In a favourite example of the behavioural economists, research participants are offered the choice between one bottle of wine a month from now and two bottles of wine one month and one day from now (alternatively, substitute cake, money or some other pay-off for wine). Most people will choose the two bottles of wine. However, when offered one bottle of wine straight away, more people will take that bottle and not wait until the next day to take up the alternative of two bottles. This suggests that people discount the value of goods received after short delays at a higher rate than for longer delays.
This set of decisions could be argued to be irrational. To understand why, suppose you face the first set of choices for one or two bottles of wine in 30 or 31 days. You choose the two bottles. Then, on the 30th day, you are allowed to reconsider your decision, which is effectively making the choice in the second scenario above. Some people will change their mind and take the single bottle of wine. Why would they make one decision at one point of time and then change their mind later? This preference reversal is a result of what is called time inconsistency, which some consider to be evidence of irrationality.
While the evidence of time inconsistent behaviour has grown, evolutionary explanations of how rates of time preference could have evolved generally do not generate these preference reversals. Time preference is consistent as any genes that increase an individual’s predisposition to have irrational decision rules should be progressively eliminated from the population. In most papers on time preference, such as those by Hansson and Stuart, Rogers and Robson and Samuelson, decisions are time consistent.
One useful paper in this area is by Peter Sozou, who seeks to offer a basis for this behaviour, which could be applied in an evolutionary context. The model in the paper matched the intuition I have in my head, so it is nice to come across an old paper that formalises the concept.
Sozou’s idea is that uncertainty as to the nature of any underlying hazards can explain time inconsistent preferences. Suppose there is a hazard that may prevent the pay-off from being realised. This would provide a basis (beyond impatience) for discounting a pay-off in the future. But suppose further that you do not know what the specific probability of that hazard being realised is (although you know the probability distribution). What is the proper discount rate?
Sozou shows that as time passes, one can update their estimate of the probability of the underlying hazard. If after a week the hazard has not occurred, this would suggest that the probability of the hazard is not very high, which would allow the person to reduce the rate at which they discount the pay-off. When offered with a choice of one or two bottles of wine 30 or 31 days into the future, the person applies a lower discount rate in their mind than for the short period because they know that as each day passes in which there has been no hazard preventing the pay-off, their estimate of the hazard’s probability will drop.
This example provides a nice evolutionary explanation of the shape of time preferences. In a world of uncertain hazards, it would be appropriate to apply a heavier discount rate for a short-term pay-off. It is rational and people who applied that rule would not have lower fitness than those who apply a constant discount rate.
While this is a neat scenario, it does leave some questions open. The most obvious is that in many of the experiments that have demonstrated time-inconsistent preferences, there is clearly no hazard. The pay-off is near certain. We could question whether time-inconsistent behaviour under certainty is simply an evolutionary hang-up from more hazardous and uncertain times – although those types of explanations seem to be a “just-so” story.
If Sozou’s explanation represents an underlying predisposition, it also seems that some people are better at overcoming it than others. As I have blogged about before, people vary widely in their ability to delay gratification (with strong links to life outcomes), and variation can be seen across countries. If this trait is sitting in our sub-conscious, it seems that some people are far better at putting aside that urge to discount in a time-inconsistent manner in situations where the pay-off is certain to occur.
There are also some questions about what form the probability distribution of the underlying hazard needs to take to generate the form of time-inconsistency shown in experiments. In Sozou’s paper, he used an exponential probability distribution, and sensitivity analysis showed that this could be relaxed somewhat. However, the question becomes what types of hazards humans faced during their evolution and what the probability distributions of these hazards are. To look at this question, Sozou suggests some cross-species analysis to examine discount rates and the particular ecological hazards faced by those species.
One other outstanding issue is that this explanation offered in the paper does not explain the irrationality in the example I used above. If someone did originally accept the two bottles of wine at 31 days, under Sozou’s model they would not change their mind at day 30 if given the chance. They now have 30 days of observation of the underlying hazard rate and would not want to discount the remaining day of waiting at a high rate. Irrationality of this form is still not explained.
Sozou, P. (1998). On hyperbolic discounting and uncertain hazard rates Proceedings of the Royal Society B: Biological Sciences, 265 (1409), 2015-2020 DOI: 10.1098/rspb.1998.0534