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Regatta starting stations – Chi-squared continued

Historic data tells us that one of the teams competing in the Henley Royal Regatta seems slightly favoured to win. We don't know why this is, but statistics lets us show that it is true, and get some ideas of what it might depend on, despite not knowing much about the Regatta.

Full article (7–17 minute read): Regatta starting stations – Chi-squared continued

Flashcard of the week

People love to hate games of chance, so they are not always socially appropriate. This week's flashcard is about what people do to hide the fact that they are arranging a lottery.

How do people arrange lotteries when they are illegal or socially discouraged?

Maybe we should first look into why we want to hold a lottery in the first place. Lotteries are great because they are a fair way of distributing resources which cannot be infinitely subdivided. If I have a bag of rice I want to get rid of, I can sort of give everyone in my neighbourhood an equally sized scoop. Most children would recognise that as fair: everyone gets the same amount.

But if I have a toy crane to get rid of, I can't very well chop it up into parts and give them away. Much of its value rests in it being in one piece.

One can imagine many ways of deciding who should get it: maybe the one who can pay most for it should get it, but on the other hand that gives more resources to those who already have many. Or someone I choose based on who I like more, but that rewards good politics and personal connections, which probably is rewarded sufficiently already.

Or I can randomly select the winner. Then, by definition, everyone has an equal chance of getting it. This passes the "would a child recognise this as fair" test if children were statistically literate, because everyone gets the same amount in expectation. It's in some sense the most fair way to distribute resources that cannot be subdivided, because it is the only way in which everyone has an equal chance, and the only way in which everyone gets the same amount in expectation.

When lotteries are socially inappropriate, people hide them thusly:

The lottery is presented as a contest of "skill", e.g. an essay writing contest or the winner being required to multiply two numbers correctly.

These two cases are slightly different:

• In the multiplication contest nearly everyone will get the right number, so the winner quite blatantly ends up being selected at random.

• In the essay writing contest, not everyone will write a good essay, but the judgment process is subjective enough that the winner ends up being selected nearly at random anyway.

(Assuming there is a judgment process at all. I'm sure in many cases the essays are bundled into a pile and one is drawn at random as the winner. Who can take the time to read through hundreds of essays on the same topic? It just seems infeasible in terms of cost.)

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