Bryan Caplan  

A Simple Proof that "National Defense" is Not a Public Good

SuperFreakonomics, II... Randian India?...
"National defense" is a textbook example of a public good.  Unlike Austrians, I have no problem with the concept of public goods.  I just deny that national defense is a valid example.  In fact, I will be so bold as to claim I can prove that national defense is not a public good.


1. For national defense to be a public good, the social benefits of its existence must exceed its social costs. (From the definition).

2. The social benefits and costs of national defense are the sum of all people's willingness to pay. (By definition).

3. On average, people's willingness to pay for their own physical security is higher than their willingness to pay to reduce the physical security of others. (My critical assumption, which I'll call Limited Malevolence).

4. If no country had national defense, people's average physical security would be higher than it is now, because the danger which any given country's national defense deters is attacks from the national defense of other countries.

5. Since the existence of national defense reduces people's average physical security (from 4), and people's average willingness to pay to increase their own physical security exceeds their average willingness to pay to reduce the physical security of others (from 3), the net social benefits of the existence of national defense are negative.

6. Therefore (from 1 and 2), national defense is not a public good.  QED.

If you wanted to reduce my proof to a slogan, it would be: "National defense: If no one had it, no one would need it." 

If textbooks were accurate, they would drop national defense as an example of a public good, and replace it with the abolition of national defense.  Unfortunately, I fear that even the typical economist is too nationalistic and hawkish to take my proof seriously.

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COMMENTS (51 to date)
Saloner writes:

"National Defense", I think is a convenient marketing misnomer for "National Offense".
Nobody would give the megalomaniacs money to further their individual vanities if they were honest about them. Sell the thing as "Defense", against imaginary enemies, though, and you can fool quite a lot of people quite a lot of the time.
It's a tragedy really.

Maxim writes:

Assumption 3 is not enough -- while the average person/country may have limited malevolence, it only takes one outlier to make it pay for everyone else to have an army (in which case, it is a public good.)

ThomasL writes:

I think you need to reconsider based on the economics of stealing and conquest.

If I am a country without a military, and I see a country next to me without a military, and they have things that I want, I may calculate it to be cheaper to raise a militia and take what they have rather than purchase it from them.

My calculation doesn't have to be accurate to be pursued, and it doesn't have to be completely effective in order to be troublesome to them.

If you have trouble accepting my use of the word "I" when the state is made up of many individuals, then you are really denying the concept of nations at all, as nations to be nations have to have some combined decision making process that exists separate from each individual's decisions.

As long as one nation anywhere on the globe realizes it can dominate others and achieve the things it wants through force and coercion (not at all unlikely--many states throughout history have enriched themselves off their neighbors successfully), then other nations have to make it more costly for to attempt than any possible benefit.

Chris Milroy writes:

In the case in which other countries/people already have national defense, though, I think ND fulfills your criterion.

You're really arguing for the abolition of *other countries'* national defense, a good that your government cannot provide (game-theoretically, if nothing else).

Ok, ok, it's a cute semantic trick. And I share your goal of reducing the amount of money everyone (and America in particular) spends on standing armies.

But it is just a cute semantic trick. The standard meaning of "public good" is far more operationalistic than the one you're using here. Implicit in the standard notion of public good is a definite body of people (the "public") capable of acting in concert, usually by establishing a government coerce freeloaders into compliance. Thus, in computing the costs and benefits of a "public good" one ordinarily considers only those costs and benefits which accrue to members of that particular group of people. The Belgian army does provide a Belgian-public-good even if it's bad for non-Belgians.

Economists who use that standard notion of public goods aren't nationalists. They're pragmatists who are trying to make policy recommendations that might actually be implemented by a real government, rather than an imaginary world-wide government which gives equal consideration to the interests of every person on the planet. Indeed, one way to read your post is as a call for One World Government.

...I should add: Those economists advocating spending money on national defence are also self-interested individuals who very strongly do not want a foreign army to pillage their stuff.

greenish writes:

I believe you misidentify the crucial premise. You assume there are no hostile "outsiders" - that all countries produce armies according to the analysis, while everyone else takes for granted that there are hostile "outsiders" regardless of the analysis.

