Evolution and irrationality

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.

This post was chosen as an Editor's Selection for ResearchBlogging.orgOne 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

6 comments

  1. Isn’t the easier answer just that people tend to perceive numeric quantities logarithmically? You have this same effect in things like light or weight perception, adding 1 lb to 5 lbs is more perceivable than adding 1 lbs to 50 lbs; yet this never causes rationality puzzles for researchers. When our mind is reasoning about the future rewards, and ‘visualizing’ them on a time number-line, the discrepancy between 30 and 31 is less obvious than between 0 and 1. Of course, just like people can be trained to say that 5 not 3 is halfway between 1 and 9, you can learn to reason your way out of this sort of time perception.

    This way, if you really need an evolutionary story, then you can pick any story used to justify the Weber-Fechner law, and then just say that this is the module for comparing quantities, be they numeric, time, or weight.

    1. It’s an interesting thought but I’m not sure this explanation helps. Logarithmic discounting [such as e^(-r*log(t))] results in time consistent decisions, which does not explain the choice reversal in the example.

      Even if we came up with a logarithmic discounting function that delivered time inconsistent decisions, appealing to justifications of the Weber-Fechner law still leaves us a long way from an answer. Many W-F explanations revolve around sensory limitations to measurement, but here the subject has access to the measurement itself. And in that case, why weren’t there evolutionary pressures to adopt a “rational” response? (not that I think there were a lot of 30 versus 31 day choices in the environment of evolutionary adaptedness)

      1. I wasn’t suggesting logarithmic discounting (why should we remain married to the idea of rational discounting when we are trying to explain an irrational behavior?). I was suggesting a much simpler scheme. For each perceived time delay, I have some associated utility cost say C_S for a small time delay and C_B for a big time delay. Similarly, there is some benefit for a big reward R_B and small reward R_S.

        When I compare today and tomorrow, it looks like a big time delay (similar to how adding 5 lbs to a 1lbs box I am holding, feels like a big difference), so my reward for getting the wine now versus later is: R_S – (R_B – C_B). On the other hand, when I am looking at a single day delay 30 days out, it looks like a small time delay (similar to how adding 5lbs to a 100 lbs box I am golding, does not feel like much of a difference)m and so my reward for getting the wine then versus later is: R_S – (R_B – C_S). Obviously, we can have the first number positive and the second negative (and thus arrive at different decisions) as long as C_B > R_ B – R_S > C_S.

      2. I’m not married to rational discounting. I was just pointing out that if people perceive time logarithmically, they do not experience preference reversals (of course, logarithmic discounting could be argued to be irrational on other grounds).

        Your alternative formulation is less strongly tied to your idea of the Weber-Fechner law. It is closer to hyperbolic discounting (which is also closer to experimental evidence). Why would you prefer that formulation to logarithmic discounting if you consider that people perceive quantities logarithmically?

  2. I think this habit could have emerged from our barter system days. If you have a debt owed to you by a notoriously bad debtor, and he offered you a choice of one bottle of wine today or two next week, you’re going to take the one right away because you know that he has the one he’s holding in his hands.

    Instant gratification has its perks in addition to its cons.

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