution of the new belief induced over the old state space coincides with the old belief. It is extended to encompass both expansion of scope and learning events, and we characterize the model with an additional property that the decision maker??s belief updating follows Bayes?? rule when she learns events.     

The implications of irreversibility in emergency response decisions

The irreversibility effect implies that a decision maker who neglects the prospect of receiving more complete information at later stages of a sequential decision problem will in certain cases too easily take an irreversible decision, as he ignores the existence of a positive option value in favour of reversible decisions. This option value represents the decision maker's flexibility to adapt subsequent decisions to the obtained information. In this paper we show that the economic models dealing with irreversibility as used in environmental and capital investment decision making can be extended to emergency response decisions that produce important irreversible effects. In particular, we concentrate on the decision whether or not to evacuate an industrial area threatened by a possible nuclear accident. We show in a simple two-period evacuation decision model that non-optimal conclusions may be drawn when evacuation is regarded as a `now or never decision'. The robustness of these results is verified by means of a sensitivity analysis of the various model parameters. The importance of `options thinking' in this decision context is illustrated in an example.     

A challenge to the compound lottery axiom: A two-stage normative structure and comparison to other theories

This paper examines preferences among uncertain prospects when the decision maker is uneasy about his assignment of subjective probabilities. It proposes a two-stage lottery framework for the analysis of such prospects, where the first stage represents an assessment of the vagueness (ambiguity) in defining the problem's randomness and the second stage represents an assessment of the problem for each hypothesized randomness condition. Standard axioms of rationality are prescribed for each stage, including weak ordering, continuity, and strong independence. The Reduction of Compound Lotteries' axiom is weakened, however, so that the two lottery stages have consistent, but not collapsible, preference structures. The paper derives a representation theorem from the primitive preference axioms, and the theorem asserts that preference-consistent decisions are made as if the decision maker is maximizing a modified expected utility functional. This representation and its implications are compared to alternative decision models. Criteria for assigning the relative empirical power of the alternative models are suggested.     

The likelihood of various stock market return distributions, part 1: Principles of inference

This is the first of two articles which apply certain principles of inference to a practical, financial question. The present article argues and cites arguments which contend that decision making should be Bayesian, that classical (R. A. Fisher, Neyman-Pearson) inference can be highly misleading for Bayesians as can the use of diffuse priors, and that Bayesian statisticians should show remote clients with a variety of priors how a sample implies shifts in their beliefs. We also consider practical implications of the fact that human decision makers and their statisticians cannot fully emulate Savage's rational decision maker.     

A representation of preferences by the Choquet integral with respect to a 2-additive capacity

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.     

Risk aversion for losses and the Nash bargaining solution

Theory and Decision - We call a decision maker risk averse for losses if that decision maker is risk averse with respect to lotteries having alternatives below a given reference alternative in...     

Consulting an Expert with Potentially Conflicting Preferences

We study a situation where a decision maker relies on the report of a self-interested and informed expert prior to decide whether to undertake a certain project. An important feature in this interaction is that, depending on the collected information, the two agents have potentially conflicting preferences. Information contained in the report is partially verifiable in the sense that the expert can suppress favorable information sustaining the project but he cannot exaggerate it. Our results show that this setting favors the agent which is the less eager to undertake the project in that he always succeeds to induce his most preferred action.      

Demand for risky assets and the monotone probability ratio order

Since Fishburn and Porter (1976), it has been known that a first-order dominant shift in the distribution of random returns of an asset does not necessarily induce a risk-averse decision maker to increase his holdings of that improved asset. To obtain the desired comparative statics result, one has to further restrict the class of changes in the distribution. In this article, we propose the “monotone probability ratio” criterion which is more general than the “monotone likelihood ratio” criterion currently used in the literature.     

Ambiguity aversion and the propensities for self-insurance and self-protection

Two models of ambiguity preferences that permit comparative statics analysis of greater ambiguity aversion yield definite predictions concerning propensities for self-insurance and self-protection: The levels of both activities that are optimal for an ambiguity-averse decision maker are higher in the presence of ambiguity than in its absence, and demands for both activities increase with greater ambiguity aversion. The reason is that, at levels optimal for one decision maker, an increase in either activity results in a mean-preserving contraction in the distribution of expected utility in the presence of ambiguity, which is valuable to anyone with the same risk preferences who is more ambiguity averse.     

The impact of testing errors on value of information: A quality-control example

In this article, we extend recent work on the inferential impact of errors in data to a decision-making setting. In the context of a simple quality-control example, we illustrate how errors can cause substantial reductions in the value of information from a sample and how uncertainty about error rates can lead to yet further reductions in EVSI. Moreover, we extend the notion of an equivalent error-free sample size (which indicates the reduction in effective sample size due to errors) from an inferential framework to a decision-making framework and find that as uncertainty about error-rate parameters increases, reductions in effective sample size are even greater for a decision maker than the inferential measures suggest.     

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.     

Re-examining the law of iterated expectations for Choquet decision makers

Yoo (Economic Letters 37:145–149, 1991) argues that the law of iterated expectations must be violated if the probability measure of a Choquet decision maker is non-additive. In this article, we prove the positive result that the law of iterated expectations is satisfied for Choquet decision makers whenever they update their non-additive beliefs in accordance with the Sarin and Wakker (Journal of Risk and Uncertainty 16:223–250, 1998) update rule. The formal key to this result is the act-dependence of the Sarin–Wakker update rule, which does not hold for the update rules considered by Yoo (1991).