The Paradox of Allais' Effect

Viewing a solar eclipse -- even a partial one, such as this morning's spectacle in Beijing -- is truly awe-inspiring. Affording a rare glimpse into the grand workings of the solar system that mystified -- and sometimes terrified -- our ancestors, it provides a clear reminder of how far civilization has come because of careful, scientific study, and how important education is in that process. Nevertheless, there is something else connected with solar eclipses that both directly and coincidentally casts a small umbra of doubt on the reasonableness of human reasoning: the "Allais effect" -- an anomalous change in a pendulum's oscillation that purportedly occurs when the moon passes directly between the earth and sun.

Maurice Allais (1911-2010), who first observed the stated effect during a solar eclipse in 1954, is a remarkable figure in the history of science. A distinguished economist, he received the 1988 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel "for his pioneering contributions to the theory of markets and efficient utilization of resources." Allais is probably best know for the "Allais paradox" of decision theory, published in 1953, which demonstrates that human beings often make decisions inconsistent with the basic tenets of expected-utility theory.

Essentially, Allais' observation was that people fail to abide by the "independence axiom": If alternative A is preferred to alternative B, then a random mixture of A with C will be preferred to the same random mixture of B with C. (For example, if one prefers a hike in the mountains to a walk on the beach on a day that is certain to be sunny, then he/she should prefer "hiking in the mountains if it's sunny and playing computer games if it's rainy" to "walking on the beach if it's sunny and playing computer games if it's rainy" on a day whose weather is variable -- an assumption that seems unequivocally reasonable to me.) Allais' paradox is often cited as the birth of the field of behavioral economics, and the beginning of a vast academic literature on alternatives to expected utility.

Allais also held a deep interest in physics, particularly the relationship between gravitation and electromagnetism, and conducted several experiments with a paraconical pendulum, a highly sensitive instrument of his own design. In the course of those experiments, he observed several anomalies, the most striking of which was an irregular change in the direction of oscillation of the pendulum during the short period in which it fell within the shadow of a total solar eclipse. Allais eventually proposed that this effect was evidence of a natural "direction" in space associated with the earth's motion through an "aether," concepts previously pushed to the scientific fringe by the successes of relativity theory. Regrettably, and perhaps because of the heterodox nature of Allais' claims, meager scientific effort has been spent in the last half-century trying to clarify his results.

In comparing Allais' two counterintuitive observations -- that pendulums behave oddly during eclipses and that human beings behave oddly when making decisions involving uncertainties -- I can't help feeling the former is much more important than the latter. After all, it's rather obvious that people are fallible when it comes to assessing matters of chance -- everyone from my childhood friend who explained very seriously that in chess, "there is a 50 percent chance of winning, a 50 percent chance of losing, and a 50 percent chance of getting a draw"; to the eminent statistician Leonard J. Savage, who admitted to being fooled by Allais' paradox, but attributed his mistake to personal error rather than a deficiency in the independence axiom.

Indeed, having been tricked by Allais' paradox myself, I wonder why scholars don't spend more effort educating people how to make decisions correctly when confronted by uncertainties, rather than trying to describe -- often with very elaborate mathematical models -- how people actually make decisions incorrectly. Along these lines, one could ponder what the world would be like today if the successors of Copernicus and Galileo had spent their time studying the consequences of believing in a geocentric universe, rather than trying to educate others that the earth revolves around the sun. Likewise, one can ponder what the world will not be like in the future if we continue to ignore Allais' effect.