There's been some recent work on ensuring fairness in automated decision making, especially around sensitive areas such as racial groups. The paper "Censoring Representations with an Adversary" looks at one way of doing this.

It looks at a binary classification task where X ⊂ Rⁿ and Y = {0, 1} is the (output) label set. There is also S = {0, 1} which is a protected variable label set. The definition of fairness is that, if η : X → Y is your classifier, then η should be independent of S. Specifically:

• P(η(X)=1|S=1) = P(η(X)=1|S=0)

There is a measure of discrimination, which is the extent to which the classifier violates that fairness assumption. The paper then suggests to tradeoff optimise the difference between discrimination and classification accuracy.

But this is problematic, because it risks throwing away highly relevant information. Consider redlining, the practice of denying services to residents of certain areas based on the racial or ethnic makeups of those areas. This is the kind of practice we want to avoid. However, generally the residents of these areas will be poorer than the average population. So if Y is approval for mortgages or certain financial services, a fair algorithm would essentially be required to reach a decision that ignores this income gap.

And it doesn't seem the tradeoff with accuracy is a good way of compensating for this. Instead, a better idea would be to specifically allow certain variables to be considered. For example, let T be another variable (say, income) that we want to allow. Then fairness would be defined as:

• ∀t, P(η(X)=1|S=1, T=t) = P(η(X)=1|S=0, T=t)

What this means is that T can distinguish between S=0 and S=1, but, once we know the value of T, we can't deduce anything further about S from η. For instance, once the bank knows your income, it should be blind to other factors.

Of course, with enough T variables, S can be determined with precision. So each T variable should be fully justified, and in general, it must not be easy to establish the value of S via T.

For a more parable-ic version of this, see here.

Suppose I make a precommitment P to take action X unless you take action Y. Action X is not in my interest: I wouldn't do it if I knew you'd never take action Y. You would want me to not precommit to P.

Is this blackmail? Suppose we've been having a steamy affair together, and I have the letters to prove it. It would be bad for both of these if they were published. Then X={Publish the letters} and Y={You pay me money} is textbook blackmail.

But suppose I own a MacGuffin that you want (I value it at £9). If X={Reject any offer} and Y={You offer more than £10}, is this still blackmail? Formally, it looks the same.

What about if I bought the MacGuffin for £500 and you value it at £1000? This makes no difference to the formal structure of the scenario. Then my behaviour feels utterly reasonable, rather than vicious and blackmail-ly.

What is the meaningful difference between the two scenarios? I can't really formalise it.

Often we cooperate to extract surplus value from the government, hotels, the physics that makes operating cars cost money, or other sources - value that we could not extract individually. When I notice such a surplus I often wonder how the surplus should be split. What is fair? Purely cooperatively, without anyone trying to game the surplus-allocation-function, and assuming the stated coalitions are fixed rather than negotiable, how much of the surplus should be attributed to each contributing party?

Some concrete examples that have come up recently in real life*:

1. Matching donations. The company I work for will match donations to charity, dollar for dollar, up to a certain maximum. Viscerally, how should I feel about donating $100 to puppies**? More than $100, since puppies get $200, certainly. But less than $200, since my employer should feel puppy-love too, and presumably there's a conservation of visceral feeling law that should apply here. Further suppose that my employer's matching offer caused me to donate $100 instead of, say, $50. What math should be done and why?

2. Exemption splitting. An amicable divorce leaves two parents wondering who should claim their student daughter as a dependent. As a purely "what is fair?" financial question, how much of the tax savings from that exemption should be distributed to the father, mother, and daughter? Suppose the father's marginal tax rate is 25% and overall tax rate is 18%, and the mother's marginal rate is 15% and overall is 12%. What math should be done and why?

3. Refinancing. My friend has a debt at 12% and for silly reasons is obviously able to pay it off but cannot this year. I can pay it off, though, and so could several other people***. Assume there are 3 people including me who could pay it off, and our current expected returns on invested money are (say) 2%, 3.5%, and 6%, and for simplicity she will repay the loan plus any surplus due in one year. Who should pay off how much of the loan (say it's $5000)? I assume the 2% person should pay all of it. That's a 10% surplus - how much do each of the four of us get? What math should be done and why?

As in The Bedrock of Fairness, are there qualities of the solutions we have strong opinions on, even if we do not know the procedure which would generate solutions with those qualities? 

*Details changed.
**I do not donate to puppies.
***Assume default risk is negligible.