Bryan Caplan  

Easy Question Almost All My Public Choice Students Miss

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A recurring final exam question for my undergraduate Public Choice class:

Suppose voters were rational [in the Rational Expectations sense] and the SIVH [Self-Interested Voter Hypothesis] were true.

T, F, and Explain: Democracies would spend a higher share of their budgets on genuine public goods.

Almost no one gets it right - and we cover the most relevant material just one week before the final exam!

Feel free to try your hand in the comments...

COMMENTS (31 to date)
Ted Sanders writes:


Free-rider problems apply to governments as well as people. For example, selfish countries won't reduce carbon emissions when the benefits apply to all but the costs lie squarely on them.

If we had a single global government, the answer might be different, but since we have many national (and smaller) governments coordinating, there will always be free-rider problems.

(Also, this question seems terribly complex and impossible to answer. That might be why students get it wrong. Imagining outcomes in alternate universes is difficult.)

Ted Sanders writes:

Also, in a world where voters were rational and self interested, the very fabric of society would look alien. Either we'd be far, far richer or far, far poorer. In either case, I suspect the portfolio of government spending would differ wildly from today's proportions, and therefore judging the fraction spent on public goods seems like an impossible request. Indeed, the very notion of government itself might be different in such a world.

Of course, this isn't at all what you meant by your words. We both know that. But for a student who is less familiar with the conventional assumptions, it could be a very plausible and confusing line of thought. Often when a professor thinks a question is easy but the students don't, that's because the professor has assumptions in mind that are invisible to the students.

Swimmy writes:

Voters would not spend more on public goods.

Take the standard public goods model. You can contribute $200, and if everyone contributes, the population as a whole gets $100*n.

By assumption, contributors are in their rational self-interest to not contribute at N = 10, an amount where researchers might play the game in a lab.

At N = 11 there's no difference. At N = 30 there's no difference. And so on. There's no threshold. Yes, in very large populations the possibility of deciding an election goes to 0. But the expected gain from the public good to the player goes to 0 ever so slightly faster than the expected loss from contribution.

In a normal public goods game, one player not contributing destroys the public good multiplier. In this imagined game, one player not contributing has a very low chance of eliminating the multiplier.

But voters only care about what happens if their single vote decides the election, because that's the only case in which their decision could matter. And by assumption, in that case, contributing still has a negative EV for that voter.

Purely self-interested voters will not vote to contribute. We would expect to see less spending on even true public goods.

Denver writes:


You still have public goods problems with the voting mechanisms themselves, i.e. rational ignorance.

Ted Sanders writes:

Furthermore, I'm not entirely sure what 'genuine public good' means and what distinguishes it from a 'public good.' Is the point of the 'genuine' label to exclude public goods that you think have bad consequences?

Also, I'm trying to classify which government spending counts as genuine public goods. Is social security a genuine public good? The checks themselves are exclusive and rivalrous, but the lack of senior homelessness is neither.

Ted Sanders writes:

P.S. Sorry for giving you a hard time over such a minor issue. But I really do think the answer is more nuanced than your tone suggests.

Ted Sanders writes:

By the way, it seems plausible to ignore national goods as qualifying as genuine public goods. Immigration controls (among other barriers) make national goods excludable. Only global public goods are genuinely public.

(Again, this is an angle you may not have intended with your question. But nothing you wrote would prevent a student from reasonably believing it. In general, students getting an "obvious" question wrong is a signal that there are implicit assumptions that should be made explicit.)

Swimmy writes:

Ted Sanders:

I think Caplan's specifically trying to say, "This question has nothing to do with what I or you think is a public good."

It's a question about what Rational Expectations and the SIVH mean and predict, not about the meaning of "public goods." You've gotta head off students who would rant about that topic instead.

Ted Sanders writes:

@Swimmy: Ah. I had assumed, perhaps incorrectly, that his intention was the opposite. For example, I think the US military qualifies as a public good. Because military spending is such a large fraction of the budget, is the question really asking whether rational self-interested voters would have a bigger or smaller military? I thought the 'genuine' label might be a way to avoid such questions by (circularly) asserting that a 'genuine' public good is whatever goods a rational self-interested voter would want. Then we wouldn't need to analyze whether militaries are good or not.

Ted Sanders writes:

Sorry, my last comment was less clear than it should have been. I agree with you Swimmy that it sounded like 'genuine' was meant as a label to avoid questions of what counts as a public good or not. Thank you for your clarifying take.

Ted Sanders writes:

Time for a better comment.

Interestingly, the statement "Democracies would spend a higher share of their budgets on genuine public goods" is equivalent to "Democracies would spend a lower share of their budgets on non-public goods."

But how can we know what a rational, self-interested population would spend on non-public goods?

