I thought I'd fulfil my promise to blog about the paper on anonymity, with David Reinstein, which we updated a few days back. It starts from a worry about the "costly signalling" theory of religion and ritual - the idea that people take part in collective activities, like rain dances and church fetes, so as to show their commitment to a particular group. Costly signalling theory comes out of game theory and has had a big impact in both social and biological sciences.
Fine... but if the penalties for not taking part are high, perhaps because the group excludes you, then there are big incentives to take part even if you aren't really committed. We propose that in some cases making the activity anonymous solves this problem. The example in the paper is "Secret Santa", which I saw for the first time at Essex. My fellow PhD students gathered together and drew names out of a hat, then each of us set off to spend £5 on a present for our name. Come Christmas, we all got our presents, but nobody knew who was the giver. The nice thing about Secret Santa is that when other people get you something thoughtful, it's truly anonymous: there's no selfish motive to show off. So you end up (hopefully) learning that your peers really are nice people.
This paper owes something to my undergraduate SPS degree, which included a year of anthropology. In fact, the original idea for the paper came from the Kula Ring institution, though we've dropped that example. But we include other examples from small-scale societies (which are especially likely to need collective solidarity): in particular, song and dance. The main interest of the paper, for me, is the insight it may offer into these very ancient forms of culture, and how they support human cooperation.
At a less exotic level, we think that the model offers some insight into why anonymous donations might be the norm in certain collective projects. When my mother's village raised money to turn the field in front of the church into a village green, they put up a sign with the amount raised so far, but they did not announce individual donations. That's not the sort of thing you do in Kingsland.
I and David Reinstein decided to test this in the lab: we ran some two-stage public goods games, in which small groups are asked to donate money to a common cause which benefits all group members. In one treatment, the first stage was anonymous so players didn't know who gave what. In the other, "revealed" treatment, amounts given were linked to player numbers. Both treatments allowed for certain players to be excluded by the others' choice.
Not surprisingly, in the revealed treatment, the lowest givers often got excluded, and as a result, stage one donations went up. But more surprisingly, stage two donations went down. Our theory explains it like this: in the anonymous treatment, players could observe stage one donations and figure out whether their fellow group members were likely to make big donations in stage two; if so, then they too would do that. (People are prepared to play nice so long as others play nice also - in the jargon, they are conditional cooperators.) In the revealed treatment, on the other hand, everybody was giving a lot in stage one just to avoid being excluded. But then nobody knew what to expect in stage two, and not wanting to be the sucker in a group full of meanies, they gave less.
Here's my favourite plot from the paper, showing stage one and stage two donations in each treatment. (Bubble size shows how many people made each combination of donations.) The anonymous treatment is on the left: you can see that guys who donated a lot in stage one did the same in stage two. On the right this is much less true: in fact many people gave 2 or even the maximum 4 in stage one, then nothing in stage two.
(The paper is on my website. My Secret Santa present was a rubber stamp, for marking students' essays, with the words "COMPLETE AND UTTER BULLSHIT". It was just what I needed. Thanks, guys.)