Calculates Response Patterns in Additive Difference Model (ADM)

This program calculates predicted response patterns of the ADM model as a function of parameters alpha and gamma.

The window contains calculated preference patterns for each combination of alpha and gamma in CSV (comma separated values) format. These can be copied and pasted for further analysis. The data are already selected: use Control&C to Copy and Control&V to paste (e.g., into Excel). Click here for more instructions

Calculates Response Patterns in ADM Model step size (/range) w =  
alpha Lower limit = alpha Upper limit = gamma Lower limit = gamma Upper limit =
Gamble X = x1 = x2 = x3 =
Gamble Y = y1 = y2 = y3 =
Gamble Z = z1 = z2 = z3 =

Instructions

This program calculates true preference patterns generated according to the Additive Difference Model (ADM) with power functions, as applied for DEPENDENT gambles by Birnbaum and Diecidue (2015). This model can represent a form of Regret Theory (Loomes & Sugden, 1982). According to this model, one prefers X = (x1,x2,x3) over Y = (y1,y2,y3) iff
sign(x1alpha - y1alpha)(|x1alpha - y1alpha|)gamma + sign(x2alpha - y2alpha)(|x2alpha - y2alpha|)gamma + sign(x3alpha - y3alpha)(|x3alpha - y3alpha|)gamma > 0
Where sign(v) is the function that returns the sign of the argument (-1, 0, or 1, if v < 0, v = 0, v > 0, respectively).

ADM Model Parameters

The parameters of the additive difference model (alpha and gamma) are varied in loops with step size based on the specified range of values and the increment size, w. Where
w is the increment factor as a proportion of the range of parameter values; that is, larger values mean fewer steps will be calculated.


alphaL is the lower limit of alpha
alphaH is the upper limit of alpha
gammaL is the lower limit of gamma
gammaH is the upper limit of gamma

Gambles and Preference Patterns

The three gambles listed as default values have been selected from a paper by Butler and Pogrebna (2018) that appeared to show the strongest evidence for systematic violations of transitivity of preference (see also Birnbaum (2020)). This program does not use the notation in their paper for preference patterns. For three gambles, X, Y, and Z, the three choice problems are XY, YZ, and ZX. The preference patterns are coded as follows (1 = choose X, 2 = choose Y). The preference pattern 111 indicates choosing X in the XY choice, Y in the YZ choice, and Z in the ZX choice; therefore, this pattern is an intransitive pattern.

Note that according to the Most Probable Winner model, one would choose X over Y because the two branches in X with 15 beat the corresponding branches in Y, which are 10. One chooses Y over Z because the two branches with 10 beat the two branches in Z with 5; and one chooses Z over X because 27 beats 15 and 5 beats 3.

The preference pattern 222 is also intransitive, corresponding to preference for Y over X, Z over Y, and X over Z. Such a pattern can occur when alpha is small and gamma exceeds 1, producing "regret." The Additive difference model of Birnbaum and Diecidue (2015) can be used to represent both "regret" as in Loomes and Sugden (1982) and the opposite patterns that might be called "rejoicing", including Most Probable Winner as the extreme limiting case.

References