**Jan 7, JDN 2458126**

In my previous post, I argued that an advertising tax could reduce advertising, raise revenue, and produce almost no real economic distortion. Now I’m going to generalize this idea to an even bolder proposal: What if we tax *political contributions?*

Donations to political campaigns are very similar to advertising. A contest function framework also makes a lot of sense: Increased spending improves your odds of winning, but it doesn’t actually produce any real goods.

Suppose there’s some benefit B that I get if a given politician wins an election. That benefit could include direct benefits to me, as well as altruistic benefits to other citizens I care about, or even my concern for the world as a whole. But presumably, I do benefit in some fashion from my favored politician winning—otherwise, why are they my favored politician?

In this very simple model, let’s assume that there are only two parties and two donors (obviously in the real world there are more parties and vastly more donors; but it doesn’t fundamentally change the argument). Say I will donate *x *and the other side will donate *y. *

Assuming that donations are all that matter, the probability my party will win the election is x/(x+y).

Fortunately that isn’t the case. A lot of things matter, some that should (policy platforms, experience, qualifications, character) and some that shouldn’t (race, gender, age, *height—*part of why Trump won may in fact be that he is *tall; *he’s about 6’1”.). So let’s put all the other factors that affect elections into a package and call that F.

The probability that my candidate wins is then x/(x+y) + F, where F can be positive or negative. If F is positive, it means that my candidate is more likely to win, while if it’s negative, it means my candidate is less likely to win. (If you want to be pedantic, the probability of winning has to be capped at 0 and 1, but this doesn’t fundamentally change the argument, and only matters for candidates that are obvious winners or obvious losers regardless of how much anyone donates.)

The donation costs me money, x. The cost in *utility *of that money depends on my utility function, so for now I’ll just call it a cost function C(x).

Then my net benefit is:

B*[x/(x+y)+F] – C(x)

I can maximize this by a first-order condition. Notice how the F just drops out. I like F to be large, but it doesn’t affect my choice of x.

B*y/(x+y)^2 = C'(x)

Turning that into an exact value requires knowing my cost function and my opponent’s cost function (which need not be the same, in general; unlike the advertising case, it’s not a matter of splitting fungible profits between us), but it’s actually possible to stop here. We can already tell that there *is *a well-defined solution: There’s a certain amount of donation *x *that maximizes my expected utility, given the amount *y *that the other side has donated. Moreover, with a little bit of calculus you can show that the optimal amount of *x *is strictly increasing in *y*, which makes intuitive sense: The more they give, the more you need to give in order to keep up. Since *x *is increasing in *y *and *y *is increasing in *x, *there is a Nash equilibrium: At some amount *x *and *y *we each are giving the optimal amount from our perspective.

We can get a precise answer if we assume that the amount of the donations is small compared to my overall wealth, so I will be approximately risk-neutral; then we can just say C(x) = x, and C'(x) = 1:

B*y/(x+y)^2 = 1

Then we get essentially the same result we did for the advertising:

x = y = B/4

According to this, I should be willing to donate up to one-fourth the benefit I’d get from my candidate winning in donations. This actually sounds quite high; I think once you take into account the fact that lots of other people are donating and political contributions aren’t that effective at winning elections, the optimal donation is actually quite a bit smaller—though perhaps still larger than most people give.

If we impose a tax rate *r *on political contributions, *nothing changes. *The cost to me of donating is still the same, and as long as the tax is proportional, the ratio x/(x+y) and the probability x/(x+y) + F will remain exactly the same as before. Therefore, I will continue to donate the same amount, as will my opponent, and each candidate will have the same probability of winning as before. The only difference is that some of the money (*r *of the money, to be precise) will go to the government instead of the politicians.

The total amount of donations will not change. The probability of each candidate winning will not change. *All *that will happen is money will be transferred from politicians to the government. If this tax revenue is earmarked for some socially beneficial function, this will obviously be an improvement in welfare.

The revenue gained is not nearly as large an amount of money as is spent on advertising (which tells you something about American society), but it’s still quite a bit: Since we currently spend about $5 billion per year on federal elections, a tax rate of 50% could raise about $2.5 billion.

But in fact this seriously *under*-estimates the benefits of such a tax. This simple model assumes that political contributions only change which candidate *wins; *but that’s actually not the main concern. (If F is large enough, it can offset any possible donations.)

The real concern is how political contributions affect the choices politicians make *once they get into office. *While outright *quid-pro-quo *bribery is illegal, it’s well-known that many corporations and wealthy individuals will give campaign donations with the reasonable expectation of influencing what sort of policies will be made.

You don’t think Goldman Sachs gives millions of dollars each election out of the goodness of their hearts, do you? And they give to both major parties, which really only makes sense if their goal is not to make a particular candidate win, but to make sure that *whoever *wins feels indebted to Goldman Sachs. (I guess it could also be to prevent third parties from winning—but they hardly ever win anyway, so that wouldn’t be a smart investment from the bank’s perspective.)

Lynda Powell at the University of Rochester has documented the many subtle but significant ways that these donations have influenced policy. Campaign donations aren’t as important as party platforms, but a lot of subtle changes across a wide variety of policies add up to large differences in outcomes.

A political contribution tax would reduce these influences. If politicians’ sole goal were to *win, *the tax would have no effect. But it seems quite likely that politicians enjoy various *personal *benefits from lobbying and campaign contributions: Fine dinners, luxurious vacations, and so on. And insofar as *that *is influencing politicians’ behavior, it is both obviously corrupt and clearly reduced by a political contribution tax. How large an effect this would be is difficult to say; but the direction of the effect is clearly the one we want.

Taxing donations would also allow us to protect the right to give to campaigns (which does seem to be a limited kind of civil liberty, even though the precise interpretation “money is speech” is Orwellian), while reducing corruption and allowing us to keep close track on donations that are made. Taxing a money stream, even a small amount, is often one of the best ways to incentivize close monitoring of that money stream.

With a subtle change, the tax could even be made to bias in favor of populism: All you need to do is exempt small donations from the tax. If say the first $1000 per person per year is exempt from taxation, then the imposition of the tax will reduce the effectiveness of million-dollar contributions from Goldman Sachs and the Koch brothers without having any effect on $50 donations from people like you and me. That would technically be “distorting” elections—but it seems like it might be a distortion worth making.

Of course, this is probably even less likely to happen than the advertising tax.