  What does it mean for a machine learning model to be `fair', in terms which
can be operationalised? Should fairness consist of ensuring everyone has an
equal probability of obtaining some benefit, or should we aim instead to
minimise the harms to the least advantaged? Can the relevant ideal be
determined by reference to some alternative state of affairs in which a
particular social pattern of discrimination does not exist? Various definitions
proposed in recent literature make different assumptions about what terms like
discrimination and fairness mean and how they can be defined in mathematical
terms. Questions of discrimination, egalitarianism and justice are of
significant interest to moral and political philosophers, who have expended
significant efforts in formalising and defending these central concepts. It is
therefore unsurprising that attempts to formalise `fairness' in machine
learning contain echoes of these old philosophical debates. This paper draws on
existing work in moral and political philosophy in order to elucidate emerging
debates about fair machine learning.
