Preferences Show Greater Stability for Transactions than for Gambles in Cost Discounting

Many factors point to the underlying instability of preferences in choice behavior. In particular, discounting reveals some effects not consistent with stable preferences. In discounting, the subjective value of a reward reduces as the uncertainty of or delay to obtaining it increases. The function relating subjective value to delay or probability must be exponential with a constant discount rate to respect transitivity over time, i.e., if A > B and B > C, then A > C (“ > ” = is preferred to). If the discount rate varies with value or time, then it is possible for transitivity to be violated, i.e., for preferences to be unstable. And people do show unstable, preference reversals over time in intertemporal choice more consistent with a hyperbolic discounting function (e.g., Myerson and Green, 1995). Thus, while someone may prefer £100 for certain now rather than £110 tomorrow, they will prefer £110 in a year and a day over £100 in a year’s time. People discount rate is very high initially, more rapid than the exponential, but over time it decreases leading to a flatter function than the exponential. Consequently, the £10 difference is almost totally discounted in the short term, but in a year’s time the extra day barely reduces the subjective value we attach to gaining an extra £10. Further effects are inconsistent with the reasonable assumption that delay works by increasing uncertainty. For example, the magnitude of a reward seems to have opposite effects for uncertainty and delay. Amount has opposite effects on the discounting of delayed and probabilistic rewards (Green et al., 1999). So, in temporal discounting people seem to discount small amounts more than large amounts, e.g., they prefer £10 now to £20 in a year but prefer £200 in a year to £100 now. However, in probabilistic discounting people seem to discount large amounts more than small amounts, e.g., they prefer £20 with a 50% chance to £10 for certain but prefer £100 for certain rather than £200 with a 50% chance. This picture is further complicated by the fact that for discounting losses, there seems to be no effect of amount for temporal discounting and inconsistent effects for probabilistic discounting (e.g., Mitchell and Wilson, 2010). These effects of amount not only violate the axioms of expected utility theory but are also not consistent with descriptive decision theories such as prospect theory. Jones and Oaksford (2011) observed that most of these results were obtained using gambles, whereas most people rarely receive a gain or incur a loss outside the context of a transaction, e.g., a choice of paying £10 now to own a commodity now or of paying £20 in 6 months time to own the commodity now. Kusev et al. (2009) showed that precautionary decision content, as in insurance situations, altered people’s choice behavior consistent with an increase in the probability weighting function for low probability events in prospect theory. Similarly, Jones and Oaksford (2011) argued that using transactional problem content rather than gambles may alter people’s decision-making. In particular, they suggested that this content may reveal more consistent effects of amount across temporal and probabilistic discounting. Transactions – but not gambles – will bring to mind previous instances of purchasing different commodities for different amounts. In particular, people would also be expected to have access to a commodity’s rate of depreciation or appreciation and they would know that the more expensive a commodity, the lower its depreciation is expected to be. Indeed, for some of their most costly purchases, people have the reasonable expectation of long-run appreciation. This information implies that in a transaction, people may discount small costs more than larger costs. So they will prefer to pay £100 now for the weekly shop rather than £200 in a week because its subjective value in a week’s time will be far less than £100 if not zero. In contrast, they may well be happy to pay £200K for a new flat in 10 years rather than £100K now. The flat is likely to be worth more than £100K in 10 years, and so, over time, its subjective value is not likely to decrease much. Jones and Oaksford (2011) also made the same prediction, more discounting for small costs than larger costs, for probabilistic discounting with transactional content. They report four experiments testing the predicted effects of transactional content on cost discounting. All these experiments used the standard adaptive staircase method to zero in on people’s certainty equivalent values for three amounts given different delays and probabilities. Temporal and probabilistic discounting curves were generated by plotting the certainty equivalent value normalized by cost amount against delay or odds against loss respectively for each amount. The area under the discounting curves (AUC) was used as the dependent variable indicating the degree of discounting: the lower the area under the curve the higher the rate of discounting. Figure 1, Panel A shows the mean AUC values using transactional content for both delay and probabilistic discounting in Jones and Oaksford’s (2011) Experiment 3, which was a replication of their Experiment 1. Both experiments showed the same pattern of discounting small costs more than large costs, i.e., lower mean AUC values for lower amounts. The trends were significant in all cases and in the same direction for both temporal (delay) and probabilistic discounting. Figure 1, Panel B shows the mean AUC values for their Experiment 4, which used gambles rather than transactions. For delay discounting, this experiment replicated previous findings of no effect for discounting losses. For probabilistic discounting of losses, a similar effect of more discounting for smaller amounts was observed. Moreover, for both the temporal