NZ writes:

Regarding point #4: What about deterring attacks from other entities that are not the "national defense" of another country (e.g. certain terrorist groups)? And what about deterring other unwanted activities, besides attacks, that involve the invasion of foreign entities (e.g. the importation of wolves into a country whose economy is based on herding sheep)? If no countries had national defenses, terrorist groups would still be just as dangerous, perhaps more so, and it would still be desirable to stop the introduction of wolves into a sheep-herding country. How might these and similar issues be addressed without national defense?

Siddharth writes:

Completely and utterly wrong.

National Defence is a disaster put option against Hitler like people.

Disaster puts cost money.

Gary writes:

On average, people's willingness to pay for their own physical security is higher than their willingness to pay to reduce the physical security of others.

What justification? We know nations and tribes go to war (reducing their own physical security in the process) in order to reduce the physical security of others, so the latter must be an attractive thing.

jean writes:

Your piece against National Defense would be valid if *other countries* acted similarly.

Similarly, you could say that police and justice are evil because if everyone decided to be smart and kind, they would not be necessary.

Unless you are advocating for a global government or a miraculous synchronized disarmement, you can't say that National Defense is a public evil.

Alan Forrester writes:

National defence isn't there to defend against attacks from other countries that have armies for self defence. For example, it would be ridiculous to say that the British government is going to attack America even though the British government has an army. National defence is there because some governments and other organisations are not armed for self defence, they are armed for aggression because they have an anti-rational worldview: that is, they have habits and ideas that are wrong and structured in a way that makes it hard for the person holding them to correct his ideas, e.g. - conspiracy theories:

Hitler had anti-Semitic and racist conspiracy theories about other countries being run by Jews and people who happened to have a different skin colour, all of whom were supposedly out to get the Germans. Al Qaeda likewise sees Israel as being an imperialist plot by the West despite widespread anti-Semitism in Western countries, including the Allied countries, even during and after World War 2. National defence policy should not be based on the idea that everybody is rational because that idea is false.

Daniel Kuehn writes:

It's a bad proof, Bryan. Number 3 may be true for a lot of people, but not nearly all.

We've only recently reached a stasis where aggressive war seems untenable to the average citizen, but for most of human history this wasn't true - and for a lot of people in the world it still isn't true.

And even if in actuality it were true for all, the risk of it not being true - the threat - might necessitate national defense.

I'm all for bringing out military down to a more reasonable size - I agree with the general thrust of the "proof" insofar as I think we often create our own security problems because of bad defense policy. But I don't think that's the same thing as the necessity of abolishing the military.

Joshua Macy writes:

On the average, people are law-abiding. Therefor average welfare would be increased if we eliminated all locks, alarms, police, criminal courts and jails.

Eric H writes:

No national defense presumes no nation to defend.

The case for national defense rests on the assumption that what "we" have as a nation should be preserved.

#4 is a great reason for national defense. Why should a generally peaceful and enlightened people without aims of conquest let their fates be determined by a bunch of ultra-non-libertarians in another countries?

Leonid writes:

I suggest an empirical test of your proof.

Stop using locks for your door and check how much money you save.

Brent Buckner writes:

You improperly change the unit of analysis.

National defense respective of Nation A is a public good respective of the public of Nation A.

In point 4 you move from the public of Nation A to the public of all nations.

Nathan Smith writes:

National defense is a public good for a nation. Abolition of national defense would be a public good for the world (if for the sake of argument we assume away terrorists etc.).

Dave Gottlieb writes:

As others point out, for a given political community, the relevant definition of "public good" covers only the good of the community's members.

This is not for "nationalistic" or "hawkish" reasons but because a government acting alone can only optimize across its own individual policy options. So long as international collective action is hard, this will often include some national defense!

Brian writes:

I think Nathan gets it right. Couldn't it be that both the presense of national defense is a public good for one country but not for an adjacent country, or maybe particularly for the world at large?

