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Paradox has been an instrument to challenge the traditional expected utility theory. Paradox arises from the inconsistency between the empirical or experimental results and the theoretical deductions. In the expected utility theory field, there are many paradoxes or effects showing behaviors that are contradictory to the “theoretical” ones. Many studies questioned the validity of the expected utility theory by means of these paradoxes; while many others disqualified the expected utility theory as a descriptive model for human decision making behaviors. Among these paradoxes or effects, the Allais Paradox raised by Allais in 1953 is the most famous one.

This chapter explains how economic analysis can contribute to the delineation of the lone wolf’s opportunities and choices in a manner that allows operationally relevant advice to be contributed to the investigative process.

Using a risk-reward analytical framework we examine the lone wolf’s attack method opportunities and choices and identify those attack methods that would be chosen by lone wolves with different levels of risk aversion. We also use prospect theory as an alternative methodology for the determination of the lone wolf’s preference orderings over the available attack methods in a context where he references his actions against those of a predecessor whom he wishes to emulate.

We find that lone wolf terrorists with different levels of risk aversion can be expected to choose different attack methods or combinations of attack methods. More risk averse lone wolf terrorists will choose attack methods such as assassination. Less risk averse lone wolf terrorists will choose attack methods such as bombing, hostage-taking and unconventional attacks. Also, we find that lone wolf terrorists who reference their actions against ‘predecessor’ lone wolf terrorists will choose differently from among the available attack methods depending on which predecessor lone wolf is being referenced.

The analysis provides two different perspectives on terrorist choice but by no means exhausts the analytical alternatives. The analysis focuses on the fatalities and injuries inflicted whereas other perspectives might include different ‘payoffs’ series, including news or media coverage.

The chapter contributes an analysis of the order in which lone wolf terrorists with particular characteristics will choose from a set of available attack methods. During the course of our discussion we point out the consistency between the ‘rise’ of the lone wolf terrorist and the diseconomies to scale that are evident within the terrorism context. This presents the opportunity for new debates.

We take Cumulative Prospect Theory (CPT) seriously by rigorously estimating structural models using the full set of CPT parameters. Much of the literature only estimates a subset of CPT parameters, or more simply assumes CPT parameter values from prior studies. Our data are from laboratory experiments with undergraduate students and MBA students facing substantial real incentives and losses. We also estimate structural models from Expected Utility Theory (EUT), Dual Theory (DT), Rank-Dependent Utility (RDU), and Disappointment Aversion (DA) for comparison. Our major finding is that a majority of individuals in our sample locally asset integrate. That is, they see a loss frame for what it is, a frame, and behave as if they evaluate the net payment rather than the gross loss when one is presented to them. This finding is devastating to the direct application of CPT to these data for those subjects. Support for CPT is greater when losses are covered out of an earned endowment rather than house money, but RDU is still the best single characterization of individual and pooled choices. Defenders of the CPT model claim, correctly, that the CPT model exists “because the data says it should.” In other words, the CPT model was borne from a wide range of stylized facts culled from parts of the cognitive psychology literature. If one is to take the CPT model seriously and rigorously then it needs to do a much better job of explaining the data than we see here.

Much of the literature on theories of decision making under risk has emphasized differences between theories. One enduring theme has been the attempt to develop a distinction between “normative” and “descriptive” theories of choice. Bernoulli (1738) introduced log utility because expected value theory was alleged to have descriptively incorrect predictions for behavior in St. Petersburg games. Much later, Kahneman and Tversky (1979) introduced prospect theory because of the alleged descriptive failure of expected utility (EU) theory (von Neumann & Morgenstern, 1947).

We review the experimental evidence on risk aversion in controlled laboratory settings. We review the strengths and weaknesses of alternative elicitation procedures, the strengths and weaknesses of alternative estimation procedures, and finally the effect of controlling for risk attitudes on inferences in experiments.

This chapter conducts a systematic comparison of behavioral economics’s challenges to the standard accounts of economic behaviors within three dimensions: under risk, over time, and regarding other people. A new perspective on two underlying methodological issues, i.e., inter-disciplinarity and the positive/normative distinction, is proposed by following the entanglement thesis of Hilary Putnam, Vivian Walsh, and Amartya Sen. This thesis holds that facts, values, and conventions have inter-dependent meanings in science which can be understood by scrutinizing formal and ordinary language uses. The goal is to provide a broad and self-contained picture of how behavioral economics is changing the mainstream of economics.

Choice under risk has a large stochastic (unpredictable) component. This chapter examines five stochastic models for binary discrete choice under risk and how they combine with “structural” theories of choice under risk. Stochastic models are substantive theoretical hypotheses that are frequently testable in and of themselves, and also identifying restrictions for hypothesis tests, estimation and prediction. Econometric comparisons suggest that for the purpose of prediction (as opposed to explanation), choices of stochastic models may be far more consequential than choices of structures such as expected utility or rank-dependent utility.

Behavioral economics poses a challenge for the welfare evaluation of choices, particularly those that involve risk. It demands that we recognize that the descriptive account of behavior toward those choices might not be the ones we were all taught, and still teach, and that subjective risk perceptions might not accord with expert assessments of probabilities. In addition to these challenges, we are faced with the need to jettison naive notions of revealed preferences, according to which every choice by a subject expresses her objective function, as behavioral evidence forces us to confront pervasive inconsistencies and noise in a typical individual’s choice data. A principled account of errant choice must be built into models used for identification and estimation. These challenges demand close attention to the methodological claims often used to justify policy interventions. They also require, we argue, closer attention by economists to relevant contributions from cognitive science. We propose that a quantitative application of the “intentional stance” of Dennett provides a coherent, attractive and general approach to behavioral welfare economics.

This work examines the joint pricing and ordering (JPO) decisions for a loss-averse retailer with quantity-oriented reference point (RP) effect under demand uncertainty.

The demand is assumed to be uncertain with the mean and variance as the only known information. The prospect theory is used to model the retailer's expected utility. An expected utility maximization model in the distribution-free approach (DFA) is then developed. Using duality theory, the expected utility under the worst-case distribution is transformed into tractable piece-wise functions. To examine the effectiveness of the DFA in coping with the demand uncertainty, a stochastic programming model is developed and its solutions are used as benchmarks.

The proposed model and solution approach can effectively hedge against the demand uncertainty. The JPO decisions are significantly influenced by the LA coefficient and the reference level. The LA has a stronger influence than the reference level does on the expected utility. An excessive LA is detrimental while an appropriate reference level is beneficial to the retailer.

The results of this work are applicable to loss-averse retailers with the quantity-oriented RP when making JPO decisions with difficulty in predicting the demands.

The demand is assumed to be uncertain in this work, but a certain demand distribution is usually assumed in the existing literature. The DFA is used to study JPO decisions for the loss-averse retailer with quantity-oriented RP effect under the uncertain demand.

In recent years Professor Shackle's numerous, highly imaginative and original works on the role of expectation and uncertainty in the modelling of economic behaviour have at last become more widely acknowledged. However, still relatively little attention is paid to one of his seminal and earliest studies, that concerned with his own theory of expectations and individual decision making under uncertainty, work on which was begun and published in the 1930s and completed in 1949 with the appearance of the first edition of Expectation in Economics. Thereafter, until the early 1960s, his theory received a modest amount of interest. However, it tended to become neglected; reference rarely appears to it in books or papers on expectation, even in those papers discussing decision making under uncertainty (see, as one of the latest examples, G. O. Schneller and G. P. Sphicas, 1983). The literature has been dominated by the risk‐based, expected utility approach to decision taking.