2. Enter the number of outcomes (for this program, it should be between 2 and 5).

3. Enter the outcomes, with the lowest outcome on the left, and higher outcomes to the right. This program is not set up to handle negative outcomes.

(For example, if you have a 50-50 gamble to win either $0 or $100, then there are two outcomes, 0 on the left, and 100 in the next adjacent position. Above 0 put .50 and above 100 you put .50. Always put the lowest outcome in the leftmost position of outcomes.)

4. Enter the corresponding probabilities in the spaces provided, directly above the outcomes.

5. When everything is complete, press the "compute" button. You will receive warnings if you have left something blank that should be filled in. If you leave one of the parameters blank, then the values will reset to the prior values. If you leave outcomes or probabilities blank, then you will be warned, and any computations are suspect. If you use an outcome of zero, then you will be warned of a missing outcome, but the computations will be ok. If you accidentally enter outcomes where you should enter probabilities, you will be warned that the probabilities don't sum to 1, and obviously, you should correct this error. If you leave a space in the field, or accidentally enter a comma or a letter, then you receive the error message that the input is not numerical. DON'T USE THE SPACEBAR TO ERASE A VALUE. Use the delete key to remove any spaces in the fields.

Try calculating the values of these two 3-outcome gambles:

G1 = .10 .05 .85 12 90 96 G2 = .05 .05 .90 12 14 96

Which gamble has the higher EV? Which Gamble is better according to CPT? Which gamble is better according to TAX model? Birnbaum (1997, 1998) noted that the TAX and RAM configural weight models predict that people should choose G1 over G2, even though G2 dominates G1. Birnbaum and Navarrete (1998) found that about 70% of undergraduates tested chose G1 over G2.

This calculator computes predictions of the Configural Weight, TAX model described in Birnbaum (1997), Birnbaum and Chavez (1997), and Birnbaum (1998). It also computes predictions for the model of Cumulative Prospect Theory (Tversky & Kahneman, 1992), using the weighting function suggested by Lattimore, et al. (1992), and incorporated in CPT by Tversky and Wakker (1995). For two outcomes, this CPT weighting function is a special case of the configural weight model of Birnbaum, et al. (1992, Equation 4) in which S(p) is a power function of p, with exponent GAMMA. Although CPT and CWT models are difficult to distinguish for the case of n=2 outcome gambles, they are quite different for n greater than 2. As shown in Birnbaum (1997; 1998) and tested in Birnbaum and Chavez (1997), the Configural weight, TAX model is similar to, but distinct from the RAM Configural weight model of Birnbaum and McIntosh (1996), which is implemented in DMCALC2 and in another on-line RAM model calculator.

The CWT TAX and CPT models illustrated here have the same number of parameters. The parameter C1 in the CPT model is analogous to the parameter DELTA of the CWT TAX model. These can be interpreted as indices of risk-seeking or risk aversion, apart from any nonlinearity in the u(x) function (which is assumed in this calculator to be a power function of x, with exponent BETA). DELTA greater (or less) than zero corresponds to C1 greater (or less) than one, and is interpreted as risk seeking (or risk aversion), respectively. Note that the TAX model exhibits "risk aversion" with u(x) = x.

The BASIC program, DMCALC, allows you to save the output for a number of gambles, and the gambles can be stored in the program. The version available in this web site is already set up to contain the gambles illustrating the Allais paradoxes, violations of branch independence, violations of cumulative independence, event-splitting effects, violations of distribution independence, and both violations and satisfactions of stochastic dominance in Birnbaum's (1998) chapter.

Birnbaum, M. H. (1998). Paradoxes of Allais, stochastic dominance, and decision weights. In J. C. Shanteau, B. A. Mellers, & D. Schum (Eds.),

Birnbaum, M. H. (1999). Testing critical properties of decision making on the Internet.

Birnbaum, M. H., & Chavez, A. (1997). Tests of Theories of Decision Making: Violations of Branch Independence and Distribution Independence.

Birnbaum, M. H., & McIntosh, W. R. (1996). Violations of branch independence in choices between gambles.

Birnbaum, M. H., & Navarrete, J. B. (1998). Testing descriptive utility theories: Violations of stochastic dominance and cumulative independence.

Lattimore, P. K., Baker, J. R., & Witte, A. D. (1992). The influence of probability on risky choice.

Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty.

Tversky, A., & Wakker, P. (1995). Risk attitudes and decision weights.

This material is based upon work supported by the National Science Foundation under Grants No. SBR-9410572 and SES-9986436. 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.