I cohabit: dual career, equal partnership. My partner has a child from a previous marriage who lives with us. We co-own our home, and we contribute equally to a joint account for paying the bills. We have had to hire a housekeeper, since he does not want to clean the house and I do not want to do all the housework. Should I be paying for the food and utilities consumed by his child? Should I have to pay the same amount towards the housekeeper that he does?
Troubled in Paradise, via e-mail
You need to work out whether the net benefit of the housekeeper is positive. You will tend to exaggerate the value of a clean house while your partner pretends not to notice grime. So you need a clever technical procedure called a Clark-Groves mechanism, which will give you and your partner an incentive to tell the truth about how much you value the housekeeper.
Both of you should pay a few thousand pounds into a “trust fund for honesty”. Then write down the net benefit to you of having a housekeeper and paying half the cost; your partner writes down the net cost to him of the same arrangement. If the benefit exceeds the cost, hire the housekeeper and share the cost equally, but you must also pay the figure he wrote down to the trust fund. He receives the figure you wrote down from the trust fund. (They will not be the same, which is why you need the fund.)
Neither of you will benefit from lying because what you pay or receive is not a function of what you write down.
This is a tremendous fuss, of course. But it will be interesting to see what happens when you use the procedure to see how much he values the kid.
Also published at ft.com.