## Thursday, June 3, 2010

### Fairness

There is a lot of talk, from time to time, about the fairness of various salaries.

Imagine what you'd like the distribution of wealth to be:

Now imagine that you've managed to elect a government which can enforce this distribution.

Now suppose that Kevin Pietersen is playing in a cricket match, and charges £1 to watch it.

Suppose 100 000 people turn up.

Everyone is happier as a result.

KP is £100 000 richer, and has presumably enjoyed his cricket match.
Those watching have had a nice day out. They chose to pay £1, and would presumably choose to do it again. They are unlikely to miss their £1.

So, since everyone is happier, how can this new distribution be less fair than the original?

This argument is known as the Wilt Chamberlain Argument, after a famous baseball player.

I'm not sure what it shows.

Things it might show are:

There is no optimal distribution of wealth, because given any distribution where 100 000 people are able to pay £1 to watch a day's cricket, we can think of a better one.

The optimal distribution of wealth is where KP has all the money, and no one else can afford £1 to watch him play.

I'm stuck.

#### 1 comment:

1. I think the following observations suffice to de-fang the argument. Your mileage may vary. I've left the actual reasoning implicit; if I've thereby left it insufficiently clear, I can try to clarify but not until at least this evening.

1. He doesn't need to have all the money for other people not to want to pay £1 to watch him play any more.

2. The following two propositions are not the same. (1) "When A is replaced by B, everyone involved is happy about it". (2) "Everyone involved is happier with B than with A". (Because people -- including clever and sensible people -- do not have anything like perfect insight into their preferences.)

3. All those people might well pay £1 to watch Pietersen play cricket. But not if they were already spending £1000/year watching him play. (Probably not if they were already spending £10/year watching him play, at £1 a time.)

4. One thing people value is *not* having what they do with their money laid down by the government (or anyone else), so while there might be an optimal distribution of wealth there probably isn't an optimal situation in which the government enforces a particular distribution of wealth.