Extensive measurement with incomparability
2008 (English)In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 52, no 4, 250-259 p.Article in journal (Refereed) Published
Standard theories of extensive measurement assume that the objects to be measured form a complete order with respect to the relevant property. In this paper, representation and uniqueness theorems are presented for a theory that departs radically from this completeness assumption. It is first shown that any quasi-order on a countable set can be represented by vectors of real numbers. If such an order is supplemented by a concatenation operator, yielding a relational structure that satisfies a set of axioms similar to the standard axioms for an extensive structure, we obtain a scale possessing the crucial properties of a ratio scale. Incomparability is thus compatible with extensive measurement. The paper ends with a brief discussion on some possible applications and developments of this result.
Place, publisher, year, edition, pages
2008. Vol. 52, no 4, 250-259 p.
IdentifiersURN: urn:nbn:se:uu:diva-98996DOI: 10.1016/j.jmp.2008.01.001ISI: 000258604000004OAI: oai:DiVA.org:uu-98996DiVA: diva2:201907