Peter writes:

The best defence is a good offence.
The hand which strikes also blocks.
If even one person on the planet does not comply with "defensive use of force only", he has an advantage over the rest of mankind. You can't solve this prisoner's dilemma.
It's like saying that everybody would be much better off if we didn't spend all that money on the "creative destruction" of the market. While true that creative destruction does require ressources, a market-less world would quickly become stagnant and backwards because no one would *have* to work for a living.
Essentially, what you're saying is "why can't we all just be nice to each other, m'kay, because nice is good, m'kay?"
Wishing the speed of light in a vacuum to be a bit faster does not make it so.

Eric Johnson writes:

The fallacy here is that people indeed don't want to pay the costs of attacking some foreign country - but there's noise, such that occasionally they do want to. We aren't prepared for the average desires of foreign powers but for the non-average ones.

Jacob writes:

Good points above (especially the clever "Hitler put" by Siddharth). I just wanted to add the concept of a simple Nash Equilibrium.

If we are at the equilibrium where everyone has military capabilities, whoever throws down their weapons will be destroyed. If we are at the equilibrium with no military capabilities, some "rational" foreign leader will see that he can improve his outcome by defecting to building military capabilities. I guess it is similar to the prisoner's dilemma.

Brian Hollar writes:

Isn't this kind of like saying about the Prisoner's dilemma that if there were no prisoners, there would be no dilemma?

I think point # 4 is the most problematic. If no country had national defense, many countries would benefit from developing "national offense" and taking over the defenseless ones. I have trouble seeing no countries with national defense as a stable outcome. (Or an outcome that could be reached given the world we live in.)

William writes:

Unfortunately, I fear that even the typical economist is too nationalistic and hawkish to take my proof seriously.

Somebody poisoned the water hole!

I understand what you are getting at in your definition of "public good" rather than "public bad", I suppose, but a lot of textbooks just stipulate that a public good be non-excludable and non-rival in consumption. The texts then say that public goods *should* be provided by the government only if the social benefits outweigh the social costs.

I'm not trying to be difficult, I was just wondering if someone could point me to a text that has the definition that you cite, mostly in the name of not confusing my students too much...

Foobarista writes:

Unfortunately, the typical economist isn't attracted to goofy utopianism enough to be impressed with this argument.

The idea that nations are some sort of pathology is what keeps me away from libertarians, even though I agree with 90% of their ideas. Sorry, they just _are_, however inconvenient they are to one's theories - and nation-states and their behavior will dominate the human world for the forseeable future.

And getting rid of them is profoundly unlikely to result in a global libertarian utopia.

mdc writes:

A world in which everyone agrees not to make (until others re-adopt national defence) invincible tools of rapine and oppression is not a very stable equilibrium. As such, I don't think we can view the situation exactly like this.

tsok writes:

Would you say that the national defense of one nation is a negative externality?

Lloyd Winburn writes:

OK, I buy it. Where do we start? I favor the Melos solution. Clear the deck with all enemies. Issue an ultimatum. Come with us or you are against us. Don't agree? Will not do it?

Then we will kill all your men and boys and enslave the women.

Reread the Melos Dialogue
'nuf said

jr writes:

On the one hand, libertarians treasure the concept of spontaneous emergence. On the other hand, they can't take that military can spontaneously emerge too.

It's about the same as the left's support of democratic decision making, that is, as long as the decision made is that of the left elites.

The slogan is: Spontaneous emergence, but only if permitted by libertarians.

jr writes:

And for heaven's sake, it's an insult to the word "proof". Please! Call your post an argument, but wait and think before you call it a proof!

Jayson Virissimo writes:

"I suggest an empirical test of your proof.

Stop using locks for your door and check how much money you save." -Leonid

This wouldn't be a test of his theory at all. Locks on doors aren't public goods, they are private goods. He pays the cost of the locks and also reaps the benefit of the locks.

David Jinkins writes:

Another thought-provoking post from Caplan. Many commentators have already made the correct critique of the "proof". The decision about funding a military must be thought of as a best response to the (imperfectly known) decisions of other countries. The national defense game Caplan is talking about is a complex version of prisoner's dilemma. Everyone may be better off without a military, but in actuality every rational actor may choose to fund a military.

