Can you be a little less specific?

29th October, 2011

Game theorists are beginning to produce rational models of deliberate vagueness

Seinfeld’s George Costanza was once invited “up for coffee” at the end of a romantic evening, and refused: caffeine would keep him awake, he explained to his perplexed date. Later, aghast, he realised: “coffee doesn’t mean coffee! Coffee means sex!”

Well, indeed – but few people, if they are wise, will baldly suggest the sex. A little ambiguity is called for. Now game theorists – masters of the mathematisation of human interaction – are beginning to produce rational models of deliberate vagueness.

Andreas Blume and Oliver Board, two economists at the University of Pittsburgh, offer up just such a model. They point out that perhaps it is too much trouble to be specific, as with a business contract offering a fee plus “reasonable expenses”. This isn’t always the reason. “Coffee” has two syllables, “sex” has only one, and surely George’s date could have made her intentions plainer without much effort.

Perhaps it’s just a matter of social norms: it would have been shocking for George’s naughty-but-nice date to ask him to sleep with her, so instead she hinted that an attempt at seduction might not be rebuffed.

But there is often a logic behind such norms – for example, the opportunity to tweak the message depending on how it is received. If George seemed taken aback by the invitation for “coffee”, his lady friend would have retained plausible deniability. If he seemed interested but hesitant, she could have clarified the message by slipping into something more comfortable.

Alan Greenspan, the mumbling maestro of mixed messages, played the markets with one vague declaration after another, each one a nudge – but not a shove – in the direction he preferred.

The Blume-Board paper lurks on the boundary between philosophy and mathematics – and, ironically, it is extremely precise about what “vagueness” means. A working paper from the economists Florian Ederer, Richard Holden and Margaret Meyer has a more practical bent, examining the boss who finds it useful to be vague about performance bonuses.

The scenario here is one of an employer who cares about two tasks and an agent who finds it easier to do only one of them. Imagine a journalist who must both write words and spell them correctly: the boss needs both of these jobs done well, within reason: a mass of spelling mistakes is no use and neither is a tiny number of correctly spelled words.

The challenge is to design appropriate performance pay for the job, and the difficulty is, there are two types of journalist: those who find it easy to churn out reams of copy, and those who find it easy to spell correctly. The boss doesn’t know which type of journalist she is hiring. It would be easy to demand the impossible, and find no takers for the job; or to pay over the odds; or to hire a journalist but then inadvertently give him an incentive to neglect half the job.

In some important cases, say Ederer, Holden and Meyer, the boss will want to be deliberately ambiguous about what sort of performance will be rewarded. Will the bigger reward go to the careful speller or to the hasty typist? One type of ambiguous contract has the boss tossing a coin and rewarding either one type of achievement or the other. An alternative contract – a variant of “you cut the cake and then I’ll choose” – allows the boss to choose one of two performance metrics after she has seen what kind of performance has actually been produced.

There’s a cost to all this ambiguity, of course: it’s risky for the journalist, who must then be compensated. Nevertheless this can be a price worth paying.

We’re used to thinking of ambiguity as a flaw in contracts, agreements and management styles. But when your boss gives you vague directions or bases your performance bonus on inconsistent and ever-changing criteria, perhaps there’s method in the madness.

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