This calculator is designed to compute predictions for the priority heuristic as described
in Brandstätter, Gigerenzer, and Hertwig (2005). The calculator now includes the
rounding to prominent numbers, by geometric spacing. The calculator permits an examination of
"how often" this model agrees with the TAX and CPT models as fit to previous data. It also
counts how often each of the four reasons is used.
to the priority heuristic, people compare gambles by considering "reasons" for choosing the
gambles. First, they examine the lowest consequences in the two gambles, and if the difference
is greater than the WeberFraction (default=1/10) of the (rounded) maximum consequence of either gamble, they choose the gamble
with the higher lowest consequence. If the difference is less than one JND (WeberFraction) of the maximum, they
consider the probability of the lowest consequence, choosing the gamble with the lower probability
of receiving the minimum, if the difference is greater than or equal 1 JND in probability (default = 1/10). If there
is still no decision, they compare the maximal consequences, and if no decision, they compare the
probabilities of the maxima. Instructions for a previous version of the calculator are given
This calculator also calculates predictions according to TAX using parameters of Birnbaum and McIntosh (1996);
see below. It also calculates the CPT value of each gamble, using parameters fit to data of Tversky and Kahneman (1992) with
the weighting function of Tversky and Wakker (1995). The program counts how often among random gambles these three
models agree, or pairs of models agree.
If you press the button labeled
Choose Pair of Random Gambles, one pair of gambles is selected randomly by the scheme described
below, and the calculations are made.
You can also enter a pair of gambles, and check what the models predict. For example, try the pair of
gambles suggested by Birnbaum (1997, p. 94) as a test between the class of rank-dependent
utility models, including Cumulative Prospect Theory and Rank and Sign Dependent
utility theory and the configural weighted TAX and RAM models.
Birnbaum's(1997) choice is as follows:
Gamble 1: .10 to win $12 Gamble 2: .05 to win $12
.05 to win $90 .05 to win $14
.85 to win $96 .90 to win $96
The program seems to run much faster and update the changing display much better with
Netscape Navigator for Mac than with Internet Explorer for Mac. To sample 10,000 pairs of
gambles, it takes less than 10 minutes in Navigator 4.73 and over one hour in Explorer on a
Mac G4 running System 9.
The sampling scheme is as follows: Each consequence is chosen randomly and uniformly from
the interval [0, 100]. The values are rounded off to the nearest dollar and .01 in probability
before being displayed. This may result in ties in the displayed gambles that are actually
different. The branches are ordered according to their consequences. To select probabilities,
random numbers are selected randomly and uniformly from the interval [0, 1]. The sum of these random
numbers might exceed or fall short of 1, so the numbers thus sampled are divided by the
sum of the random numbers to ensure that they behave as proper probabilities.
The TAX model default parameters are as follows: delta = -1, gamma = .7, and beta =1.
The CPT parameters are listed below. The WeberFraction is used in the Priority Heuristic and
is assumed the same in both money and probability, except that probability always assumes the
same scale of 1, with the same JND (default is .1); however, the maximal gain in either gamble
is first rounded to the nearest prominent number and then multiplied by the WeberFraction to find
the JND. For example, if the largest consequence in either gamble is $96, the nearest prominent number is $100,
and the JND is $10, so gambles in which the lowest consequence differ by $10 or more are decided on that basis.
If the largest consequence in either gamble is $60, however, the nearest prominent number is $50, so the JND is $5.
You can change these in the following display:
In a sample run of 100,007 trials, it was found that TAX, CPT, and PH agree in their predictions 81% of
the time. In addition, TAX and CPT agree with each other 94.4% of the time; TAX and PH agree 84.1% of the time;
and CPT and PH agree with each other 83.8% of the time. When the rules are ordered: Min Gain, Prob of Min Gain,
Max Gain, Prob of Max gain, the decision is determined by these reasons 72.0%, 19.3%, 7.5%, and 1.1%, respectively; the rule
based on 4 reasons does not reach a decision in about .1% of the choices. When the WeberFraction was set to .2,
the degree of agreement stayed about the same, but the reasons were less decisive. In a run of 10,002, it was found
that the Min Gain, Prob of Min Gain, Max Gain, and Prob of Max gain were decisive in 49.1%, 22.5%, 21.1, and 7.1% of cases,
with no decision reached in 0.2% of the cases.
One should not expect to be able to test theories by randomly throwing together some
gambles and testing properties, since the models agree so often with each other.
The recipe devised by Birnbaum (1997, p. 94) for testing CPT, which also distinguishes TAX and PH, produced a predicted violation of
stochastic dominance (according to TAX and RAM), later shown to produce 73% violations, would
have been very unlikely to have been discovered by trial and error.
Tech Reports, supplementary data, and preprint versions of many of these papers are available
for download from this link.
This material is based upon work supported by the National Science Foundation under Grants No. SBR-9410572, SES-9986436, and BCS-0129453. Any opinions,
findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily
reflect the views of the National Science Foundation.