|London Mathematical Laboratory|
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Behavioural economics provides labels for patterns in human economic behaviour. Probability weighting is one such label. It expresses a mismatch between probabilities used in a formal model of a decision (i.e. model parameters) and probabilities inferred from real people's decisions (the same parameters estimated empirically). The inferred probabilities are called ``decision weights.'' It is considered a robust experimental finding that decision weights are higher than probabilities for rare events, and (necessarily, through normalisation) lower than probabilities for common events. Typically this is presented as a cognitive bias, i.e. an error of judgement by the person. Here we point out that the same observation can be described differently: broadly speaking, probability weighting means that a decision maker has greater uncertainty about the world than the observer. We offer a plausible mechanism whereby such differences in uncertainty arise naturally: when a decision maker must estimate probabilities as frequencies in a time series while the observer knows them a priori. This suggests an alternative presentation of probability weighting as a principled response by a decision maker to uncertainties unaccounted for in an observer's model.
An important question in economics is how people choose when facing uncertainty in the timing of rewards. In this paper we study preferences over time lotteries, in which the payment amount is certain but the payment time is uncertain. In expected discounted utility (EDU) theory decision makers must be risk-seeking over time lotteries. Here we explore growth-optimality, a normative model consistent with standard axioms of choice, in which decision makers maximise the growth rate of their wealth. Growth-optimality is consistent with both risk-seeking and risk-neutral behaviour in time lotteries, depending on how growth rates are computed. We discuss two approaches to compute a growth rate: the ensemble approach and the time approach. Revisiting existing experimental evidence on risk preferences in time lotteries, we find that the time approach accords better with the evidence than the ensemble approach. Surprisingly, in contrast to the EDU prediction, the higher the ensemble-average growth rate of a time lottery is, the less attractive it becomes compared to a sure alternative. Decision makers thus may not consider the ensemble-average growth rate as a relevant criterion for their choices. Instead, the time-average growth rate may be a better criterion for decision-making.