Consider the example of probability matching: an experimenter asks a subject to guess the outcome of a coin toss, where, unknown to the subject, the coin is biased—75% heads and 25% tails—and the experimenter agrees to pay the subject $1 if she guesses correctly, but will expect the subject to pay $1 if she guesses incorrectly. This experiment is then repeated many times with the same subject and coin (and the tosses are statistically independent). After a sufficiently long sample of tosses, it should be possible for the subject to observe that the coin is biased toward heads, at which point the subject should always guess heads so as to maximize her cumulative expected winnings. However, the vast majority of subjects do not follow this expected-wealth-maximizing strategy; instead, they appear to randomize, guessing heads 75% of the time and tails 25% of the time!
This strange and well-known example of irrationality in human judgment may not be so irrational after all when viewed from the perspective of evolutionary biology (Lo and Brennan, 2009). To see why, consider the hypothetical case of animal deciding whether to build its nest in a valley or on a plateau. If the weather is sunny, nesting in the valley will provide shade, leading to many offspring, whereas nesting on the plateau provides no cover from the sun, leading to no offspring. However, the opposite is true if the weather is rainy: the valley floods, hence any offspring will drown in their nests, but nests on the plateau survive, yielding many offspring. Now suppose the probability of sunshine is 75% and the probability of rain is 25%. The “rational” behavior for all individuals to follow is to build their nests in the valley, for this maximizes the expected number of each individual’s offspring. Suppose the entire population exhibits such individually optimal behavior—the first time there is rain, the entire population will cease to reproduce, leading to extinction. Similarly, if the entire population behaves in the opposite manner, always choosing the plateau, the first time sunshine occurs, extinction also follows. Lo and Brennan (2009) show that the behavior that maximizes the growth of the population is for individuals to randomize their nesting choice by choosing the valley with probability 75% and the plateau with 25% probability. Matching probabilities confers an evolutionary advantage, not for the individual, but rather for the population as a whole. And since, by definition, the current population consists of the survivors, it will reflect such advantageous behavior disproportionately to the extent that behavior is heritable. While probability matching is, indeed, irrational from the perspective of maximizing an individual’s expected wealth, its evolutionary advantage is clear.
—humans usually do maximize their expected wealth but, under certain circumstances, they may engage in other types of “hard-wired” behavior that are far more primitive… several commonly observed behaviors such as risk aversion, loss aversion, and randomization are adaptive traits that can emerge organically through evolution
Andrew W. Lo SBE 2020: A Complete Theory of Human Behavior, September 30, 2010, http://ssrn.com/abstract=1889318