Vanberg's experiment
The whole design
The instructions and screens that Vanberg (2008) published fill in what the story leaves out.
- The experiment has 8 rounds. In each one you are matched with another participant, chosen at random, and never with the same one twice.
- At the end, one of the 8 rounds is drawn at random, and only that one is paid.
- Roles are drawn again in every round, with the same chance of getting either.
- In the chat, messages alternate, and a draw decides who writes first.
- A dictator whose partner was switched can read both chats: their own, and the one their new partner had with someone else.
- At the end of each round, the recipient only sees their own payoff.
- The guesses were paid, in the rounds not drawn for the decision. The recipient picked one of five answers, from “certainly rolls” to “certainly doesn’t roll”, and earned 65, 60, 50, 35 or 15 cents depending on the answer and on what the dictator did: 65 for a sure answer that turned out right, 15 for one that turned out wrong. The dictator, in turn, guessed the recipient’s answer and earned 50 cents for getting it right.
Every cell of the switch treatment
The story compares two of the cells. The treatment has six: whether the dictator promised, crossed with whom they faced: the same partner, a new partner who had been promised by another dictator, or a new partner whom no one had promised anything. Each count is of decisions, one per dictator and round, written as it is in the data, over the cell’s total.
The last column is the dictators’ second-order belief: what a dictator believes their partner expects of them, on the same five-point scale, read from 0 to 100.
| Cell | Rolled the die | Second-order belief |
|---|---|---|
| Promised · Same partner | 73%227 of 309 | 80 |
| Didn't promise · Same partner | 52%39 of 75 | 60 |
| Promised · New partner, promised by another dictator | 54%129 of 238 | 76 |
| Didn't promise · New partner, promised by another dictator | 54%30 of 56 | 70 |
| Promised · New partner, promised by no one | 52%29 of 56 | 62 |
| Didn't promise · New partner, promised by no one | 56%19 of 34 | 58 |
Source: Vanberg (2008), supplementary data.
Vanberg’s argument
Vanberg (2008) reads the table through one comparison. Among dictators who had promised, rolling falls from 73% with the same partner to 54% with a new partner who had been promised by someone else. What those dictators believed their partner expected hardly moves: 80 against 76. Behaviour changes where beliefs do not, so a change in beliefs cannot be what makes promises work.
The baseline treatments
Vanberg also ran two simpler treatments, reported in his Appendix A: the same game with the chat and without it, with no partner switch. With the chat, the die was rolled in 92 of 128 decisions; without it, in 67 of 128. Each treatment had 32 people, over 8 rounds.
Counted again, in fractions
The counts on this page were not copied from the article. Each was counted again from the data
Vanberg published with it, switch.dat and baseline.dat, following his own program,
promises.do. The page keeps every count as a fraction of whole numbers and rounds only when it
writes a rate out of 100: to the nearest whole number, halves up, in integer arithmetic, so no step
adds an error of its own. A test checks that the six cells hold every decision of the treatment:
half of its 192 people decide in each of its 8 rounds.