This program assumes gambles are of the form (x, p; 0), where x is the cash prize, p is the probability to win the prize, and one receives nothing with probability 1 - p.
To check for Intransitivity of Preference
1. Enter the values of the parameters. The three parameters are beta0, beta1, and w. When w = 1, the model becomes transitive. The default parameters are values that will illustrate violation of transitivity.
2. Enter three gambles, A, B, and C of the proper form. These should be binary gambles of the form (x, p; 0). This version of the program does not actually use the numbers you type in for the lower consequence (zero) and for the probability of that consequence (1 - p). Perhaps a later version of the program will allow for more complex gambles.
3. Push the button labeled Compute with Entered Values. You will see that the predicted (calculated) values of the gambles may depend on the gamble with which they are paired. The Variables labeled, AB, BC, and CA indicate whether the model predicts that A is preferred to B, B to C, and C to A, respectively. 1 = the first is preferred, and 2 = the second is preferred. For example, if AB = 1, that means that A is predicted to be preferred to B. The patterns 111 and 222 are intransitive, and the other patterns are transitive.
To choose three randomly selected gambles, A, B, and C
1. Enter the values of the parameters you wish to explore.
2. Press the button labeled, Choose random gambles. The program will select three gambles, A, B, and C, of the form (x, p; 0) as follows: x will be selected to be uniform on the interval from $0 to $100; p will be selected to be uniform on the interval from 0 to 1. However, if p is equal to 0, the value of p = .000000001 is used instead. Be aware of caveats regarding the Math.random() function in JavaScript, in case they are relevant to your application. Note that the values are rounded off in the panel display, but the saved results in the textarea below show more precision in the numbers.
To Simulate Many Random Choice problems and Check for Violations of Transitivity
1. Enter values of the parameters, as described above.
2. Push the button, 100000 Random Draws. This is equivalent to 100,000 pushes of the button, Choose Random Gambles. This button can be pushed repeatedly to generate many simulated sets of gambles. One can then copy and paste the contents of the textarea at the bottom of the panel as follows: When it is highlighted, use CTRL & C to copy the data, then click in your program (such as Excel) where you want to use the results, and click CTRL & V. In Excel, you may need to use the "text to columns" feature to indicate the the data are comma separated values (CSV). The numbers in each line the amounts and probabilities of the three gambles, A, B, and C, and the predicted response pattern for that triple.
3. Push the button, Totals to see the number of times that each of the preference patterns has occurred. 111 and 222 are the intransitive patterns. These totals appear in the little window below the main results.
This program is deterministic: That is, if Value of A when paired with B exceeds the Value of B when paired with A, it is assumed that A was preferred to B and a 1 is generated by the program. Perhaps a future version of the program will simulate data with a stochastic variation, in which the probability of this preference depends on the values of A(B) and B(A). Pele Schramm has a model in which this probability is generated by a version of Thurstone's model of comparative judgment.