— Ch. 1 · The Wager of 1670 —
Decision theory.
~4 min read · Ch. 1 of 7
Blaise Pascal published his Pensées in 1670, introducing a famous wager about the existence of God. This text marked an early moment when probability theory began to influence how humans thought about choices under uncertainty. Pascal argued that one should calculate the potential outcomes and their probabilities before making a decision. His approach laid groundwork for later thinkers who would formalize these ideas into mathematical models. The concept of expected value emerged from this era as a way to weigh risks against rewards. Christiaan Huygens later refined these initial thoughts on risk and uncertainty during the same century. These pioneers created a framework that allowed society to understand decisions involving chance.
Rationality Versus Reality
Daniel Bernoulli published Exposition of a New Theory on the Measurement of Risk in 1738 to challenge existing views on financial value. He used the St. Petersburg paradox to show that people do not always choose based on pure monetary gain. A Dutch merchant trying to insure cargo sent from Amsterdam to St. Petersburg in winter faced a choice between financial loss and peace of mind. Bernoulli defined a utility function to compute expected utility rather than just expected financial value. John von Neumann and Oskar Morgenstern later formalized these concepts in the 1940s through Game Theory. Their work established a rational basis for decision-making under uncertainty but ignored human psychological factors. Modern scholars like Daniel Kahneman and Amos Tversky challenged these assumptions decades later by highlighting cognitive biases.The Paradoxes of Value
Maurice Allais and Daniel Ellsberg demonstrated that human behavior often departs systematically from expected-utility maximization. The Allais paradox and Ellsberg paradox revealed situations where people make choices that contradict standard probability models. Daniel Kahneman and Amos Tversky found three regularities in actual human decision-making during their research. They observed that losses loom larger than gains, meaning people feel pain from losing money more intensely than pleasure from gaining it. People focus more on changes in their utility-states than they focus on absolute utilities. The estimation of subjective probabilities is severely biased by anchoring, which distorts how individuals assess risk. These findings led to the development of prospect theory, which modified expected utility theory to account for psychological factors.