Expected utility versus the changes in knowledge ahead

Abstract

We present a decision theory appropriate for use in serious choices such as insurance. It extends standard decision theories like expected utility or cumulative prospect theory which are atemporal single stage theories. Instead it employs stages of knowledge ahead to track satisfactions and dissatisfactions. In the first stage of the risk, the uninsured face dissatisfactions of worries and planning difficulties (avoided by the insured), also perhaps positive satisfactions of thrills (missed out by the insured). In the second stage when the risk is past, the uninsured may face the dissatisfactions of ridicule and blame if they learn that they were unlucky. From experimental and questionnaire data, 80% of our subjects are influenced by such secondary satisfactions. Only five percent of our participants employ the usage of integrated quantitative aggregation rules for evaluating acts as assumed under expected utility theory.

Introduction

When some aspects of the future are unknown, knowledge ahead is limited and people face risks and uncertainties. For instance if people think that the good outcome has a probability of 0.6 and the bad outcome has a probability of 0.4, then they have limited knowledge ahead what the outcome will be. People experience benefits and cost from these risks and uncertainties, i.e. from having only limited knowledge ahead. This means that their experiences will be different during these stages of limited knowledge ahead from what they will be later when these risks and uncertainties are in the past and they will have full knowledge ahead. This paper focuses on the material and emotional effects of different extents of knowledge ahead, from very limited to full knowledge ahead (complete certainty).

Experimental economics has been bound by the examples developed under the knowledge ahead-independent framework of expected utility and game theory. The experimental examples and the theoretical formulations of the external economy are by and large bereft of knowledge-ahead-based effects, whether material or emotional. This accords with their exclusion from expected utility theory. As Friedman and Savage (1948) put it, under axiomatised expected utility theory (EUT), each outcome must be valued “as if certain”. This means that in expected utility and standard game theory the value of each outcome is identical under risk and certainty. This identity is preserved in all the standard generalisations of EUT namely those that preserve a preference for first order stochastically dominating distributions over outcomes, such as the Quiggin (1982) rank dependent theory and cumulative prospect theory. This study seeks to overcome that confining knowledge ahead-independent framework and offer some information on the importance of incorporating knowledge-ahead-based effects.

In other investigations it was feasible to identify choices in which the knowledge-ahead-based effects excluded in the theories were determining factors in the choices. It was established that in risky choice modelling knowledge ahead-based factors are important both in descriptive work, e.g. Albers et al. (2000) and in prescriptive and normative work, e.g. Pope (2001). Such investigations established empirically the need to go beyond the knowledge ahead-independent framework and adopt the stages of knowledge framework of Pope (1995). These studies however shed no light on the details of the new class of theories required in either descriptive or normative risky choice modelling.

The alternative investigative approach taken here offers insight into such modelling details. It first invites participants to choose, and then before they learn the outcome and payoff of their choice, asks them series of questions on factors behind both their decisions to avoid risk, and their decisions to take risks. This, as shown in this paper, offers hints on how to model actual risky choice procedures, and rather decisive evidence on what sort of modelling is inappropriate for descriptive and prescriptive risky choice modelling.

We find that 80% of our subjects are influenced by those secondary satisfactions (such as thrill or worry) about which we ask in the experimental setting. In the context of this special issue on Facilitated Decision Analysis we want to contribute to the understanding of decision making on a fundamental level. Facilitators who base their assumptions of rational decision making on pure expected utility considerations might be affected by a restricted mindset ignoring other relevant factors. The paper is mainly focused on an insurance decision with a time interval between decision and the knowledge of the risky outcome. This scenario is analysed in an experiment and the implications of various decision theories are tested. However, the results can be applied to any decision making situations under risk. Additional supporting evidence is to be found in Pope et al. (2006).