Majorization, entropy and paired comparisons. (English) Zbl 0721.62067

Joe, Harry

Ann. Stat. 16, No. 2, 915-925 (1988).

Constrained majorization orderings and entropy functions are used to study the class of probability matrices associated with paired comparisons. Majorization orderings are also defined to handle the cases of order effects and/or ties. Results are obtained for maximal and minimal probability matrices with respect to the majorization ordering; these are related to transitivity conditions.
The Bradley-Terry and Thurstone-Mosteller models are shown to be maximum entropy models. New models based on maximum entropy are obtained for the cases of order effects and ties.

MSC:

62J15	Paired and multiple comparisons; multiple testing
06A06	Partial orders, general

Keywords:

Davidson models; Bradley-Terry model; Constrained majorization orderings; entropy functions; probability matrices; paired comparisons; order effects; ties; transitivity conditions; Thurstone-Mosteller models; maximum entropy models