Sunday, April 22, 2012

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."


Xerographica said...

Who doesn't want the most bang for their buck? Who doesn't want more for less? Who doesn't kick themselves when they discover that their sacrifice was in vain?

I really enjoyed reading a few of your blog entries...A Libertarian Case Against Non-Voting...Ashton, Demi and Coase...and have RSS subscribed to your blog.

If you get a chance, it would be really great if you could critique pragmatarianism. It's basically where taxpayers choose where their taxes go. Here's the Wikipedia entry I created for the concept...Tax Choice and here's the most recent critique...Troy Camplin's Critique of Pragmatarianism.

Blar said...

It could be that Buffett thinks that the government is not the optimal use of his money, but it is a very good use of the money, and the best option that he can get other people to go along with.

Say that Buffett thinks that $1 in the hands of the optimal charity is worth 1 utile, $1 for the government is worth 0.5 utiles, and $1 in the hands of a typical rich person is worth 0.1 utiles.

Then if Buffett pays $100 to the government instead of giving it to the optimal charity, that has a net cost of 50 utiles (+50 government - 100 charity). But if another rich person pays $100 to the government, that has a net benefit of 40 utiles (+50 government - 10 individual). So if Buffett and 10 other rich people all pay $100 extra in taxes, that has a net benefit of 350 utiles (10x40 - 50).

Similar logic applies if Buffett does think that the government is the optimal altruistic use of money, but he is somewhere between perfect altruism and perfect selfishness. For instance, maybe each dollar he keeps is worth 0.1 utile to him, and each dollar the government has is worth 0.5 utiles to the people who get it, but he weights himself 10x anyone else. Then Buffett and other rich people like him face a collective action problem, where each dollar a person gives to the government produces half as much value from the point of view of the person who gave it (because he weighted it 10x when it was in his own hands), but it produces 5 times as much value from the point of view of anyone else. The math is identical to the first case - if 11 rich people each give $100 to the government then they each benefit by 350 utiles.

JimD said...

Here’s my view. At some point, we will need to bring the budget substantively into balance. This can be accomplished by some mix of raising taxes and cutting spending. But given the choices of (1) raising taxes, (2) cutting spending, (3) not making a decision, we are choosing option (3). The problem is how do we move away from (3) and towards (1) or (2).

Buffet is just saying that his preferred solution is (1), even if it costs him a lot of money personally. However, Buffet donating to the government doesn’t move us away from (3), and for that matter, doesn’t even make it more likely that we move to (1).

Say that we currently have a shortfall of $100 per year. Buffet wants to raise taxes by $100 (where he pays $50) and not cut spending. You want to cut spending by $100 and not raise taxes (indeed, you’d like to cut taxes). If he promises to donate $50 per year, your policy might shift to cutting spending by $100 and cutting taxes by $50.

In other words, people interpret Buffett unwillingness to donate as evidence that he doesn’t value government services. Maybe he’s not willing to pay for other people’s tax cuts.