The expected number of pairwise comparisons needed to learn a partial order on n elements is shown to be at least /4 − (), and an algorithm is given that needs only /4 + () comparisons on average. In addition, the optimal strategy for learning a poset with four elements is presented

It is shown that each continuous transformation from Euclidean -space ( > 1) into Euclidean -space that preserves the equality of distances (that is, fulfils the implication is a similarity map. The case of equal dimensions already follows from the Beckman-Quarles Theorem

Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for representability probabilities are produced by...

Actual individual preferences are neither complete (=total) nor antisymmetric in general, so that at least every must be an admissible input to a satisfactory choice rule. It is argued that the traditional notion of “indifference” in individual preferences is misleading and should be...