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Wednesday, 17 July 2019

Alan Turing and the Banknote Problem


In a long tradition, a moral claim is only sound when it is universalisable. Morally, policy or decision X can only be good for the goose if it is also good for the gander. What I wish for myself I must be willing to wish for anyone else similarly situated. Any other form of a wish is discrimination, usually in its own favour. Log rolling campaigns aim to get X for me but not for you. So there are people who are unhappy with the decision to put Alan Turing on the new £50 note. For example, they thought it was time for a black person.

Suppose there are seven colours of the rainbow and four banknote denominations. Suppose a rule says that only one colour can appear on a banknote denomination besides black and white. (I will leave this rule unchallenged for purposes of the argument; Coca Cola advertisements challenge it).

A first task now is to find a rule for securing “fair representation” of all rainbow colours, a rule which is universalisable. There are a couple of obvious possibilities: rotate colours through time or pick colours by repeated  lotteries. These are non-discriminatory methods or algorithms.

Now suppose that bank notes of different denominations are issued in unequal quantities. This then seems to require that to secure overall fairness in colour distribution, any appearance of a colour should be weighted by the number of banknotes issued in that colour. Otherwise, some colour could be left languishing on a denomination banknote that very few people ever see (like the 500€ note).

But suppose that the colours of this metaphorical rainbow do not occur with equal real-world frequency. So to measure for fairness, we now have to weight for colour frequency and also be prepared for those frequencies to change. Unlike the colours of the real rainbow, the distribution of colours in the social rainbow change through time.

A mathematically minded reader might like to keep going and try to produce the decision-making algorithms which would secure fair representation through time. Can lotteries achieve it?Can rotation achieve it?

However, there was a prior question to which an answer was simply assumed. There are seven colours of the real rainbow. How many colours of the metaphorical rainbow? In other words, how many categories exist which require representation?

As far as I can see, when you get past two (male and female the obvious ones), the going very quickly gets very hard. Are blind people and deaf people one category or two? Are cyclists and pedestrians one or two? How many categories is BAME? How many categories is LGBTQ+  ? (For human resources managers tasked with achieving diversity, the gay black woman is a gift from heaven since she occupies three categories at once. When does that become an unfair advantage, a sort of new Eton and Oxford and male? And is it an unfair disadvantage that old and male and pale also occupies three categories not one?).

Unless there is an agreed answer to the How many categories? question,  we will never be able to satisfy all of the people all of the time. Instead, we will continue to live in a world of serial log-rolling campaigns But social justice always used to be envisaged as an alternative to log-rolling, not its justification.

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