This morning I was reading an article, in a national (US) news magazine, that discussed energy policy decisions. It mentioned executives of companies in various energy-related industries contributing to the coffers of various congressmen (from both parties), and it mentioned their votes on key policy issues. The implication was clear: the votes were being bought, or at least influenced, by interested parties.
I understand why writers do this: it spices up the articles (a hint of corruption) without making any explicit charges that cannot be backed up with hard evidence; and it appeals to voters looking for confirmation of their prior belief that congressmen are crooks. I tend to view our elected representatives as by and large venal to some extent myself. The last part of the title of this post is motivated by a quote from Simon Cameron (Abraham Lincoln's first Secretary of War): "An honest politician is one who, when he is bought, will stay bought." As you can tell from the title, I am not sanguine about finding honest politicians.
As an OR professional, though, I understand the flaw in the argument (if we can characterize what is really innuendo as an "argument"). It relates in part to confusing correlation with causation and in part with confusing the direction of causation. Let's say that our fearless reporter accurately reports that Representative A votes for subsidies for domestic production of buggy whips, and Ms. B, CEO of a large manufacturer of buggy whips, donates regularly and/or generously to Rep. A's election campaigns. With minimal effort choosing words, our reporter can make this sound as if A voted for subsidies because B (and perhaps others of a similar mind) paid him off. That is indeed one possibility.
Another possibility is that A voted for subsidies first and then B donated, recognizing A (from his vote) as a friend of the buggy whip industry. There's causation, but in the opposite direction from what the reporter implied, and nothing venal. The nature of political contributions is that you usually contribute to candidates with whom you agree. (I say usually because lobbyists sometimes contribute to both sides, hoping the winner will remember their contribution to her and not to her opponent.)
Yet another possibility is that B contributed to A first, either anticipating a pro-buggy whip platform or for reasons unrelated to industrial policy, and A favors subsidizing domestic production for sincerely held (if possibly misguided) reasons. This is a case of trying to infer causation from what may be mere correlation.
How can we tell whether A's vote is in fact being purchased? Anyone who has done much with statistics recognizes how hard it is to establish causality, especially in the absence of a designed experiment with an appropriate control group. We could try tracking A's votes over time, matching them with B's contributions (or the contributions of B and other pro-subsidy individuals or groups), and look for a positive cross-correlation with lag 1 or higher (so that swings in donations lead swings in votes). A positive cross-correlation would still not be solid proof of vote-buying, though, and might also lack "power" as a test of vote-buying: if A fits Cameron's definition of an honest politician, and consistently votes pro-buggy whip because he is taking graft, there will be no variance in his votes and therefore no cross-correlation.
This leaves me in the unsatisfying position of not knowing whether or not A is a crook. There have been enough US congressmen convicted of malfeasance to convince me that the proportion of occupants of Capitol Hill who are crooks is not zero. Still, there is also a well known aphorism (of uncertain provenance) that might apply: "Never ascribe to malice that which is adequately explained by incompetence." We have ample evidence that incompetence is not in short supply on the Hill.