The only way this question has an easy answer is if it uses to circular logic to define genuine public goods as what rational, selfish democracies would spend more on.

MikeP writes:


Truly rational self-interested voters would realize that governments are inefficient mechanisms for effecting the production of goods and services, whether in their private interest or genuinely public, especially in the game where all other voters are the same way.

Therefore the pressure on the government would be to reduce the rent seeking, which lowers the budget and consequently increases the share of budget that goes to genuine public goods.

Wallace Forman writes:

My first impulse is to ask, "Higher than what?" Setting that aside:

* Rational SIVH voters vote for public goods only if expected benefits outweigh expected costs.

* Normal voters vote based on some other criteria (somewhat unclear what that is). Perhaps, "what sounds good", which may lead to them voting for public goods they haven't taken care to see aren't worth their costs.

Jeff G writes:


If the SIVH is true then there is no expressive voting and no "feel good" spending, thus more public good spend.

Brian writes:

Here goes:


A nearly-perfectly self-interested electorate with rational expectations will see that the chance of one person's vote affecting the election is infinitesimal. And therefore only the very most interested citizens will vote at all. The majority rationally stay home.

So politicians and their immediate families and professional special interests and their lobbyists will vote. The result will be a pure kleptocracy chosen by a small elite that has engineered lavish giveaways to themselves. Public goods will be neglected unless they are necessary to avoid complete collapse.


I had a different theory based on rational ignorance, which is the main driver of current voting behavior but I'm not sure it's compatible with rational expectations in the present sense.

Scott writes:

It's been a while since I've thought about things like this, but here goes:


I'm assuming that Rational Expectations means that voters correctly forecast the effects of different policies. If I'm missing something here, then I'm toast ;)

SIVH means that individual voters will vote only for policies which will benefit themselves, more than the cost to themselves, which they correctly understand.

Observation 1:

Things that are true public goods that have benefits that extend beyond half of the voting public will be funded (if they provide a greater benefit than the cost incurred by the added taxation needed to fund them).

Observation 2:

As a first approximation, I would expect that private goods would be less likely than public goods to provide benefits to more than half of the population, although that's not a necessary condition.

Observation 3:

Private goods are more efficiently provided by private producers, thus the taxes needed to provide the private good through the government will be higher than the cost of buying the good in the private market without government provision.

Observation 4:

In the real world voters frequently think that private goods are public goods and, at the very least, don't connect their future tax rates to the provision of anything.


The real world will see a higher percentage of the budget devoted to private goods than the hypothetical world.

Things that I can think of that I'm ignoring:

1: Distribution of tax rates. If the tax system is rigged in such a way that a minority of voters pay for all of the taxes (not as far from our system as one might think, I think), then SIVH will lead to more private goods being provided to the non-taxpayers.

2: Distribution of benefits of the public goods. Public goods that are highly valued by a minority that come at a small cost to the majority will not be produced in the hypothetical world. I can't think of an argument that the current world does a better job of specializing in these sorts of goods, but perhaps there is one to be made.

MikeDC writes:

I think most people don't read questions of proportion correctly, and skip to absolutes.

Further, they get wrapped up in the somewhat misleading term "genuine".

The answer is clearly TRUE.

Why? Because
1. Regardless of whether everyone would agree on what are public goods, there are certainly a lot of government expenditures on private goods. And under the RE/SIVH rubric, they would clearly fall.

2. Thus regardless of how "genuine" the public goods are, the share of public goods as a part of the budget would rise.

Example: Suppose the government spends $100. It spends $20 on the purest of pure public goods you can imagine (say, defense). It spends another $30 on public goods of debatable merit (say health and education). It spends $50 on pure private goods.

After an RE/SIVH "revolution", the government would stop spending on the private goods, so the budget would fall to $50. Thus, the share of genuine public goods would raise from 20% to 40% of the remaining budget.

To some degree this might be offset by a decline in expressive preference for something like defense spending, but it would have to fall from $20 to $10 to be proportionately a lower share of the budget (<20%). Which seems unlikely.

[broken html fixed. You can't use the keyboard less-than sign in text.--Econlib Ed.]

Ted Sanders writes:

Here's another argument for false.

Suppose the following law/candidate/party platform is put up to a vote: 49% of the country pays 10% of their wealth to the other 51% of the country.

If voters are self-interested, this law should pass. (Even if turnout is rationally low, ~51% of those turning out will vote yes.)

Such a policy is not a public good. Wealth transfers are excludable and rivalrous.

In a world with self-interested rational voters, you could argue wealth transfers would go up and thus public goods would go down.

[Of course, you can argue that if these rational voters like equality, they might selfishly vote for a more egalitarian society. But that opens a new can of worms. At some point, you can call any behavior selfish, justified under the correct utility function.]

James writes:

This is a repeated prisoners dilemma problem so it depends on the discount rate.

