If I were to give you a budget to choose your perfect house, you would quickly have a clear idea of what to buy. And typically your perfect house will be a bit boring. That’s because, when you can only have one house, it cannot be too weak in any one dimension. It cannot be too small, too far from work, too noisy or too weird. So you’ll opt for a conventional house.

On the other hand, if I were to double your budget and tell you to buy two houses, your whole pattern of decision-making would change. You would now be looking to buy two significantly different properties with complementary strengths — perhaps a small flat in a city and a house in the countryside. Your criteria for the two houses would be wildly different. Neither would be the one you had chosen as a single home.

We know this instinctively in the domain of houses. Or cars. Nobody would buy four identical cars. One person choosing four things isn’t the same as four people each choosing one. Yet, intriguingly, in other realms of decision-making we seem not to understand this at all. For instance, in assessing job applicants or parliamentary candidates or university admissions, no one gives any thought to this effect. It is assumed that ten groups each choosing one candidate will make the same ‘optimal’ choice as one group choosing ten. They won’t.

If you are choosing a single parliamentary candidate, the safe default option is to pick a vapid but presentable PPE graduate. Yet no one choosing ten people would choose ten of those. They might choose two or three, but they’d also throw in a few wild cards — maybe someone who’d had a proper job, a woman, someone from a poorer background and someone with a science degree. The admirable Cecil ‘Bertie’ Blatch clearly understood this when, as President of the Finchley Conservative Association, he decided to ‘lose’ a couple of votes for a more conventional candidate to give Margaret Thatcher her first winnable seat. He wasn’t cheating; he was correcting a mental bias.

Once you understand this, the potential exists to increase the level of (social, gender, ethnic, mental) diversity in employment, education or politics without imposing any quotas: it arises naturally once you choose people in batches. I know this from personal experience. Years after I was first hired, someone involved in the selection process revealed that I would never have been offered a job had they been recruiting one person at a time, but they had four vacancies, so decided ‘to take a punt on the weirdo’, or words to that effect.

Everyone worries about declining social mobility, rising inequality, the hideous homogeneity of politicians and so on. Yet it is possible these have arisen from well-meaning attempts to make the world seem fairer.

Meritocracy assumes that merit resides exclusively in individuals. So it assumes that you reward merit fairly by applying identical, transparent and objective selection criteria to everyone, one person at a time. This has the appearance of seeming fair at the individual level, and makes the system easy to defend, but because you can’t vary your criteria, you lose out on the chance to recruit diverse groups with complementary abilities.

Here’s the quandary. You can create a fairer, more equitable society with (admittedly fairly random) opportunities for all, where luck plays a significant role, or you can create a society which maintains the illusion of complete, objective and non-random individual fairness, yet where opportunities are open to only a few.

The problem when ‘the rules are the same for everyone’ is that the same boring bastards win every time.