# Acronyms that contain the term stochastic transitivity

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#### What does stochastic transitivity mean?

Stochastic transitivity
Stochastic transitivity models are stochastic versions of the transitivity property of binary relations studied in mathematics. Several models of stochastic transitivity exist and have been used to describe the probabilities involved in experiments of paired comparisons, specifically in scenarios where transitivity is expected, however, empirical observations of the binary relation is probabilistic. For example, players' skills in a sport might be expected to be transitive, i.e. "if player A is better than B and B is better than C, then player A must be better than C"; however, in any given match, a weaker player might still end up winning with a positive probability. Tighly matched players might have a higher chance of observing this inversion while players with large differences in their skills might only see these inversions happen seldomly. Stochastic transitivity models formalize such relations between the probabilities (e.g. of an outcome of a match) and the underlying transitive relation (e.g. the skills of the players). A binary relation ≿ {\textstyle \succsim } on a set A {\displaystyle {\mathcal {A}}} is called transitive, in the standard non-stochastic sense, if a ≿ b {\displaystyle a\succsim b} and b ≿ c {\displaystyle b\succsim c} implies a ≿ c {\displaystyle a\succsim c} for all members a , b , c {\displaystyle a,b,c} of A {\displaystyle {\mathcal {A}}} . Stochastic versions include of transitivity include:

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