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Generalized to stochastic versions (stochastic transitivity), the study of transitivity finds applications of in decision theory, psychometrics and utility models. [19] A quasitransitive relation is another generalization; [5] it is required to be transitive only on its non-symmetric part. Such relations are used in social choice theory or ...
There are four axioms of the expected utility theory that define a rational decision maker: completeness; transitivity; independence of irrelevant alternatives; and continuity. [11] Completeness assumes that an individual has well defined preferences and can always decide between any two alternatives.
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function. This function is known as the von Neumann–Morgenstern utility function.
The concept of transitivity is highly debated, with many examples suggesting that it does not generally hold. One of the most well-known is the Sorites paradox, which shows that indifference between small changes in value can be incrementally extended to indifference between large changes in values. [39] Another criticism comes from philosophy.
Game Theory - Fairness of random knockout tournaments is strongly dependent on the underlying stochastic transitivity model. [16] [17] [18] Social choice theory also has foundations that depend on stochastic transitivity models. [19]
A transitive set (or class) that is a model of a formal system of set theory is called a transitive model of the system (provided that the element relation of the model is the restriction of the true element relation to the universe of the model). Transitivity is an important factor in determining the absoluteness of formulas.
The mathematical notion of quasitransitivity is a weakened version of transitivity that is used in social choice theory and microeconomics. Informally, a relation is quasitransitive if it is symmetric for some values and transitive elsewhere. The concept was introduced by Sen (1969) to study the consequences of Arrow's theorem.
Transitivity or transitive may refer to: Grammar. Transitivity (grammar), a property regarding whether a lexical item denotes a transitive object;