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

 NUMBER OF OUTCOMES : CWT Parameters Gamma Beta CPT Parameters Gamma1 Beta1 GAMBLE OUTCOMES AND PROBS Lowest Highest Probabilities Outcomes Weights CWT Pred CPT Pred EV
Help, Info, Credit, & Blame  Email: Michael Birnbaum  CWT TAX Model Calculator

### How to Use the Calculator. Back to Calculator

1. To try out the calculator for the first time, press the "Clear" key to make everything blank, then enter a number of outcomes, such as 2. Next, hit the "Set Values" button at the bottom of the form. Previously published parameters for the case of n = 2 outcomes will be inserted for CWT and CPT.

2. Now, enter the probabilities and outcomes for a 2-outcome gamble. For example, try a .5 probability to win \$1 and a .5 probability to win \$100, and hit the "compute" button. The outcomes must be in rank order, with the lowest outcome in the leftmost position. Note that if you use the default parameters (they will be inserted if you leave them blank, along with warnings and error message), that predictions for CPT = Cumulative Prospect Theory Model of Tversky & Kahneman (1992) and CWT = the Configural Weight, RAM Model of Birnbaum & McIntosh (1996) are approximately equal. However, for n = 3 outcomes, predictions of these models will be quite different

3. Next, delete the weights (press "clear"), and enter the number n = 3 outcomes. Hit "Set Values" again, and new weights for CWT will appear. Then enter the probabilities and values for your three outcome gamble, and hit compute again.

Try these 4 three-outcome gambles:

```S  =  ( \$2,.50; \$40,.25;  \$44,.25)  R  = ( \$2,.50; \$10,.25;  \$98,.25)
S' =  (\$40,.25; \$44,.25; \$108,.50)  R' = (\$10,.25; \$98,.25; \$108,.50).
```
Branch independence requires that S is preferred to R if and only if S' is preferred to R'. Both models violate branch independence, but do so in opposite ways.

The cash equivalent (CE) values of the gambles, according to the CPT model of Tversky and Kahneman (1992), are as follows:

```CE(S)  = \$17.68 < CE(R) =  \$27.52
CE(S') = \$68.26 > CE(R') = \$61.51
The RAM CWT model of Birnbaum and McIntosh (1996) predicts:
CE(S)  = \$16.61 > CE(R) =  \$15.65
CE(S') = \$57.27 < CE(R') = \$59.56
```

4. This calculator handles only outcomes greater than or equal to zero. Zero outcomes will create a warning, but the results should be ok. However, negative outcomes will create a warning and the results will not agree with the model of CPT for negative and mixed outcomes. When shifting between cases of differing numbers of outcomes, be sure to erase the weights if you want the program to supply them for you. If you know what you are doing, then enter the weights you want to use, and pay close attention; the program will reset the weights to prior values if you leave something blank, make some other error in data entry, or hit the "set values" button.

The RAM model implies distribution independence, unlike the configural weight TAX model (Birnbaum & Chavez, 1997). The TAX model predictions can be examined using DMCALC and the CWT TAX Model Calculator

#### The models and their parameters are given in these articles:

Birnbaum, M.H., & McIntosh, W.R. (1996). Violations of branch independence in choices between gambles. Organizational Behavior and Human Decision Processes, 67, 91-110.
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297-323.

#### A test of the above predictions is in the following paper:

Birnbaum, M.H., & Chavez, A. (1996). Tests of theories of decision making: Violations of branch independence and distribution independence. Organizational Behavior and Human Decision Processes, 71, 161-194.

### Credits and Disclaimers

This program is based on DMCALC2 by Michael Birnbaum, and was turned into a calculator in JavaScript by Rob Bailey, with a few adjustments by Michael Birnbaum. Copyright, 1998, All rights reserved. This program may be used and shared freely for educational and scholarly purposes. No warranties or guarantees can be made for this program. DMCALC2 (in BASIC), is available via the list of programs; that program gives additional information, and also allows you to save your calculations.

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.