caa a22 4500 46577489X CHVBK 20180323111939.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02204847 doi (NATIONALLICENCE)springer-10.1007/BF02204847 Fishburn Peter AT&T Bell Laboratories, 07974, Murray Hill, New Jersey, USA aut Unique nontransitive additive conjoint measurement on finite sets [Elektronische Daten] [Peter Fishburn] Nontransitive additive conjoint measurement for a binary relation>on a setX 1 ×X 2 ×...×X n ofn-tuples(x 1,...,x n ), (y 1,...,y n ),... is concerned with the representation $$(x_1 ,...,x_n ) > (y_1 ,...,y_n ) \Leftrightarrow \sum\limits_{i = 1}^n {\phi _i (x_i ,y_i ) > 0,} $$ whereφ φ is a skew symmetric real valued function onX i ×X i . The representation is said to be unique if, whenever (φ 1,...φ n ) and (φ 1 ′ ,...φ n ′ ) satisfy it, there is a positive constant λ such thatφ i ′ =λφ i for alli. This paper investigates unique representation for nontransitive additive conjoint measurement when everyX i is finite. It begins with background on measurement theory, followed by conditions for uniqueness that are based on equations ∑φ i (x i ,y i )=0 that correspond to the symmetric complement of >. We then examine aspects of sets of unique solutions forn=2, for arbitraryn with |X i |=2 for alli, and forn=3. Various combinatorial and number-theoretic arguments are used to derive results that count and characterize sets of unique solutions. J.C. Baltzer AG, Scientific Publishing Company, 1990 Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 23/1(1990-12-01), 213-234 0254-5330 23:1<213 1990 23 10479 https://doi.org/10.1007/BF02204847 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02204847 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Fishburn Peter AT&T Bell Laboratories, 07974, Murray Hill, New Jersey, USA aut NATIONALLICENCE 773 0- Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 23/1(1990-12-01), 213-234 0254-5330 23:1<213 1990 23 10479 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer