I am trying to compare a database of campaign finance contributions to candidates with a database of congressional votes, and see if I can unearth any causal relationships between campaign finance sources and legislative action.
Causal relationships are difficult to establish of course, because it is not necessarily obvious whether a donor is supporting a candidate who agrees with their policy objectives, or is offering money to change a candidate's policy objectives. There are many many practical difficulties with determining the sources of campaign financing, which I will ignore for the purposes of this question.
Therefor, my primary assumption is that campaign finance contributions from a given source would have a strong correlation to a certain voting block for a piece of legislation relevant to their interests.
Suppose we take a list of campaign contributions from the following PACs to federal congressmen and senators:
And we run an analysis of all congressmen and senators' votes on only one piece of legislation, something healthcare-related like the Affordable Care Act. We would expect that Lockheed Martin and Boeing's contributions to have comparitively little causal relationship on a representatives' vote, and the rest of the PACs (which are healthcare-related) would have a strong relationship, either with a vote for, or a vote against, the legislation.
How would you run this analysis? Linear Regression seems silly because a vote is a binary yes/no value.