#### Configural Weight, TAX Model and Cumulative Prospect Model     Help

 NUMBER OF OUTCOMES : CWT Parameters Gamma Beta Delta CPT Parameters Gamma1 Beta1 C1 GAMBLE OUTCOMES AND PROBS Lowest Highest Probabilities Outcomes CWT Pred CPT Pred EV
Help         Information          Credit & Blame          References

#### How to use the calculator       CalculatorInformation

1. To use the calculator for the first time, press the "Set Values" button. This button sets the parameters of the models to values that have been published in the literature. (If you know what you are doing, you can edit these values to examine the effects of variation of the parameters.)

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.

#### Information       CalculatorReferences

This calculator implements the program DMCALC as an on-line JavaScript calculator. These programs are very useful in the design and analysis of experiments in decision making. For example, BEFORE running an experiment, one can calculate the predictions of these models to see if different theories make different predictions in the experiment. It is also possible to vary parameters to examine their effects in the models.

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.

#### References        Calculator

Birnbaum, M. H. (1997). Violations of monotonicity in judgment and decision making. In A. A. J. Marley (Eds.), Choice, decision, and measurement: Essays in honor of R. Duncan Luce(pp. 73-100). Mahwah, NJ: Erlbaum.
Birnbaum, M. H. (1998). Paradoxes of Allais, stochastic dominance, and decision weights. In J. C. Shanteau, B. A. Mellers, & D. Schum (Eds.), Decision Research from Bayesian approaches to normative systems: Reflections on the contributions of Ward Edwards (pp. 27-52). Norwell, MA: Kluwer Academic Publishers.
Birnbaum, M. H. (1999). Testing critical properties of decision making on the Internet. Psychological Science, 10, 399-407.
Birnbaum, M. H., & Chavez, A. (1997). Tests of Theories of Decision Making: Violations of Branch Independence and Distribution Independence. Organizational Behavior and Human Decision Processes,71(2), 161-194.
Birnbaum, M. H., & McIntosh, W. R. (1996). Violations of branch independence in choices between gambles. Organizational Behavior and Human Decision Processes, 67, 91-110.
Birnbaum, M. H., & Navarrete, J. B. (1998). Testing descriptive utility theories: Violations of stochastic dominance and cumulative independence. Journal of Risk and Uncertainty, 17, 49-78.
Lattimore, P. K., Baker, J. R., & Witte, A. D. (1992). The influence of probability on risky choice. Journal of Economic Behavior and Organization, 17, 377-400.
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297-323.
Tversky, A., & Wakker, P. (1995). Risk attitudes and decision weights. Econometrica, 63, 1255-1280.

#### Credits and Disclaimers         Return to Calculator

Copyright, Michael H. Birnbaum and Robert Bailey, 1998, all rights reserved. This calculator may be used and shared freely for educational and scholarly purposes. No warranties or guarantees can be made for the software.

This material is based upon work supported by the National Science Foundation under Grant No. SBR-9410572. 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.