The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the incorrect belief that, if an event has occurred more frequently than expected, it is less likely to happen again in the future. The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been fewer than the expected number of sixes.
Amos Nathan Tversky was an Israeli cognitive and mathematical psychologist and a key figure in the discovery of systematic human cognitive bias and handling of risk.
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome.
Prospect theory is a theory of behavioral economics, judgment and decision making that was developed by Daniel Kahneman and Amos Tversky in 1979. The theory was cited in the decision to award Kahneman the 2002 Nobel Memorial Prize in Economics.
Decision theory is a branch of applied probability theory and analytic philosophy concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome.
The St. Petersburg paradox or St. Petersburg lottery is a paradox involving the game of flipping a coin where the expected payoff of the theoretical lottery game approaches infinity but nevertheless seems to be worth only a very small amount to the participants. The St. Petersburg paradox is a situation where a naïve decision criterion that takes only the expected value into account predicts a course of action that presumably no actual person would be willing to take. Several resolutions to the paradox have been proposed, including the impossible amount of money a casino would need to continue the game indefinitely.
Loss aversion is a psychological and economic concept which refers to how outcomes are interpreted as gains and losses where losses are subject to more sensitivity in people's responses compared to equivalent gains acquired. Kahneman and Tversky (1992) have suggested that losses can be twice as powerful, psychologically, as gains. When defined in terms of the utility function shape as in the cumulative prospect theory (CPT), losses have a steeper utility than gains, thus being more "painful" than the satisfaction from a comparable gain as shown in Figure 1. Loss aversion was first proposed by Amos Tversky and Daniel Kahneman as an important framework for prospect theory – an analysis of decision under risk.
The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour.
In decision theory, subjective expected utility is the attractiveness of an economic opportunity as perceived by a decision-maker in the presence of risk. Characterizing the behavior of decision-makers as using subjective expected utility was promoted and axiomatized by L. J. Savage in 1954 following previous work by Ramsey and von Neumann. The theory of subjective expected utility combines two subjective concepts: first, a personal utility function, and second a personal probability distribution.
In gambling, economics, and the philosophy of probability, a Dutch book or lock is a set of odds and bets that ensures a guaranteed profit. It is generally used as a thought experiment to motivate Von Neumann–Morgenstern axioms or the axioms of probability by showing they are equivalent to philosophical coherence or Pareto efficiency.
In economics, Knightian uncertainty is a lack of any quantifiable knowledge about some possible occurrence, as opposed to the presence of quantifiable risk. The concept acknowledges some fundamental degree of ignorance, a limit to knowledge, and an essential unpredictability of future events.
Howard Raiffa was an American academic who was the Frank P. Ramsey Professor (Emeritus) of Managerial Economics, a joint chair held by the Business School and Harvard Kennedy School at Harvard University. He was an influential Bayesian decision theorist and pioneer in the field of decision analysis, with works in statistical decision theory, game theory, behavioral decision theory, risk analysis, and negotiation analysis. He helped found and was the first director of the International Institute for Applied Systems Analysis.
The Allais paradox is a choice problem designed by Maurice Allais (1953) to show an inconsistency of actual observed choices with the predictions of expected utility theory. Rather than adhering to rationality, the Allais paradox proves that individuals rarely make rational decisions consistently when required to do so immediately. The independence axiom of expected utility theory, which requires that the preferences of an individual should not change when altering two lotteries by equal proportions, was proven to be violated by the paradox.
The ambiguity effect is a cognitive tendency where decision making is affected by a lack of information, or "ambiguity". The effect implies that people tend to select options for which the probability of a favorable outcome is known, over an option for which the probability of a favorable outcome is unknown. The effect was first described by Daniel Ellsberg in 1961.
In decision theory and economics, ambiguity aversion is a preference for known risks over unknown risks. An ambiguity-averse individual would rather choose an alternative where the probability distribution of the outcomes is known over one where the probabilities are unknown. This behavior was first introduced through the Ellsberg paradox.
Cumulative prospect theory (CPT) is a model for descriptive decisions under risk and uncertainty which was introduced by Amos Tversky and Daniel Kahneman in 1992. It is a further development and variant of prospect theory. The difference between this version and the original version of prospect theory is that weighting is applied to the cumulative probability distribution function, as in rank-dependent expected utility theory but not applied to the probabilities of individual outcomes. In 2002, Daniel Kahneman received the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel for his contributions to behavioral economics, in particular the development of Cumulative Prospect Theory (CPT).
David Schmeidler was an Israeli mathematician and economic theorist. He was a Professor Emeritus at Tel Aviv University and the Ohio State University.
The end-of-the-day betting effect is a cognitive bias reflected in the tendency for bettors to take gambles with higher risk and higher reward at the end of their betting session to try to make up for losses. William McGlothlin (1956) and Mukhtar Ali (1977) first discovered this effect after observing the shift in betting patterns at horserace tracks. Mcglothlin and Ali noticed that people are significantly more likely to prefer longshots to conservative bets on the last race of the day. They found that the movement towards longshots, and away from favorites, is so pronounced that some studies show that conservatively betting on the favorite to show in the last race is a profitable bet despite the track’s take.
Risk aversion is a preference for a sure outcome over a gamble with higher or equal expected value. Conversely, rejection of a sure thing in favor of a gamble of lower or equal expected value is known as risk-seeking behavior.
The uncertainty effect, also known as direct risk aversion, is a phenomenon from economics and psychology which suggests that individuals may be prone to expressing such an extreme distaste for risk that they ascribe a lower value to a risky prospect than its worst possible realization.
