Timmy Tiptoes and the Tale of Costly Punishment

By Dr David Hugh-Jones

timmy-tiptoes-2This post is about a paper of mine with Carlo Perroni of Warwick University, The Logic of Costly Punishment Reversed. It has just been accepted in the Journal of Economic Behavior and Organization (ungated version at my website).

The germ for this paper came in 2006 at Northwestern University, in a chat with my game theory lecturer, Christoph Kuzmics. He mentioned to me that he was working on evolutionary game theory explanations for costly punishment.

The idea of costly punishment is that people are prepared to pay costs so as to punish bad behaviour or take revenge. For example, if a guy starts a bar fight because you spilled his beer, or someone lectures you for leaving litter, that might be costly punishment. Why is that important? Well, all societies need to maintain order – to prevent crime and ensure that people contribute to community goods. Modern societies have the machinery of the state –  the policeman and the tax office – to do this.  But throughout history, most people have lived in small societies without states; and there are many kinds of bad behaviour, like littering, that it would be too expensive or intrusive to control using the state’s coercive power. Instead,  people in the group must punish bad behaviour, either verbally, financially or physically.

Most modern social scientists assume that this is a serious problem.  Why would I go through the hassle of punishing someone else’s bad behaviour? That benefits the group, but it doesn’t benefit me much personally. Or to put it technically, there is a Second Order Collective Action Problem.

There are two kinds of solutions out there. The first invokes repeated game theory (the most famous example is Robert Axelrod’s book The Evolution Of Cooperation). The central idea of this is tit-for-tat: if you behave badly, people will behave badly to you in future. This has been hugely influential: many important works in social science have argued that the ideal community is very hard to enter or leave, so that people cannot escape future punishment is, and has a lot of gossip so everybody knows how everybody else has behaved. If this does not sound like Utopia to you, then I sympathise.

The second solution is costly punishment. The argument is that people have special motivations to punish bad behaviour: it just makes them angry and willing to take revenge.  This is been very influential too: “costly punishment” has about 4000 google scholar hits.

Christoph scribbled down the game tree and explained the puzzle. A self-interested person would love to have a reputation for starting bar fights and being a tough guy – they would get their way a lot. But they would never want to actually start a bar fight, as they might lose! So, he wondered how these motivations could evolve.

But, I said, why does it matter? Surely in the real world, if I am strong enough, I can blackmail you to do something which harms you and benefits me – like buying me a new drink. He replied: well, it’s just an interesting problem! I was naïve back then, and thought that there must be some deeper reason for the interest in this idea.

Since then, I’ve come to believe that academia quite often goes down rabbit holes of faddism and groupthink, and perhaps costly punishment is an example. We don’t claim it never exists, but I suspect it has been greatly exaggerated. For some behavioural economists, costly punishment has become a pillar of social order.

In real societies, punishment of bad behaviour is often not costly, but beneficial to the punishers. For example, in Japan, villagers caught taking too much wood from the forest had to pay a fine, often commuted by the village official to a bottle or two of sake. Not so bad for the official!

Or, here’s a nice example from the anthropologist Colin Turnbull. This is what happens when Cephu the pygmy is caught by his fellow hunter-gatherers, putting his traps out of place to get more meat than others:

Cephu knew he was defeated and humiliated…. He apologized profusely, reiterating that he really did not know he had set up his nets in front of the others, and that in any case he would hand over all the meat. This settled the matter, and accompanied by most of the group he returned to his little camp and brusquely ordered his wife to hand over the spoils. She had little chance to refuse, as hands were already reaching into her basket and under the leaves of the roof of her hut where she had hidden her liver in anticipation of just such a contingency. Even her cooking pot was emptied. Then each of the other huts was searched and all the meat taken.

(Cited in an excellent paper by Francesco Guala.) Again, it’s nice to get other people’s meat. The logic behind this is simple – the rest of the group can do more harm to Cephu than he can do to them, either by physically harming him or simply by leaving him to fend for himself. As a result, they have a credible threat, which Cephu has to avoid by handing over his resources.

We argue this is common. In many social contexts, the majority, or even a few, have such overwhelming power that they can easily punish any individual’s bad behaviour and gain from doing so.

Unfortunately, this is not all good news. Communities often have too much coercion, not too little. A lot of societies are extremely repressive and control individual behaviour very tightly, even without a formal state (just read Thomas Hardy). And if punishing miscreants is profitable, you face a temptation to call anybody a miscreant, and demand money with menaces. People you don’t like. Wealthy people. Outsiders. Ethnic minorities. Witches.

We look at societies from this perspective – trying to balance the power to punish with the danger of abusive expropriation. So, the paper is subtitled Expropriating Free-riders and Outsiders. We analyse this situation using a simple model. Then we describe the history of the Californian gold rush, which featured a lot of expropriation, often in the name of “rules” that someone had just invented on the spot. Last, we run a lab experiment, to give us some credible examples of what happens when punishment is profitable.


Figure 1: In our lab experiment, outcomes got worse when punishment was easier

Here’s one nice graph. It shows what happens when punishment is easier, i.e. when it can be inflicted by a smaller coalition of players (M, the “minimum size of expropriating group” on the x axis). When M is smaller, contributions to the community are lower, not higher, and at the same time there’s much more punishment – or if you prefer, more stealing. The groups in our experiment had the problem that  punishment was too easy, not that it was too hard.

Of course, as with most ideas in the social sciences, artists got there first. In Beatrix Potter’s Tale of Timmy Tiptoes, the grey squirrel Timmy and his wife Goody lay up a store of nuts for the winter. But then some little birds fly by, singing “Who’s-been-digging-up my nuts?”

Timmy Tiptoes went on with his work without replying; indeed, the little bird did not expect an answer. It was only singing its natural song, and it meant nothing at all.

But when the other squirrels heard that song, they rushed upon Timmy Tiptoes and cuffed and scratched him, and upset his bag of nuts. The innocent little bird which had caused all the mischief, flew away in a fright!

Timmy rolled over and over, and then turned tail and fled towards his nest, followed by a crowd of squirrels shouting—”Who’s-been digging-up my-nuts?”

They caught him and dragged him up the very same tree, where there was the little round hole, and they pushed him in. The hole was much too small for Timmy Tiptoes’ figure. They squeezed him dreadfully, it was a wonder they did not break his ribs. “We will leave him here till he confesses,” said Silvertail Squirrel, and he shouted into the hole—

“Who’s-been-digging-up my-nuts?”


Figure 2: a coalition of squirrels punishing Timmy Tiptoes.

Moral. Social scientists worry a lot about how to protect the community from the individual. As Timmy Tiptoes would tell you, sometimes the individual needs protecting from the community.

 A previous version of this paper appeared on my blog. Quotations and images from Beatrix Potter are in the public domain.


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