Is the System Fair?

At this point in the course, you’ve seen how variance in outcomes can be understood in terms of random, or noisy, statistical processes. If you bet on red at the roulette table five times in a row, and if you lose five times, that doesn’t mean the roulette wheel isn’t fair. That just could be bad luck (for you; possibly good luck for someone else who betted on black). Of course, the casino odds are stacked against you in the long run, since the casino always has an edge. For example, bets on red or black have even odds, but there are two out of 38 possible roulette outcomes in which neither black nor red will win. Now, in principle everyone knows that this is how casinos work and stay in business. So if you end up losing more often than you win in a casino, you can only blame yourself.

Sometimes, though, outcomes are distributed in a certain way that causes us to question whether everything is indeed working as it is supposed to be, according to the rules of probability and some inner sense of fairness. In particular, when outcomes differ for some group or groups of people, we sometimes worry if the system is fair. You may have heard people say, the system isn’t fair. Well, sometimes it isn’t. And we might be able to identify a problem and even fix it. For this to work, though, we need to understand what outcomes are fair outcomes, and this turns out to be a complicated issue! At the root of this inquiry is understanding and explaining differences between groups.