I have a couple of news stories on Nature’s site this week. Here’s the first. This is, I think, more of a cautionary tale than a surprising discovery. One researcher I spoke to put it like this:
“Imagine a person trying to clime to the top of the hill. Each step up takes this decision maker toward her goal. We see this person trudging along upward, but then we see this person not step uphill, but step downhill. Is this irrational? As it turns out there is a large bolder in her way and stepping down and around the boulder made sense considering the larger goal of getting to the top of the hill. But, if you only look at her behavior step by step, then moving downhill will look “irrational” or “intransitive” but really that’s a misunderstanding of the problem and landscape which is larger than just one step at a time. Moreover it is a fundamental misunderstanding of the idea of rationality to demand that every step of the decision maker be upward in order to be rational.”
The moral, I think, is that when we see choices like this that appear to be irrational, it pays to look for “boulders” before assuming that they are truly the result of error, limited cognitive resources, or sheer caprice.
Theory shows it may be best to rearrange your preferences if the options might change
You prefer apples to oranges, but cherries to apples. Yet if I offer you just cherries and oranges, you take the oranges. Are you stupid or crazy?
Not necessarily either, according to a new study. It shows that in some circumstances a decision like this, which sounds irrational, can actually be the best one. The work is published in Biology Letters .
Organisms, including humans, are often assumed to be evolutionarily hard-wired to make optimal decisions, to the best of their ability. Sticking with fixed preferences when weighing up choices – for example, in selecting food sources – would seem to be one aspect of such rationality. If A is preferred over B, and B over C, then surely A should be selected when the options are just A and C? This seemingly logical ordering of preferences is called transitivity.
What’s more, if A is preferred when both B and C are available, then A should ‘rationally’ remain the first choice from only A and B – a principle called the independence of irrelevant alternatives (IIA).
But sometimes animals don’t display such apparent logic. For example, honeybees and gray jays  and hummingbirds  have been seen to violate IIA. “On witnessing such behaviour in the past, people have simply assumed that it is not optimal, and then proposed various explanations for it”, says mathematical biologist Pete Trimmer of the University of Bristol in England. “They assume that the individual or species is not adapted to solve the given task, or that it is too costly to compute it accurately.”
The theoretical model of Trimmer and his colleagues shows that in contrast, violations of transitivity can sometimes be adaptively optimal and therefore perfectly rational. “It should mean that researchers will be less prone to quickly claiming that a particular species or individual is behaving irrationally” in these cases, he says.
The key to the apparent “irrationality” in the Bristol group’s model is that the various choices might appear or disappear in the future. Then the decision becomes more complicated than a simple, fixed ranking of preferences. Is it better to expend time and energy eating a less nutritious food that’s available now, or to ignore it because a better alternative might become available in a moment?
The researchers find that, for some particular choices of the nutritional values of food sources A, B and C, and of their probabilities of appearing or vanishing in the future, an optimal choice for pairs of foods can prefer B to A, C to B and A to C, which violates transitivity.
Trimmer and colleagues also find some situations where IIA is violated in the optimal solution. These choices look irrational, but aren’t.
Behavioural ecologist Tanya Latty of the University of Sydney, who has observed violations of IIA in the food choices of a slime mould , points out that some examples of apparent irrationality seen in the foraging decisions of non-human animals are already understood to come from the fact that animals rarely have all their options available at once. “The choice is not so much ‘which item should I consume’ as ‘should I spend time consuming this particular item, or should I keep looking’?” she explains. “Some of what we perceive as irrational behaviour would then simply be the result of presenting animals with the unusual case of a simultaneous choice, when they have evolved to make optimal sequential choices.”
Latty feels that the new work by Trimmer and colleagues “goes some way toward combining the sequential and simultaneous viewpoints”. It helps to show that “decision strategies that appear irrational in simplified experimental environments can be adaptive in the complex, dynamic worlds in which most organisms live.”
She thinks it might be possible to test these ideas. “I suspect it would be easy enough to train animals (or humans) to forage on items that had different probabilities of disappearing or reappearing. Then you could test whether or not playing with these probabilities influences preferences.” The difficulty is that organisms may already take into account natural tendencies for choices to disappear.
“I think it is absolutely worth investigating further”, Latty says. “It has certainly given me some ideas for future experiments.”
“The paper is very nicely done”, says economist and behavioural scientist Herb Gintis of the Santa Fe Institute in New Mexico, but he adds that “there is nothing anomalous or even surprising about these results.”
Gintis explains that the choices only seem to violate transitivity or IIA because there are in fact more than three. “Usually when IIA fails, the modeler is using the wrong choice space”, he says. “An expansion of the choice space to include probabilities of appearance and disappearance would correct this.”
Trimmer sees no reason why the results shouldn’t apply to humans. “Of course, much of the time we make errors, which is a very simple explanation for any behaviour which appears irrational”, he says. “But an individual who displays intransitive choices is not necessarily behaving erroneously.”
He feels that such behaviour could surface in economic contexts, for example in cases where people are choosing investment strategies from savings schemes that may or may not be available in the future. In other words, while economic behaviour is clearly not always rational (as some economists have assumed), we shouldn’t be too hasty in assuming that what seems irrational necessarily is.
1. McNamara, J. M., Trimmer, P. C. & Houston, A. I. Biol. Lett. 20130935 (2014).
2. Shafir, S., Waite, T. A. & Smith, B. H. Behav. Ecol. Sociobiol. 51, 180-187 (2002).
3. Bateson, M., Healy, S. D. & Hurly, T. A. Anim. Behav. 63, 587-596 (2002).
4. Latty, T. & Beekman, M. Proc. R. Soc. B 278, 307-312 (2011).