Procedure for Selecting Winners of the Decision-Making Experiments and playing the Gambles

List of Winners

1. Each completed and valid entry will be given an integer number in order of completing the experiment. (Incomplete forms and multiple entries from the same email address are deleted) In other words, the first valid entry is #1, the second is #2, and so on.

2. For each block of n participants (i.e., #1-100, 101-200, etc.), the following procedure is used to select a winner. A ten-sided die (with sides numbered 0, 1, ...,9) is rolled twice. The first roll returns the 10's digit, the second roll returns the ones' digit. For example, if the first roll is 0 and the second roll is 8, then the winner is #8, if the first roll is 4 and the second roll is 5, the winner is #45. If the first roll is 0 and the second roll is 0, the winner is #100. For the second block of 100, if the dice show 8 then 0, the winner is #180, etc.

This procedure is used to select one winner from each block of n participants. If the last group of participants is not exactly n, then dice numbers not corresponding to people will not produce a winner. In other words, if n=100 and there are 89 people in the last group, if the dice show 95, then #95 indicates that none of the 89 were winners. If the rolls show 23, then there is a winner among those 89.

These procedures ensure that all participants have an equal chance to be selected as a winner. It also constrains this probability to be relatively uniform over the run of the experiment. In the 2A experiment, the probability of being a winner was .01, or 1%.

3. For each winner, the trial (choice) number is selected by the following procedure. A twenty-sided die (with sides numbered from 1 to 20) is rolled, and the number on the die indicates the number of the choice (or trial) to be played. Recall that there were 20 choices.

Experimental materials for experiments 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 2i (no longer active) can be viewed at the following URLs:

http://psych.fullerton.edu/mbirnbaum/exp2e.htm

http://psych.fullerton.edu/mbirnbaum/exp2f.htm

http://psych.fullerton.edu/mbirnbaum/exp2g.htm

http://psych.fullerton.edu/mbirnbaum/exp2h.htm

http://psych.fullerton.edu/mbirnbaum/exp2i.htm

4. For each choice, the player receives the gamble that he/she chose on that trial. For example, suppose #45 were selected as a winner, and suppose the 20-sided die showed 2, then we look at the decision that participant #45 made on trial 2. Trial 2 was the following choice:

```C: .50 to win \$0          D: .50 to win \$45
.50 to win \$100           .50 to win \$50
```

If person #45 chose C, then person #45 would play C. If #45 chose D, then gamble D would be played. This person will win the outcome of the gamble as a prize.

4. The gamble selected will have "tickets" assigned according to the following scheme. Tickets represent probability and outcomes, with .01 corresponding to one ticket, and lower ticket numbers assigned to lower valued outcomes. For example, the gamble C above will have tickets numbered 1-50 yield the prize \$0, and tickets #51-100 yield the prize \$100.

5. To play a gamble, a 10-sided die (with numbers from 0 to 9) is rolled twice. The first roll represents the 10's digit, and the second represents the 1's digit. This value will vary from 1 to 100. In the example of gamble C above, if the rolls of the die show 2 and then 8, the ticket is 28 and the prize is \$0, since tickets 1-50 win the prize of \$0. If the die rolled 8 then 2, the ticket is 82, and the prize is \$100. Any ticket from 51 to 100 would yield the prize of \$100, and any ticket numbered 1-50 will yield \$0.

6. A neutral witness will roll the dice, record their values, and witness that these procedures have been followed correctly.

7. Winners will be notified by email. To claim the prize, the winner must send their name, mailing address, and social security number (U.S. residents) promptly by return email. Residents of other nations with addresses outside the U.S. should provide their nation's equivalent tax identification or government identification number. In cases of invalid email addresses, bounced back email, and other failures to contact the winner, a few reasonable attempts will be made to contact the winner, and if these attempts fail for 30 days, then the prize is forfeit. Those who do not claim their prize by sending a name, address (and their government's tax identification-- SS numbers for U.S. residents) within 60 days (of the email announcement) will forfeit their prize.

Winners Selected at Sept 15, 1998 Drawing:

Experiment 2a Winners below, including date and time of participation.

In addition to those listed, there have been 5 winners who did not claim their prizes.

"4/15/98","2:44:04 PM","holbrojb@ctrvax.vanderbilt.edu", \$90

"4/23/98","12:16:33 PM","mellisu@ibm.net",\$12

"4/28/98","6:09:55 AM","than_stuntz@hotmail.com",\$96

"5/14/98","2:10:58 AM","bazner_ah@wvwc.edu",\$96

"5/22/98","9:17:49 AM","stud0756@di.uoa.gr",\$10

"6/9/98","6:32:08 AM","marip@sepa.tudelft.nl",\$96

"6/18/98","6:21:09 AM","d.racine@mail.utexas.edu",\$12

"7/2/98","9:50:45 AM","hubrig@ser.de",\$108

"7/29/98","5:42:38 PM","rcimma@aol.com",\$98

"7/31/98","7:58:31 AM","drakeage@hotmail.com",\$96

"8/6/98","12:05:35 PM","chengj2@sas.upenn.edu",\$99

"8/7/98","6:11:39 AM","annmbarber@yahoo.com",\$12

Exp 2b winners below _____________

"8/17/98","10:06:43 AM","pcms19a@prodigy.com",\$25

"8/26/98","3:43:55 PM","harryt@sbca.org",\$94

"8/30/98","10:54:12 PM","gvb103@psu.edu",\$96

"9/10/98","7:02:07 AM","ysol@usa.net",\$40

Winners Selected at Dec 24, 1998 Drawing:

Dec 24, 1998 drawing used the same procedure as used for Sept 24, except that dice were rolled to identify 6 winners, three of whom did not claim their prizes. Winners played one of their chosen gambles for cash.

Web Winners Games 2C and 2D

"10/23/98","8:05:23 AM","tremoir@rocketmail.com",\$40

"11/25/98","2:06:13 PM","sorsha@my-dejanews.com",\$65

"11/28/98","9:41:06 AM","nancymhill@hotmail.com",\$50

Mar 10, 1999 Drawing: Game 2E

Same procedures were used as for Dec 24 drawing. There were 6 contestants selected as winners. Three won \$0, and three who won larger prizes are listed below:

"1/19/99","1:02:51 PM","khimed@gateway.net", prize=\$96

"2/10/99","8:20:07 AM","toolou4u@yahoo.com", prize=\$100

"3/2/99","12:37:41 PM","millerdt@sce.com", prize=\$96

Drawing of June 21, 1999: Web Winners Games 2F and 2G

"4/23/99","9:32:54 AM","linz78@aol.com", prize=\$10

"6/5/99","1:32:34 PM","del4444@yahoo.com", prize=\$96

Drawings of Sept 21, 1999 and Dec. 21, 1999: Games 2H, 2I, 2J

Those who won \$0 are not listed.