Test of a subtractive theory of "fair" allocations.

Abstract

The authors would like to express appreciation to Michael Birnbaum, Jerome Busemeyer, and Richard Harris for valuable comments or discussions, to Karen Biagini for help with data collection, and to Norman Anderson for providing his data for reanalysis.

Cognitive and social effects in allocation behavior: A new view on loci of developmental differences

“…When the monotonic J is linear, then the factorial plot of the I A ¥ I B effect should be parallel across the low through high levels of O A . Statistically, therefore, only the three main effects of O A , I A , and I B should be significant in ANOVA (Mellers & Hartka, 1989;Singh, 1995). This prediction follows because of the adding and subtracting operations among the three experimentally manipulated factors of O A , I A , and I B in the allocation task.…”

“…Towards this end, we employed a three-factor task of deciding 'fair' pay for person B (O B ) after knowing the pay of person A (O A ), input of person A (I A ), and input of person B (I B ). Singh (1995) found that the majority of Indian adults considered the differences between subjective values of inputs, relative to the pay of the comparison person, in allocating 'fair' pay as the subtractive model, in fact, prescribed (Mellers & Hartka, 1989). However, the allocation behavior was adjusted because of the 'floor' effect at the lower end and the 'ceiling' effect at the upper end of the outcome scale.…”

“…With a sigmoidal-shaped J, however, the factorial plot of the same I A ¥ I B effect should diverge at low-valued O A but converge at high-valued O A . The patterns of divergence and convergence would emerge because the allocations in the conditions of the low-and high-valued O A would be constrained by the respective 'floor' and 'ceiling' effects (see Mellers & Hartka, 1989; upper panels of Figure 2. p. 693, for the prediction of the subtractive model with sigmoidal-shaped J).…”

“…Proponents of the alternative subtractive rule (Mellers, 1982(Mellers, , 1985Mellers & Hartka, 1989;Singh, 1995Singh, , 1996Singh, , 1997, therefore, assume the J to be only monotonic, rank-order preserving. In other words, the outcomes allocated are assumed to be no more than simple rank orders of the felt 'fair' shares driven by perceived inputs.…”

A mean for all seasons

“…That particular transformation has long been used with sigmoidal data (Cochran, 1940), because the arcsin has little effect on intermediate values but stretches out the ends of the scale. Specifying the transformation in advance is a more definitive statement, one justified by Mellers and Hartka's (1989) account of the distortion induced by the response scale. If this hypothetical operation had been able to make the transformed means plot in accord with the parallel pattern called for by the model, subsequent research in which tasks in which respondents make similar judgments are used (e.g., Singh, 1995) might fruitfully apply the same transformation.…”