Wang, Di
(2018)
Essays on decision-making under uncertainty.
PhD thesis, University of Nottingham.
Abstract
This thesis consists of three closely related studies investigating individual decision-making under risk and uncertainty, with a focus on decision weighting. Chapter 1 provides an overview of the common themes and theoretical framework for this research.
Chapter 2 reports the development of a simple method to measure the probability weighting function of Prospect Theory (Kahneman & Tversky, 1979) and rank-dependent utility theories. Our method, called the Neo-Lite method, is based on Abdellaoui et al. (2011)’s source method and the Neo-additive weighting function (Chateauneuf et al., 2007). It can be used for both risk (known probabilities) and for ambiguity (unknown probabilities). The novelty of our method lies in how data of decision weights are used to obtain the measurement of the whole function. Compared to the more widely used parametric fitting, our method is simpler, as it minimizes the number of decision weights required and does not rely on the elicitation of subjective probabilities (for ambiguity). An experiment of choice under risk demonstrates the simplicity and tractability of our method. The predictive performance of probability weighting functions measured using our method is shown to be almost equally good to that measured using the standard parametric fitting method.
Chapter 3 presents a theory of choice under risk primarily to explain why individual probability weighting functions are often found to be non-linear and inverse-S shaped. Our rationale for non-linear probability weighting is based on a psychologically grounded feature of choice making, a feature we call attention-based state weighting. We show that, under well-defined circumstances, our theory can be equivalent to Cumulative Prospect Theory (Tversky & Kahneman, 1992) with a probability weighting function depending on not only ranks but also sizes of outcomes of risky prospects. This allows our theory to accommodate evidence about probability weighting that cannot be explained by Prospect Theory or Cumulative Prospect Theory.
The evidence just mentioned refers to recent findings that people have stake-sensitive probability weighting functions. Chapter 4 reports an experiment that further explores the idea of stake-sensitive decision weighting. In addition, the experiment also tests hypotheses derived from the theory presented Chapter 3. In this chapter, we use a more general concept, decision weights, to refer to probability weights that can be stake-sensitive. Particularly we investigate whether and how decision weights are affected by two main properties of a lottery: outcome level (or expected payoff level) and outcome spacing (or the ratio of the best outcome of the lottery to its worst outcome). We elicit subjects’ Certainty-Equivalents for carefully-designed sets of lotteries and estimate their decision weights and utility curvatures using a model slightly more general than Cumulative Prospect Theory. Our main finding is that only outcome spacing has significant and systematic influence on decision weighting at the aggregate level, and that both outcome level and outcome spacing have systematic and significant effects at individual levels. This finding, together with the theory of Chapter 3, challenges the common understanding of probability weighting.
Chapter 5 concludes the thesis by summarizing all findings in previous chapters, discussing the implications, and pointing to directions for future research.
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