If people discount future utility a lot then public goods would go down as a fraction of total government spending. Being rational, the voters defect and vote for all the pork they can get.

If voters have a low discount rate they will vote for a government that only provides defense and security. Voting for pork might lead to a temporary gain but the corresponding decline in the rate of economic growth will make them poorer in future periods.

Jacob Thompson writes:

Gut answer: True. It's not so much a gut reaction but rather the result of modeling this game with a truth-table.

Absent government, the dominant strategy for all parties wrt public goods is to not contribute to their maintenance.

However, when the provision of a public good becomes a "pass/fail" in which everyone pays for the public good if and only if a majority decides it, then the payoffs, as a function of the votes of the other players, changes.

In a three-person game for instance, when each 100$ of spending yields $50 to each member of the game, the dominant strategy for each player is to vote *for* the public good if and only if she is the deciding vote. In a three person game, if the two other players vote for the public good, then the single player is indifferent between voting for or against. Similarly, if both the other players vote against the public good then the single player is indifferent. However, when one player opposes the public good and another supports it, then the single player will vote *for* the public good because she will gain an extra $50.

There does not seem to be a general Nash equilibrium however since there is no generally dominant strategy.

Pajser writes:

Answer: it depends on spending opportunities. Explanation: It is possible, and in fact, rather easy to construct two situations; in one of these, "rational" and self-interested voters purchase more "genuine public goods" than "normal voters" and in other they purchase less.

Government's proposal A: expensive "genuine public good" such that only poor minority benefits more than they pay for it through taxes. "Normal voters" purchase it, due to solidarity; "rational" and self interested voters do not.

Government's proposal B: Alternatives (1) "genuine public good" such that everyone benefits more than he pays through taxes (2) charity program such that only poor minority benefits from it, but they benefit a lot. The state has money for only one of these programs. "Normal" voters purchase only charity program, "rational" and self-interested voters purchase "genuine public good." QED.

From utilitarian point of view, "rational" and self-interested voters make worse decisions than equally "rational" but empathetic voters, due to selfish bias and diminishing utility of wealth.

James writes:


If only a poor minority of citizens benefit from something, it is not a "genuine public good."

Peter writes:


People are far more likely to desire taxes be spent on things that benift themselves versus expenditures on a public good everyone can use.

An example is the old call for the military to hold bake sales to buy airplanes and tanks, but free lunch ought to be provided to kids in school.

Pajser writes:

James - Why? Definition of public good doesn't require that everyone benefit from that good; only that good is non-excludable and non-rivalrous. Classical examples of public goods are defense, knowledge; people who prefer that their country lose the war do not benefit from defense. People who do not care for quantum physics do not benefit from free quantum physics book.

Andrew_FL writes:
People who do not care for quantum physics do not benefit from free quantum physics book.

Do you have a better argument that "knowledge" is a public good than some knowledge being esoteric? Lots of things are not desirable to most people, it does not follow that those they are desirable to are underserved.

How do you define "genuine public good"? I suppose such a thing is subjective; it appears only in a learned point of view as I once described in a theoretical article for libertarians.

Jim writes:


Do you have a better argument that "knowledge" is a public good than some knowledge being esoteric?

Pajser is not arguing that knowledge is a public good (that is a given). Knowledge is a straightforward public good because it is non-rivalrous and non-excludable.

He is pointing out that

(The) Definition of public good doesn't require that everyone benefit from that good

Andrew_FL writes:

@Jim-Lots of knowledge is excludable.

John writes:

If voters were rational they would not take the time to learn about issues or vote unless there was a policy that would benefit them more than their time is worth. Therefore politicians trying to get elected will only enact policies which will yield intense benefits to certain subsets of society even if they have small costs to the rest of society. Therefore F

MountainView writes:

False. The key is the word "higher". Higher than what? I assume you mean: Higher than real-world democracies currently spend on public goods, given that real-world voters aren't RE/SIVH-compliant. As I know from reading The Myth of the Rational Voter, real-world voters are more altruistic than the SIVH model predicts*. So we must presently spend more on public goods than self-interested voters would.


Nick writes:

While it is not clear what we are comparing to, if the alternative is to a rational, self-interested dictator, then we should expect democracy to spend more on redistribution (the median voter votes for parties that divert resources from the wealthiest).

Furthermore, a rational dictator should spend the efficient amount on public goods and extract the rents through the tax system. (Less than optimal quantities of public goods may be provided to the extent that information constraints and technological constraints on taxation prevent the full extraction by the Dictator of the rents from public goods).

While not all redistribution will count as government spending per-se (for example tax credits are off budget), much of redistributive spending is on budget (such as Medicaid) which suggests democracies with rational self-interested voters will spend a lower proportion of their budget on public goods than a dictatorship.

Did I get it?

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