What is the distribution of the impact of immigration? I ask because there's tendency to discuss immigration only in terms of average effects - the average being slightly positive (pdf) (in economic terms) if you're (pdf) in the reality-based community and negative if you're not.

This discourse, however, misses something - that there's a distribution around any average. Consider each particular immigrant. His effect on British society might be heavily negative (if he's a serious criminal), slightly positive (if he's a typical worker), or hugely positive - if he's a brilliant entrepreneur, scientist or sportsman.

We should, therefore, think of an "immigration curve", with a few serious criminals at one extreme, a mass of ordinary folk around the middle and a few great benefactors at the other. (I stress that I'm not thinking in narrow economic terms here - the benefits and losses are cultural as well.)

But here's the thing. There's no reason to suppose that this curve is bell-shaped.Quite the opposite. It's more likely to be positively skewed. There's a limit to the amount of cultural and economic damage an immigrant criminal can do - unless he gets to run a bank or football club. But the upside gains from a great migrant are potentially vast. The gains we make from getting an Andre Geim, Elias Canetti*, Ola Jordan, Wojciech Szczesny**, Friedrich Hayek, Michael Marks or Mo Farah - to name but a handful - offset a lot of petty criminals.

Thinking of an "immigration curve" helps explain why attitudes to migration differ:

- The more you believe a few great people can tranform society, the more you should favour free migration, as it raises our odds of attracting such people. Randians who believe in heroic entrepreneurs, or economists who think that socio-technical change is increasing the significance of superstars should therefore favour open borders - because that right tail of big contributors is a fat one.

- Hayekians, who doubt that governments have the knowhow to exclude "bad" immigrants and admit "good" ones, will favour more open borders.

- People of a conservative disposition - Oakeshottians (pdf) whose instinct is to regard change as deprivation - will oppose immigration, as they put less weight upon the small chance of a large upside, and worry more about the larger chance of loss.

- People who are more open to new experiences will favour migration, as they put more weight than conservatives upon the potential upside. It could be that liberals favour freer migration because liberal political views are correlated (pdf) with psychological openness.

- People who are in a position to reap the cultural rewards that a tiny minority of migrants bring will be more supportive of open borders than those who aren't. If you appreciate the work of Peter Medawar or V.S. Naipaul you're more likely to be pro-immigration than you are if your experience is confined to hearing disconcerting languages on the bus.

Herein, though, lies a problem. We know from behavioural finance that our thinking about probability distributions is clouded by numerous cognitive biases. It could be, therefore, that we all misperceive the shape of the immigration curve - including me.

* Is it just me, or is Auto da Fe one of the best novels ever written?

** You might object that Szczesny is a source of disutility for Sp*rs fans. But when Jeremy Bentham said that in measuring utility everybody should count for one and nobody for more than one, he didn't have Sp*rs fans in mind.