Philosophical Notes: Towards a fairer share of dishwashing

ONE OF my college house-mates, Greg, use to refuse to divide anything by lot. He objected that this procedure discriminates against what he called "the unlucky people". Steadfast randomisers reply to this that "unlucky" fails to select a natural class of people. The fact that someone is Indian today is a good enough reason to believe he will also be Indian tomorrow. But being unlucky today provides no grounds for predicting being unlucky tomorrow.

I had the good fortune of marrying an acquaintance of the said college housemate. My wife and I moved into a cheap flat and we agreed to transcend gender-based division of labour. This made dishwashing a somewhat delicate issue. Initially we tried team dishwashing. But two people cannot wash much quicker than one. Then we tried rotating the chore between us. But that raised the suspicion of "insensitive dish-dirtying" on one's days off. So, dismissing Greg's reservations, we changed to a policy of determining who would be the night's dishwasher by flipping a coin after dinner.

At first, our chancy arrangement created an exciting casino-night atmosphere. But then I lost five times in a row. I kept thinking about the coin in the opening scene of Tom Stoppard's play Rosencrantz and Guildenstern Are Dead. It lands heads down for 179 consecutive tosses. For a while I did have the consoling thought that the law of averages would ensure that everything would even out in the long run. But then I realised that this thought was simply an instance of the gambler's fallacy. If a coin lands heads on five consecutive tosses, those devotees of the gambler's fallacy will bet on tails. They think that the law of averages works by compensation. But the law of averages actually works by brute force. A lop-sided run of five heads disturbs the ratio of heads to tails over the short run. But the five-toss streak has steadily less impact on the 1:1 ratio over the long run. This does not mean the five-heads surplus disappears; it is merely dwarfed into statistical insignificance by the growing number of coin tosses.

Luck has no memory. The law of averages does not try to make up for past imbalances. So the bottom line was that my five nights' worth of dishes were a dead loss! Just processes do not guarantee just outcomes. Here is a dishwashing scheme that does, in fact, guarantee a just outcome because it does work by compensation. Instead of flipping a coin, you choose from a deck of cards. If the card is red, my wife washes. If the card is black, I wash. Since the card is not returned to the deck, the washer has a lower chance of being selected on the next round. Moreover both parties are guaranteed to wash an equal number of times. Cards are fairer than coins. Coins may well provide a fair process but they fail to ensure a fair result.

The belief that just processes ensure just results is important to those political philosophers who reject the principle that the end justifies the means. For instance, in his book Anarchy, State and Utopia, Robert Nozick uses the principle to defend the unfettered accumulation of wealth by capitalists. As long as each small transaction is fair, then the cumulative redistribution of wealth will be fair: i.e. the transfer of money from the many poor to the few rich.

Perhaps Robert Nozick would try to smooth troubled waters with the observation that people do tend to acquiesce to the results of processes they perceive to be fair. Agreed, but there are other explanations. For the sake of domestic tranquillity, I might agree to abide by the outcome of some process - regardless of whether it is fair. But that means that it is my consent which obliges me to accept the outcome, rather than the justice of the actual procedure. The means do not justify the end.

Roy Sorensen is the author of `Thought Experiments' (Oxford University Press, pounds 16.99)