Should we really encourage people to become more rational, as nudge theory says? Two things I've seen in my day job suggest perhaps not.

First, I suggest that investors who are strongly prone to the disposition effect might be better off investing in actively managed funds than in individual stocks. This is because investors tend to be quicker to sell poorly performing funds than poor stocks, and so investing in funds might be a backdoor way of investing in momentum.

Generally speaking, I think actively managed funds, because of their high fees, are sub-optimal. But if the alternative is stock-picking with a disposition effect, they might be an improvement.

Secondly, Annamaria Lusardi and colleagues show that financial education doesn't always improve decision-making. In their example, teaching people about the power of compound interest led some people who initially over-estimated its power to do so to an even greater extent. I suspect that point generalizes to some extent. Encouraging people to save for retirement, for example, causes some to save too much.

To see what's going on here, remember Lancaster and Lipsey's theory of the second best. They show that if there is a market imperfection welfare might be improved by introducing another imperfection. For example, if there is a monopoly, price controls might be welfare-enhancing.

So, here's my theory: what's true for welfare economics might also be true for rationality. Where there is irrationality (such as the disposition effect) introducing another irrationality (such as expensive funds) might actually improve investors' performance. By the same reasoning, trying to remove an irrationality - such as people's tendencies to under-estimate compound interest or save too little - can worsen the decisions of those who over-estimate compounding or save too much.

Of course, just as the second best isn't of widespread relevance in welfare economics, so it might not be in rationality: there are many things in the social sciences which are true but not very much so. Nevertheless, here are some other examples:

- If someone is prone to the hot hand fallacy ("red is on a roll"), they might be corrected by the gambler's fallacy: "black is due."

- Alcoholics sometimes try to stay sober by over-estimating the cost of a drink: "another one will kill me."

- Mental accounting can prevent us from spending to much, by putting some of our money off limits.

These are examples of how irrationality, when in the presence of other irrationalities, can help an individual. But there are also cases where encouraging individuals to be irrational might help others at the expense of themselves. For example, strengthening the norm "don't commit crime" might do more to reduce crime than permitting individuals to adopt an instrumentally rational cost-benefit assessment of doing so. Or encouraging "tax fairness" and tax morale might be preferable to imposing higher tax rates upon those who don't dodge their taxes.

There's also a hybrid example. Luke Johnson says: "virtually all giant business successes and technological breakthroughs depend on overconfidence." And he quotes Keynes:

If the animal spirits are dimmed and the spontaneous optimism falters, leaving us to depend on nothing but a mathematical expectation, enterprise will fade and die.

This suggests that it would be a good thing if we had more irrational overconfidence. And not just good for society. There's evidence that overconfidence is good for individuals too (though perhaps at the expense of others!) - which is the logic behind assertiveness training.

Now, I don't say this as a hippieish celebration of all forms of irrationality. My point is merely that small steps towards greater rationality are not always to be welcomed. Which, at least, justifies some scepticism about nudge theory.