Proportionality, linearity, and parameter constancy: Messick and Sentis reconsidered

Messick and Sentis found greater support for weak proportionality in subjects' outcome allocations (suggesting that subjects wish to maintain a constant ratio between outcomes across situations when inputs are held constant) than for constant differences between outcomes. They claimed that their data thus provided stronger support for Adams' ratio definition of equity than for Harris' linear formula. A dialogue between the two sets of authors establishes that (1) so far as their specification of fair outcomes is concerned, Adams' formula is a special case of the linear formula; (2) weak proportionality does not necessarily follow from Adams' formula and can be derived from the linear formula; (3) Adams' formula applied to subjective (rather than experimenter-defined) inputs nevertheless provides a more natural base from which to derive weak proportionality than does the linear formula in its general form; (4) excellent fits to several sets of data, including much better fit to Messick and Sentis' data than that provided by weak proportionality, are obtained if we assume that subjects use allocations which are a weighted average of those implied by Adams' formula, the Equality principle, and Komorita and Kravitz' Equal Excess Norm; and (5) a fit to Messick and Sentis' data that is almost as good as that provided by the weighted solutions model is obtained by assuming that subjects apply Adams' formula to subjective inputs and subjective outcomes that are different from the corresponding experimenter-defined values. It is agreed that the delineation of the relationships among observable properties of outcome distributions, alternative equity formulae, and different psychological processes is as important as it can be devious.