Is it rational to give to political campaigns?

The other day my politics seminar discussed campaign finance. Elections are by definition won by getting the most votes, but too often the reality is that money buys elections. During this seminar I was naturally thinking about Public Choice. We had just covered that voting isn’t rational, assuming that the only utility gained from voting is outcomes driven by policy and that you cast the deciding vote. So I wondered whether donating money to political campaigns, contributing the money needed to buy the election, was rational or irrational in a similar way to voting. I started scribbling a model in the margins of my notes and I reached the following:

|V2 - V1| C/F > C - B

The first notable difference is that the probability of your vote being the deciding vote has been replaced by the probability of one one of your dollars being “the deciding dollar.” C/F is your contribution divided by the total funds the campaign puts towards the election. C-B is the cost of giving, your contribution minus any benefit gained from giving; I had tax write-offs in mind, but this could also presumably be personal altruistic benefit, access to fancy donor cocktail parties, or whatever else.

How rational it is to give to political campaigns depends on how much gain one would receive for one candidate winning over the other and how much other money the campaign has raised. If you’re an owner of a large oil company and one candidate wants to require all new cars to be electric, you will have a massive monetary incentive to help the other candidate to win. Further, if the candidate you prefer doesn’t have a lot of funds, your incentive to give further increases. For the average citizen however, it looks a lot like voting, so I wouldn’t recommend spending your next paycheck on helping your favorite candidate win.