What Makes a Good Decision? Robust Satisficing as a Normative Standard of Rational Decision Making

Most decisions in life involve ambiguity, where probabilities can not be meaningfully specified, as much as they involve probabilistic uncertainty. In such conditions, the aspiration to utility maximization may be self‐deceptive. We propose “robust satisficing” as an alternative to utility maximizing as the normative standard for rational decision making in such circumstances. Instead of seeking to maximize the expected value, or utility, of a decision outcome, robust satisficing aims to maximize the robustness to uncertainty of a satisfactory outcome. That is, robust satisficing asks, “what is a ‘good enough’ outcome,” and then seeks the option that will produce such an outcome under the widest set of circumstances. We explore the conditions under which robust satisficing is a more appropriate norm for decision making than utility maximizing.     

Time and risk

Intertemporal choice has obvious similarities with choice under uncertainty. However, because of technical difficulties in mapping results between the two domains, theoretical analysis of these topics has proceeded independently. In this article, we show that, using Rank Dependent Expected Utility rather than Expected Utility as the basic uncertain choice model, numerous analogies between the two fields may be identified and exploited. The key result is the derivation of a natural analogy between risk-aversion and impatience. This permits the reinterpretation of well-known results on stochastic dominance and comparative risk-aversion in the context of intertemporal choice. It is also possible to reinterpret results on intertemporal optimization in order to derive new results for portfolio choice problems under uncertainty.     

Regret theory with general choice sets

The regret theory of choice under uncertainty proposed by Loomes and Sugden has performed well in explaining and predicting violations of Expected Utility theory. The original version of the model was confined to pairwise choices, which limited its usefulness as an economic theory of choice. Axioms for a more general form of regret theory have been proposed by Loomes and Sugden. In this article, it is shown that a simple nonmanipulability requirement is sufficient to characterize the functional form for regret theory with general choice sets. The stochastic dominance and comparative static properties of the model are outlined. A number of special cases are derived in which regret theory is equivalent to other well-known theories of choice under uncertainty.I would like to thank Graham Loomes, Robert Sugden, Peter Wakker, and Nancy Wallace for helpful comments and criticism.     

Combining strength and uncertainty for preferences in the graph model for conflict resolution with multiple decision makers

A hybrid preference framework is proposed for strategic conflict analysis to integrate preference strength and preference uncertainty into the paradigm of the graph model for conflict resolution (GMCR) under multiple decision makers. This structure offers decision makers a more flexible mechanism for preference expression, which can include strong or mild preference of one state or scenario over another, as well as equal preference. In addition, preference between two states can be uncertain. The result is a preference framework that is more general than existing models which consider preference strength and preference uncertainty separately. Within the hybrid preference structure, four kinds of stability are defined as solution concepts and a post-stability analysis, called status quo analysis, which can be used to track the evolution of a given conflict. Algorithms are provided for implementing the key inputs of stability analysis and status quo analysis within the extended preference structure. The new stability concepts under the hybrid preference structure can be used to model complex strategic conflicts arising in practical applications, and can provide new insights for the conflicts. The method is illustrated using the conflict over proposed bulk water exports from Lake Gisborne in Newfoundland, Canada.     

Choice uncertainty and the endowment effect

Journal of Risk and Uncertainty - We experimentally test for the role of choice uncertainty in generating “endowment effects” - the robust empirical finding that endowing participants...     

Decision Making in `Random in a Broad Sense' Environments

It is shown that the uncertainty connected with a `random in a broad sense' (not necessarily stochastic) event always has some `statistical regularity' (SR) in the form of a family of finite-additive probability distributions. The specific principle of guaranteed result in decision making is introduced. It is shown that observing this principle of guaranteed result leads to determine the one optimality criterion corresponding to a decision system with a given `statistical regularity'.     

