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In order theory, a branch of mathematics, … In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are compared by their scores and where scores within a given margin of error are deemed incomparable. Semiorders were introduced and applied in mathematical psychology by Duncan Luce as a model of human preference. They generalize strict weak orderings, in which items with equal scores may be tied but there is no margin of error. They are a special case of partial orders and of interval orders, and can be characterized among the partial orders by additional axioms, or by two forbidden four-item suborders., or by two forbidden four-item suborders.
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https://www.imbs.uci.edu/files/personnel/luce/pre1990/1956/Luce_Econometrica_1956.pdf +
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Two mutually incomparable two-point linear orders
, A three-point linear order, with a fourth incomparable point
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R. Duncan Luce
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Forbidden: three linearly ordered points and a fourth incomparable point
, Forbidden: two mutually incomparable two-point linear orders
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Duncan
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Luce
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In order theory, a branch of mathematics, … In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are compared by their scores and where scores within a given margin of error are deemed incomparable. Semiorders were introduced and applied in mathematical psychology by Duncan Luce as a model of human preference. They generalize strict weak orderings, in which items with equal scores may be tied but there is no margin of error. They are a special case of partial orders and of interval orders, and can be characterized among the partial orders by additional axioms, or by two forbidden four-item suborders., or by two forbidden four-item suborders.
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Semiorder
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