Imagine the following scenario. I give you and a stranger an envelope each, one of which contains twice as much money as the other. I then say you can swap envelopes if you give me £1. Do you do so?

You might think: yes, for the following reason. Let's say my envelope contains £10. Then the other contains either £5 or £20. So I have a 50-50 chance of losing £5 or making £10. This has an expected value of £2.50. For moderate levels of risk aversion - or for those who gamble (pdf) with the house money! - it makes sense to pay to swap.

But having swapped, the same logic suggests you should swap again. And again. And again. And each time, I make a pound out of you. I've got me a money pump.

In fact, though, there's a simple way to protect yourself from this mistake. You should put yourself in the shoes of the stranger with the other envelope. He's reckoning - by the same logic - that he should swap envelopes. But if he wants to swap with you, you should reject the offer, because his gains are your losses.

Putting yourself in the other guy's shoes can therefore save you from losses that can arise from apparently good thinking.

This is no mere abstract thought experiment. One of the strongest stock market anomalies - in both the US and UK (pdf) - is the tendency for newly-floated shares to do badly in the months after flotation. Investors pay too much for new companies.

One reason why they do so is that they make the same mistake we see in the envelopes problem. They fail to consider the other guy's position. They don't ask: "if this business is worth buying why is the owner - who presumably knows more about it than me - so keen to sell?" Asking this would alert investors to the possibility that the company is over-priced and its owners are trying to cash out at the best time.

In both situations, the same mistake is made. David Navon calls it the egocentric framing error - then tendency to consider problems only from our point of view rather than the other guy's.

To put this another way, it's the failure to distinguish between parametric and strategic rationality. Parametric rationality asks: how can I maximise utility, given particular parameters? Strategic rationality, however, recognises that the parameters aren't fixed, and that your choice depends upon the choice of the other fellow.

I say all this because I fear that some people might be making the same mistake about Brexit. Looking at much of the reaction to May's speech yesterday makes one suspect that the UK is the only actor in this drama. But this, of course, isn't the case. The UK's demands and strategy is only half the story. We shouldn't overlook the EU's position - such as discontent with the UK's "cherry-picking" and a desire to ensure that a nation can't be better off outside the single market than in. In calling May's position solipsistic, Martin Sandbu is right: she's looking at it solely from a UK perspective.

In this respect, the tendency towards the egocentric framing error is exacerbated by our traditional insularity ("Fog in the channel: continent cut off") and monolingualism. As Simon Kuper says:

Foreign countries are opaque to mostly monolingual Britons and Americans. Foreigners know us much better than we know them. This asymmetry probably helped Russia get its favoured candidate into the White House, and it will handicap Britain in the Brexit negotiations.

Perhaps, though, I'm missing the point. Maybe May wasn't speaking to Europe yesterday so much as to right-wingers here: she's trying to placate Ukip. In this, she's continuing a long tradition of treating UK relations with the EU as a by-product of internal Tory party politics.