ABSTRACT. This paper provides a formalization of reference dependence, initial wealth, and final wealth, concepts that are central in the distinction between classical expected utility and prospect theory. The formalization will clarify some misunderstandings about Rabin's (2000, Econometrica) calibration paradox for expected utility. Cox & Sadiraj (2006, Games and Economic Behavior 56, 45-60) argued that Rabin's paradox can easily be explained in terms of utility of income, which descibes outcomes as changes with respect to a given level and which they consider part of expected utility, and that paradoxes similar to Rabin's apply to prospect theory and other theories as well. Our formalization shows that utility of income is part of prospect theory and not of expected utility, that utility of income was suggested by Rabin himself as the most plausible explanation of his paradox under the term loss aversion, and that the “similar” paradoxes for prospect theory are, contrary to Rabin's paradox, based on empirically implausible assumptions so that they have no bite.
This paper, a criticism of Cox & Sadiraj (2006), was rejected by Games and Economic Behavior, and would not fit in another journal. The material has now been incorporated in Ch. 8 of my book “Prospect Theory for Risk and Ambiguity,” 2010, Cambridge University Press.
ABSTRACT. This note explains that the method for eliciting the value function, used by Fox & Tversky (Management Science 1998) and Fox, Rogers, & Tversky (Journal of Risk and Uncertainty 1996) is not valid under cumulative prospect theory. This does not affect the empirical findings of the former paper because it applies the method only to falsify expected utility. It neither seems to affect the latter paper because its claim of expected value for risk as found remains highly plausible.
This paper was rejected by Management Science, and Journal of Risk and Uncertainty, unfortunately, does not consider comments on previous publications. It would not fit in other journals.
ABSTRACT. As yet, no general agreement has been reached on whether the Bayesian or the frequentist (Neyman-Pearson, NP) approach to statistics is to be preferred. Whereas Bayesians adhere to coherence conditions of de Finetti, Savage, and others, frequentists do not consider these conditions normative and deliberately and knowingly violate them. Hence further arguments, bringing more clarity on the disagreements, are warranted. Providing such arguments, by refining the coherence conditions, is the purpose of this paper. It invokes recent arguments from the economic literature demonstrating that some seemingly self-evident principles for dynamic decision making have a surprising implication for static decisions: They imply Bayesianism. These principles are forgone-event independence (independence of past counterfactual events, often called consequentialism in decision theory and known as the conditionality principle in statistics), dynamic consistency (what is optimal at some given time point is independent of the time point at which that is decided), and two other conditions. Thus, a more sensitive diagnostic tool is obtained for identifying the disagreements between Bayesians and frequentists. If a frequentist does not mind violating Bayesian coherence, a Bayesian can now ask a follow-up question: Which of the dynamic principles will the frequentist give up? The debate may lead either to Bayesianism or to better implementations of non-Bayesian models in dynamic decision situations and to better non-Bayesian methods for updating information.
The diagnostic tool sheds new light on NP hypothesis testing. NP theory requires that statistical procedures are laid down before data are observed. It adheres to dynamic consistency but violates forgone-event independence. Forgone-event independence, however, is so natural that NP practitioners adhere to it and observe the data before deciding on a statistical procedure. They are thus led into violations of dynamic consistency.
ABSTRACT. This paper discusses the role of preference axioms in expected utility, building on previous discussions in Medical Decision Making. The independence axiom, if accepted, provides the proper terms (probabilities and utilities) for risky decisions, without specifying what values those terms should take. Thus, while necessary for rationality, it can never be sufficient. Expected utility concerns the aggregation over different resolutions of uncertainty. It does not concern aggregation over different persons (welfare and policy making), different time points (repeated decisions), or different attributes (e.g., duration versus quality of life). People can deviate from expected utility for normative (“rational”), psychological (“irrational”), and tractability reasons. We believe that discrepancies between expected utility and behavioral decision making, and the resolution of those, are an essential part of expected utilityys prescriptive contribution.
This paper, a criticism of a Cohen paper and others discussing expected utility in the journal Medical Decision Making, was resubmitted to the journal Medical Decision Making twice. The reviewers, however, continued to ask for many confused rewritings, each time bringing in new arguments, and each time embarking upon their own views of what rational was, and I did not want to continue the inefficient process.
ABSTRACT. This paper proposes a new updating method that preserves dynamic consistency in nonexpected utility. Given nonseparability of disjoint events, preferences conditional on an observed event also depend on counterfactual outcomes, i.e., outcomes that would have resulted outside of the conditioning event; this point has been well-understood in the literature. This paper argues that, as a consequence, also counterfactual decisions are relevant. A new “strategic” method for updating then follows.
I think that this paper refutes most of the preference updatings commonly used in nonexpected utility theory. Unfortunately, the topic of dynamic decision principles is subtle, and referees invariably started discussing the conditions in confused manners. I would often run into a referee in this field who would reject everything for always the same reason, being a claim that he could make a “Dutch book” against whatever I would write. I then decided to no more write on this topic.
ABSTRACT. It is shown that Choquet integrals satisfy comonotonic additivity. While this result has often been used in the literature, no derivation in full generality had been provided yet.
I consider this to be one of my best papers. It was later split up into several different papers.
Last updated: 31 July, 2017
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