A Theory of Ratio Magnitude Estimation

Parametric weighting functions

“…There exist, however, several recent foundations restricted to binary lotteries where one consequence is the zero payoff (see e.g. Luce 2000, Narens 1996, Luce 2001, Aczél and Luce 2006, al-Nowaihi and Sanjit Dhami 2006. The motivation for restricting the analysis to binary lotteries stems from the descriptive shortcomings of the independence conditions required to derive RDU for general lotteries (for a review see Marley and Luce 2005).…”

Empirical and Theoretical Studies of Psychophysical Phenomena

“…Steingrimsson and Luce (2007) showed that a certain commutative property proposed by Narens (1996) was equivalent to measurement on a ratio scale, i.e. whether x p = "p times x" followed by x p,q = "q times x p " is the same as when the order of p and q is reversed to q and p. That is, does x p,q = x q,p ?…”

The judgment operation of ratio production

“…Thus, when n 1 n 2 n 3 , the equality 2 3 occurs when n i v i . The condition that 2 3 when n 1 n 2 n 3 is called the multiplicativity axiom (Narens, 1996). Ellermeier and Faulhammer (2000) and Zimmer (2005) found that this axiom was violated.…”

“…Let participants produce the sensory intensities b (Narens, 1996). By having participants produce multiples or fractions of sensory intensities, Ellermeier and Faulhammer (2000) and Zimmer (2005) have found that the commutativity axiom was satisfied-for example, the production of two thirds of the production of one fourth of s matched the production of one fourth of the production of two thirds of s .…”

“…However, one should consider that the commutativity axiom is satisfied both in the event that sensory intensities are produced on the basis of sensory ratios and in the event that sensory intensities are produced by adding some amount of sensory intensity to s (Narens, 1996 …”