Decomposition of multiple attribute preference models
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This dissertation consists of three research papers on Preference models of decision making, all of which adopt an axiomatic approach in which preference conditions are studied so that the models in this dissertation can be verified by checking their conditions at the behavioral level. The first paper “Utility Functions Representing Preference over Interdependent Attributes” studies the problem of how to assess a two attribute utility function when the attributes are interdependent. We consider a situation where the risk aversion on one attribute could be influenced by the level of the other attribute in a two attribute decision making problem. In this case, the multilinear utility model—and its special cases the additive and multiplicative forms—cannot be applied to assess a subject’s preference because utility independence does not hold. We propose a family of preference conditions called nth degree discrete distribution independence that can accommodate a variety of dependencies among two attributes. The special case of second degree discrete distribution independence is equivalent to the utility independence condition. Third degree discrete distribution independence leads to a decomposition formula that contains many other decomposition formulas in the existing literature as special cases. As the decompositions proposed in this research is more general than many existing ones, the study provides a model of preference that has potential to be used for assessing utility functions more accurately and with relatively little additional effort. The second paper “On the Axiomatization of the Satiation and Habit Formation Utility Models” studies the axiomatic foundations of the discounted utility model that incorporates both satiation and habit formation in temporal decision. We propose a preference condition called shifted difference independence to axiomatize a general habit formation and satiation model (GHS). This model allows for a general habit formation and satiation function that contains many functional forms in the literature as special cases. Since the GHS model can be reduced to either a general satiation model (GSa) or a general habit formation model (GHa), our theory also provides approaches to axiomatize both the GSa model and the GHa model. Furthermore, by adding extra preference conditions into our axiomatization framework, we obtain a GHS model with a linear habit formation function and a recursively defined linear satiation function. In the third paper “Hope, Dread, Disappointment, and Elation from Anticipation in Decision Making”, we propose a model to incorporate both anticipation and disappointment into decision making, where we define hope as anticipating a gain and dread as anticipating a loss. In this model, the anticipation for a lottery is a subjectively chosen outcome for a lottery that influences the decision maker’s reference point. The decision maker experiences elation or disappointment when she compares the received outcome with the anticipated outcome. This model captures the trade-off between a utility gain from higher anticipation and a utility loss from higher disappointment. We show that our model contains some existing decision models as its special cases, including disappointment models. We also use our model to explore how a person’s attitude toward the future, either optimistic or pessimistic, could mediate the wealth effect on her risk attitude. Finally, we show that our model can be applied to explain the coexistence of a demand for gambling and insurance and provides unique insights into portfolio choice and advertising decision problems.