Axiomatic evaluation of k-multiplicativity in ratio scaling: Investigating numerical distortion

作者：Birkenbusch Jana; Ellermeier Wolfgang

来源：Journal of Mathematical Psychology, 2016, 75: 26-33.

DOI：10.1016/j.jmp.2015.12.004

• Multiplicativity
• Weighting function
• Power function
• Ratio production

It is a well established empirical observation that most human participants do not process the numerical instructions used in production or estimation tasks veridically. Luce and collaborators (e.g., Luce, 2002; Steingrimsson and Luce, 2007) have analyzed the kind of "numerical distortion" that appears to be operating. They stated the relationship between perceived and mathematical numbers to be described by a power function, if the empirically testable axiom of k-multiplicativity holds. This study examined the validity of k-multiplicativity by testing whether the stimulus intensities resulting from successive adjustments xp x q multiplied by a constant factor k are equal to the stimulus intensity resulting from single adjustments xr. Therefore, the data of three different ratio production experiments with a total of N = 35 participants were (re-)analyzed. In Experiment I, integers were used as ratio production factors (p >= 1), while in Experiment II, only fractions (p < 1) were applied. In Experiment III, both p >= 1 and p < 1 were intermixed. In Experiments I and II, k-multiplicativity held for all n = 20 participants. Experiment III revealed axiom violations for 13 of n = 15 participants. The failure of 1-multiplicativity confirms the common observation that the participants' number representation is often not veridical. However, the validity of k-multiplicativity shows that the relationship between mathematical and perceived numbers follows a power function of the form W(p) = kp(omega) with k not equal 1 and omega not equal I. However, the numerical distortion differs for fractions compared to integers.

• 出版日期2016-12