When can information from ordinal scale variables be integrated?

Abstract

Many theoretical constructs of interest to psychologists are multidimensional and derive from the integration of several input variables. We show that input variables that are measured on ordinal scales cannot be combined to produce a stable weakly ordered output variable that allows trading off the input variables. Instead a partial order is obtained in which the amount of ordering depends on the number and nature of the input variables and the relationship between them. However, if trade-offs are excluded, it is still possible to obtain a weak order using lexicographic ordering of the input variables. An implication is that psychological processes that integrate information from different input variables and that produce consistent output require that the input variables be measured on more than ordinal scales. A further implication is that the level of measurement of the input variables affects the kind of psychological model that can be applied to the process.