Wilkinson vs. Zwolinski on Voluntary Tax Contributions

Matt Zwolinski offers an old chestnut libertarian argument: that rich people like Warren Buffett, who advocate greater tax rates on people like themselves, should voluntarily give more money to the government. The fact that they don’t – as when Buffett donates $37 billion to the Gates Foundation instead of the government – indicates that they think their money is best spent elsewhere.

Will Wilkinson thinks this is a bad argument, because there’s obviously a collective action problem. It’s perfectly coherent for Buffett to say he would give more money provided that many others in his situation did the same, but that he doesn’t want to donate money unilaterally.

I believe I can arbitrate this dispute. Whether Matt or Will is right turns on two questions: first, whether Buffett is assumed to be acting altruistically or selfishly; and second, what kind of collective action problem is involved.

Let’s suppose the collective action problem is a form of prisoners’ dilemma. For simplicity, imagine two potential taxpayer/donors, Warren Buffett and Bill Gates. By contributing $100 to the government, each donor could generate benefits of $75 to both parties, for a total benefit of $150 when summed across the taxpayers. If both Buffett and Gates contributed, each of them would get a net benefit of $50 (that is, $75 from each contribution’s benefit, minus the $100 contribution cost). If neither contributed, each would get a net benefit of $0. If one contributed and the other did not, the non-contributor would get a net benefit of $75 (from the other guy’s contribution), and the contributor would suffer a net loss of $25 (that is, $75 from their contribution’s benefit minus $100 from its cost).

To confirm this is a genuine prisoners’ dilemma, note that each party has a rational incentive not to contribute. Regardless of what the other guy is doing, any contribution creates only $75 of personal benefit and $100 of personal cost. Non-contribution is a dominant strategy. And yet both Gates and Buffett would be better off if both contributed, since $50 net benefit (from both contributing) is better than $0 net benefit (from neither contributing).

So this would seem to support Will’s position: it’s sensible to refuse to contribute unless you know that both parties will be forced to do so. But here’s where altruism versus selfishness comes in. The reasoning above depends on the two parties acting on rational self-interest. But if they were reasoning based on an altruistic utilitarian calculus, they would each contribute regardless of what the other guy was doing. A $100 contribution generates a $150 total gain, and that’s enough to justify the contribution. And this, I believe, is Matt’s whole point. Buffett at least claims to be taking an altruistic position – and his actual charitable contributions lend support to that claim. If so, he should be giving more money to the feds if he actually believes doing so will generate the greater altruistic bang for his buck.

On the other hand, let’s suppose the collective action problem is more of a coordination game. Imagine that a $100 contribution from one donor really won’t do any good at all – it will just be wasted. But two $100 contributions will generate a benefit of $150 each. The benefit only occurs when both parties act together in a coordinated fashion. In this situation, it doesn’t make sense to contribute at all unless the other party does so as well – and this is true regardless of whether you’re selfish or altruistic.

If the real-world situation is more like a coordination game, then Will’s position looks stronger. Even as an altruist, Buffett is correct to withhold his contribution to the government until he’s sure the government will make sure Gates (and others) contribute as well. To put it differently, it makes sense to withhold contributions if there’s a kind of non-linearity in the impact of contributions, so that twice as much money creates more than twice as much benefit. (The structure of my coordination game does this in extreme fashion by asserting that the lone contribution has zero benefit.)

So which is it? Is the real-world situation vis-à-vis the federal deficit more like a prisoner’s dilemma or a coordination game? On this question, I don’t have a strong opinion, but my instinct is that it’s more like the former. Why? Because I suspect there’s no real non-linearity in the impact of deficit reduction on social benefits. A $100 reduction in the deficit surely has a negligible impact on any macroeconomic variable, but it’s only negligible because $100 is not much money, not because $1000 is more than ten times as effective as $100. In other words, we shouldn’t confuse “small impact because of small contributions” with “small impact because of coordination failure.” From an altruistic utilitarian perspective, only the latter should affect your decision to contribute. However, since I’m not a macroeconomist, I’m open to the idea that there are non-linearities here that I’m not recognizing.

UPDATE:  Arnold Kling makes essentially the same point about non-linearity; as he puts it, Will's position seems to require "some extreme 'lumpiness' of public goods."