Defining Fairness - 
These days questions as fundamental as who goes to prison, who goes to college, and who gets a loan are (in part) decided by machine learning algorithms.  These algorithms have the potential to be more accurate and objective than prior methods.  However, researchers have found that many of these algorithms seem to be discriminating on the basis of race, gender, or other protected traits.  But before we can try to fix this problem, we have to answer a more basic question: What is the desired behavior of these algorithms?  What counts as discrimination and what counts as fairness?  Trying to answer these questions for algorithms forces us to think more carefully about how we answer them for society in general.  In this talk, I'll talk about some attempts to define these things mathematically and a crucial impossibility result that shows just how hard this problem is.