This column deals graphically with two distasteful subjects: excessive executive pay, and potty training. You have been warned.

Let me start with the elder Miss Harford, who this week demonstrated that she is well capable of controlling her bodily functions. She peed on the floor five times in quick succession in an attempt to divert her mother from feeding the younger Miss Harford.

Fine. She knows how to use the potty, so all that is now required is the right incentive. Chocolate coins turn out to be the sort of currency a two-year-old understands. Successful use of the potty earns such a coin. It works, and is money well spent.

Yet two days into the contract, problems are emerging. What is “successful use of the potty”? She doesn’t always make it there in time. But at this early stage, we choose to accentuate (and reward) the positive. In a month’s time I will be less impressed, but can we really move the goalposts then?

Even straightforward incentives can be manipulated. The great pole vaulter, Sergei Bubka, repeatedly broke the world record by a centimetre - and earned a cash bonus every time. I have visions of the near future in which Miss Harford empties her bladder one drop at a time in order to scoop bagfuls of chocolate coins.

As we are discovering, apparently black-and-white matters of performance can quickly become shades of grey. It is much more tempting to resort to discretion: if we’re happy with Miss Harford’s performance, chocolate coins will be forthcoming.

This sounds a bit like your boss’s vague promise to review your pay some time the year after next. Employees know that bosses are lying weasels and wisely ignore such empty words. Daughters know that parents are lying weasels too, which is why we must keep our incentive payments as unambiguous as possible.

Employers want to offer incentives for good behaviour, just as parents do. But how to combine oh-so-important discretion with the credibility needed to make the promises persuasive? One possibility is to rely on relative performance: the boss can announce that the best three performers in the office will receive a £1,000 bonus at the end of the year. There is no getting out of such a promise, and no incentive to give the bonus to bad workers instead of good ones, but the boss retains the flexibility to decide what a good performance actually means.

This sort of pay structure is called a “tournament” and was described by the economists Ed Lazear and Sherwin Rosen in a famous article. Tournaments not only combine credibility with flexibility, they also protect workers from risks outside their control: in a bad year, everyone might do poorly, but the people who did least poorly will still be rewarded.

Unfortunately, as Lazear and Rosen were well aware, tournaments also have unwelcome features. They discourage co-operation: one study of Australian companies found workers in tournament-style pay structures were less likely to ring in sick, but also less likely to share tools.

Still, tournament theory explains a lot about the inequities of working life. The managing director’s huge salary, it turns out, is not designed to motivate him but to motivate potential successors - as they strive to win the reward of the top job. Think of the MD’s wage as a sort of “lifetime achievement” award for somebody whose productive contribution is long over.

Since we do not have twins, I will not be able to put tournament theory into practice at home. Perhaps the idea is a little potty anyway.