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Bernoulli's paradox: How does infinite expected value challenge our economic thinking?
In the world of economics, the expected utility hypothesis is the cornerstone of many theories that attempt to describe mathematically how decision makers behave in the face of uncertainty. The expected utility hypothesis assumes that rational actors will choose the option that maximizes their utility, where utility represents their subjective satisfaction with different options. However, this theory seems to be stretched when faced with certain psychological experimental data. At this point, Bernoulli's paradox triggered new thinking and challenged the long-standing economic theories.
Perhaps sometimes, what we think of as rationality is actually just a subjective judgment?
Bernoulli’s paradox stems from his St. Petersburg paradox, which he proposed in 1713, which states that the emergence of infinite expected values in certain bets makes it difficult to understand why people would still choose not to participate in these bets. This has triggered a reflection on expected utility theory and prompted us to reassess the relationship between risk and utility.
Bernoulli believed that the gain of utility should not be linear for people, and he proposed that a nonlinear utility function should be used to replace the expected monetary value. This view implies that for an already wealthy person, the utility of extra money will be much less than for a poor person. He further emphasized that the utility obtained by individuals has diminishing marginal utility, that is, as the level of wealth increases, the additional utility felt will decrease.
In the mind of a gambler, what he pursues is not the expected monetary gain, but the moral expectation obtained.
In this context, the utility theory created by Bernoulli not only occupies an important position in mathematical economics, but also provides us with a more sophisticated decision-making framework than simply using expected values. This theory has inspired a variety of emerging economic perspectives, particularly in social psychology and behavioral economics.
With Frank Ramsey's proposal of the Ramsey representation theorem in 1926, the economics community continued to explore how to introduce subjectivity and uncertainty into decision making. Ramsey believes that understanding individuals' choices and preferences can help us predict their behavior. This established a psychological model for scientists behind personal choices and, more importantly, revised the traditional understanding of rational choices.
In the 1950s, American statistician Leonard Savage proposed a series of axioms to solve the problem of utility prediction and established a more complete framework, which allows us to have a theoretical basis in uncertain situations. to make a choice. His theory is based on observable choices, integrates subjective utility with individual cognitive preferences, and further forms one of the cornerstones of modern behavioral economics.
We are neutral with respect to uncertainty, and observable behavior is sufficient to predict future outcomes?
For many people, the concepts of utility and expected value are deeply rooted in their minds, but as the theory deepens, we find that many known and taken-for-granted things are actually full of uncertainty. Similarly, different people will have different risk preferences and perceptions of the same event. This brings us to an important discussion in behavioral economics: how do the preferences of actors influence collective choices?
Over time, many new theories have emerged in the economics community to explain and extend the expected utility hypothesis, such as prospect theory and bounded rationality theory, which attempt to fill the gap between human behavior and economic theory. The development of these concepts has given us a deeper and more nuanced understanding of economic decision-making.
So, when people are busy making consumption and investment decisions, perhaps they should stop and think about whether it is money or the moment of helping others. Is it the deeper psychological and behavioral motivations behind the seemingly rational choices that really influence our decisions? ?