Stochastic superiority

This paper introduces a definition of stochastic superiority. One random variable is stochastically superior to another whenever it stochastically dominates the other after the risk in each random variable has been optimally reduced. Stochastic superiority is implied by stochastic dominance, but the reverse is not true. Stochastic superiority allows more pairs of random alternatives to be ranked, and efficient sets to be smaller. A very strong sufficient condition for stochastic superiority is demonstrated to also be necessary when preferences are risk averse. This condition provides a relatively easy way to conduct stochastic superiority tests. As an alternative to “almost stochastic dominance,” stochastic superiority also provides a natural solution to the “left tail problem” that arises often when comparing random alternatives.

     

Third-generation prospect theory

We present a new theory of decision under uncertainty: third-generation prospect theory (PT³). This retains the predictive power of previous versions of prospect theory, but extends that theory by allowing reference points to be uncertain while decision weights are specified in a rank-dependent way. We show that PT³ preferences respect a state-conditional form of stochastic dominance. The theory predicts the observed tendency for willingness-to-accept valuations of lotteries to be greater than willingness-to-pay valuations. When PT³ is made operational by using simple functional forms with parameter values derived from existing experimental evidence, it predicts observed patterns of the preference reversal phenomenon.

Expected utility with lower probabilities

An uncertain and not just risky situation may be modeled using so-called belief functions assigning lower probabilities to subsets of outcomes. In this article we extend the von Neumann-Morgenstern expected utility theory from probability measures to belief functions. We use this theory to characterize uncertainty neutrality and different degrees of uncertainty aversion.We are grateful to Birgit Grodal, Salvatore Modica, David Schmeidler, and an anonymous referee for comments, help, and encouragement. Financial support from the Danish Social Sciences Research Council is acknowledged.     

Equivalent decision trees and their associated strategy sets

The purpose of this paper is to examine the structure of individual decisions under uncertainty in extensive (i.e., decision-tree) form at a sufficient level of generality to encompass many traditional as well as novel criteria of general choice under uncertainty. Considerations both of structure and of strategic effect arise. In § 2 we define weak and strong forms of strategic equivalence of decision trees and describe partial-normalization procedures by which all economically defined complete pure strategies may be identified for the decider and for chance. In § 3 we examine characteristics of locally randomized, behavior strategies for the decider as the degree of normalization is varied, and we deduce useful properties of the function which specifies an outcome lottery for each behavior strategy of the decider in conjuction with a deterministic or stochastic selection by Chance. In § 4 we list a wide variety of choice criteria which may be invoked within the framework developed here.     

A new axiomatic foundation of partial comparability

The paper presents some results obtained in searching for a new axiomatic foundation for partial comparability (PC) in the frame of non-conventional preference modeling. The basic idea is to define an extended preference structure able to represent lack of information, uncertainty, ambiguity, multidimensional and conflicting preferences, using formal logic as the basic formalism.A four-valued paraconsistent logic is therefore described in the paper as a more suitable language for the purposes of the research. The concepts of partition, general binary relations properties, fundamental relational system of preferences (f.r.s.p.), maximal f.r.s.p. and well founded f.r.s.p. are then introduced and some theorems are demonstrated in order to provide the axiomatic foundation of PC. The main result obtained is a preference structure that is a maximal well founded f.r.s.p. This preference structure facilitates a more flexible, reliable and robust preference modeling. Moreover it can be viewed as a generalization of the conventional approach, so that all the results obtained until now can be used under it.Two examples are provided at the end of the paper in order to give an account of the operational potentialities of the new theory, mainly in the area of multicriteria decision aid and social choice theory. Further research directions conclude the paper.This research has been done while the first author was in the Université Libre de Bruxelles under the Research in Brussels actions.     

The limits of uncertainty: A note

Discussions of decision making by individuals and organizations invariably touch on the issue of uncertainty. Decision theory axiomatizations are based on the assumption that uncertainty cannot be unlimited, but that there must exist a minimal interval of value stability. This note makes explicit that assumption for individual choice. For group and organizational decision making, a proof is presented which deduces a limit to uncertainty from the existence of deliberate social action.     

