Thanks to La Boveda for writing this enjoyable and informative article (read the Spanish version). Maybe some day we can pursue this subject over a good meal...

In Life, the Universe and Everything, Douglas Adams describes an interstellar transport system, the bistromathic drive, which is based on a revolutionary mathematical principle: Numbers written on restaurant bills within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe.

This is not a totally outrageous idea: Our behaviour in restaurants is quite strange, above all in groups.

Let's take the case of a group of people at a restaurant who decide to split the bill evenly. In this case the total amount will be much higher than everybody expected and most of them will be annoyed. The motive is clear: If everybody pays for himself, he just consumes until the benefit of consuming an increment more is equal to the cost of doing so /* At the utility maximising consumption level, marginal cost must equal marginal benefit */. On the other hand, when the bill is split evenly and if one decides to consume the equivalent of one additional Euro, the cost is equally shared among the diners. So if someone has another glass of wine for 10 Euro in a group of 5 people, he only has to pay 2 Euro for it /* When splitting the bill, diners consume such that the marginal social cost they impose is larger than their own marginal utility and, as a result, they over-consume relative the social optimum */.

Clearly, the problem is that diners consume more when the cost is split. Readers acquainted with basic knowledge of economics will recognise that this is a variant of the old problem of the financing of public goods, where everybody has to make a contribution to obtain a public service (like national defense), but every individual has incentives to evade paying his share. In short, people act egoistically.

Nevertheless, some hold the view that in praxis people are aware that they can take advantage of others but on average choose not to do so due to feelings of solidarity and altruism. To figure out whether this is the case, investigators did run an experiment (here is the summary and here is the whole article). They invited various groups of students (who were modestly payed for participation), who didn’t know each other, to a restaurant under different conditions: In one treatment the diners payed individually; in a second treatment they split the bill evenly between the six group members. In yet a third treatment, the meal was paid for entirely by the experimenter. As economic theory prescribes, consumption was smallest when the payment was individually made, and largest when the meal was free, with the even split treatment in-between the other two. In other words: diners behave like perfectly egoistic agents.

Interestingly, researchers ran a similar experiment (in which no meals were involved) in a laboratory but this time subjects were allowed to talk to each other without restrictions. In this case the average consumption was statistically not different to the consumption level attained under the conditions of individual payment. This tells us that if an experiment of that kind is run, the results obtained in a laboratory are suspect, since subjects don’t act (for the good or for the bad) as they would in a more natural context. This case confirms that when incentives are present and serve egoists, we take advantage of them. It is not a result that helps us reach the stars, but it is definitely worth taking it into account in the design of public policies or, at least, the next time colleagues propose to split the bill at a restaurant.


related links:
The Social Dilemmas, by Leon Felkins