Let's just say we are interested in identifying the causal effect of campaign communications on vote choice. Before we start thinking about ways to collect and analyze data, we want to think through clearly what it means to say that an action a political campaign took "caused" someone to change their vote.

1. Using potential outcomes notation, write down what your treatment and outcome variables are, and how you will denote them.
2. Create a table of potential outcomes and causal effects for ten people. Assume that in the real world, five of them will receive a communication and five will not. Also assume that four of them would always vote Democratic, four would always vote Republican, and two would vote Democratic only if they receive a Democratic campaign communication and vote Republican otherwise. (If you prefer, you may do this outside the text editor here, save the results as an image, and include the image as part of your response.)
3. In this world, is there a causal impact of campaign communications on vote choice?
4. Using the table as an example, explain the "fundamental problem of causal inference