2. A government is considering making alcohol consumption illegal as part of a public health campaign. Let's think of making alcohol illegal as the treatment, T. Write T = 1 if the government makes alcohol illegal and T = 0 if the government leaves alcohol legal. We will think of a binary outcome for each person, either they drink alcohol or they do not. If person i drinks at treatment status T, we write her potential outcome as YTi = 1 and if she doesn't drink, we write it as YTi = 0. Suppose the society is made up of three groups: the always drinkers, the legal drinkers, and the never drinkers. The always drinkers will drink whether or not alcohol is legal. The legal drinkers will drink if and only if alcohol is legal. The never drinkers won't drink whether or not alcohol is legal. (a) Write down, in potential outcomes notation and as a number (0 or 1), each of the two potential outcomes for each of the three groups. (b) Write down, in both potential outcomes notation and as a number (0 or 1), the causal effect of making alcohol illegal on drinking for each of the three groups. (c) Is there an effect, on average, of banning alcohol in this society? (d) Suppose you are out to lunch with some friends and one of them says, "My uncle lives in a place where they banned alcohol and all of his friends kept drinking, so I don't think it does anything." Explain, in terms of our example, why this isn't a convincing argument.