The Transnational Organization of Production and Environmental Degradation: A Cross‐National Study of the Effects of Foreign Capital Penetration on Water Pollution Intensity, 1980–1995*

Objective. This study attempts to increase our understanding of the environmental impacts of the transnational organization of production in the context of foreign capital penetration. Methods. With a sample of 53 countries, panel analyses using OLS and robust regression are conducted to assess the effects of foreign direct investment in the manufacturing sector on growth in organic water pollution intensity, 1980–1995. Slope‐dummy interaction variables are used to compare the effects in developed countries and less‐developed countries. The tested models include a variety of relevant controls, such as domestic investment, state environmentalism, size of the manufacturing sector, and level of economic development. Results. Findings for the analyses indicate that foreign direct investment in manufacturing positively affects growth in organic water pollution intensity in less‐developed countries, while the effect in developed countries is nonsignificant. Conclusions. This research illustrates the need for social scientists to investigate the environmental impacts of both the transnational organization of production and the overall scale of production in different sectors.     

Reporting probabilistic expectations with dynamic uncertainty about possible distributions

We study how experimental subjects report subjective probability distributions in the presence of ambiguity characterized by uncertainty over a fixed set of possible probability distributions generating future outcomes. Subjects observe draws from the true but unknown probability distribution generating outcomes at the beginning of each period of the experiment and state at selected periods a) the likelihoods that each probability distribution in the set is the true distribution, and b) the likelihoods of future outcomes. We estimate heterogeneity of rules used to update uncertainty about the true distribution and rules used to report distributions of future outcomes. We find that approximately 65% of subjects report distributions by properly weighing the possible distributions using their expressed uncertainty over them, while 22% of subjects report distributions close to the distribution they perceive as most likely. We find significant heterogeneity in how subjects update their expressed uncertainty. On average, subjects tend to overweigh the importance of their prior uncertainty relative to new information, leading to ambiguity that is substantially more persistent than would be predicted using Bayes’ rule. Counterfactual simulations suggest that this persistence will likely hold in settings not covered by our experiment.     

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.     

The Aversion to the Sequential Resolution of Uncertainty

This paper sets forth and offers an explanation for preferences for the form of the timing of resolution of uncertainty; namely for uncertainty to be resolved all at one time rather than sequentially. The explanation is based on a weakening of the independence axiom, in particular on the notion of disappointment aversion developed in Gul's (1991) axiomatic model of preferences. Implications of this aversion are discussed for issues in finance, intertemporal decision making under uncertainty, high stakes risky situations and consumer self-regulation. The analysis encourages a formulation of preferences over all attributes of interest to the decision maker, including psychological satisfaction.     

Endogenous risk and protection premiums

Endogenous risk implies an individual perceives he can influence the likelihood that a state of nature will occur. To add structure to endogenous risk models, I define a protection premium for reduced uncertainty about protection efficiency when a stochastic variable enters the probability functionp(x) rather than the utility function. For a binary lottery, a measure of aversion of uncertain protection efficiency(x) =-p(x)/p(x) is defined to unambiguously determine the effects of increased risk on an individual's voluntary contribution to public good supply earmarked to reduce the probability of an undesirable state. Finally, I examine the protection premium in ann-state discrete lottery and when uncertainty exists in both the probability and utility function.     

Stake effects on ambiguity attitudes for gains and losses

We test the effect of stake size on ambiguity attitudes. Compared to a baseline condition, we find subjects to be more ambiguity seeking for small-probability gains and large-probability losses under high stakes. They are also more ambiguity averse for large-probability gains and small-probability losses. We trace these effects back to stake effects on decisions under risk (known probabilities) and uncertainty (unknown probabilities). For risk, we replicate previous findings. For uncertainty, we find an increase in probabilistic insensitivity under high stakes that is driven by increased uncertainty aversion for large-probability gains and for small-probability losses.