The previous paragraph refers to the real world. On the other hand, we know that one counter-example will disprove an incorrect statement. To that effect, consider the following situation. Imagine a world in which there is a nation Freedonia which is surrounded by belligerent nations with large armies. The surrounding nations are constantly attacking each other. Further presume (and this is the main assumption of Caplan's proof) that the citizens of Freedonia are willing to pay more for personal safety than they are willing to pay to threaten others. It seems plausible that in this case the funding of national defense will make the citizens of Freedonia better off.

Mr. Econotarian writes:

In post-WWII history, the US has mainly used military force "to help othes" avoid Communism or dictators. Until 9/11....

Most Americans now feel the greatest threat is from non-state actor terrorist organizations - while sometimes supported by non-democratic governments, terrorists can remain fairly effective even when funded by voluntary, private actions, either donations or drug dealing.

So most recently, the US has used military force to oppose an Islamic government that was pro-terrorist. Or force has been used to try to "nation build" in "failed states" where terrorist NGOs might operate.

Steve Roth writes:

Sadly, the flaw is that people will in fact frequently pay more to see the other person get less (than them). Or even to avoid the *chance* that the other person will get more. Even (as in the case of national defense) when there's an obvious win-win solution sitting on the table for both to see.

This has been proven, on undergraduates! (Though not yet, to my knowledge, on rats.)>

Scott Sumner writes:

Bryan, I really like this piece. I don't know why I never thought of it. Would you agree with the following:

"National defense is never a public good. It is either a public evil, or a "second-best" policy trying to offset another bad public policy elsewhere."

My thought is that to the extent that someone has valid reasons in arguing for national defense, it is always a second best argument. In contrast, true public goods are generally first best policies.

My apologies if this idea already appeared in the comments.

Doc Merlin writes:

Wow, brilliant. I am fairly hawkish (for a libertarian), but I can't disagree with you here, except to disagree with number 2. Number 2 is usually the case, but not always. A good example is suicide bombers and "terrorists" they clearly value harming the other person more than their own safety.

Doc Merlin writes:

Er, I mean 3 not 2.

Dr. T writes:

2. The social benefits and costs of national defense are the sum of all people's willingness to pay. (By definition).

No, not by defition. This is the step that makes the logic chain collapse. People often fail to recognize and assess the magnitude of threats, and they fail to take actions (or spend money) to minimize threats. Just because people aren't willing to pay enough for an adequate national defense doesn't prove that national defense has little (or negative) value. I recently read about people who wanted a flu vaccine but refused it after learning that it wasn't free. That doesn't prove that the flu vaccine is worthless, it just proves that many people are dolts.

I cannot understand how economists, who supposedly understand how people make choices, can assume that the majority is right. The majority is rarely right, a conclusion that has been validated many times on this blog.

Swimmy writes:

It is irrelevant that national defense may be a best option given the circumstances. They key is in Bryan's #2, he even italicized it for us: "all people." That means literally all people, including those outside the country in question. Roads and clean air in the United States have positive benefits even for those living internationally; when they are tourists here they can drive and breathe clean air. These goods allow us to produce more, meaning more trade and higher incomes worldwide. Internationally, people would on average be willing to pay a positive amount for America to have roads, even if a miniscule amount.

National defense doesn't fare so well when you look at ALL people. Pretty sure willingness to pay is gonna be negative on average. Even free-riders on the American army (like Canada) who would be willing to pay to keep our defense around would also be willing to pay to eliminate the defenses of several other countries.

geckonomist writes:

Costa Rica has no army. with much more unstable neighbours than the USA.

What more proof does Prof. Caplan need to provide?

D. Smolken writes:

When I read "If no country had national defense" the first thing that popped into my head was "I'd be tempted to raid Slovakia". I guess my malevolence isn't all that limited, and unfortunately there are more than a few people like me in the world.

Alex Birch writes:

This might work in theory, but in practice humans are too distrustful to give up defense, on any level.

Dr. T writes:

geckonomist: I recently visited Costa Rica, a lovely country, whose citizens bragged about no military. They joke that the large vultures are their air force. However, all of them believe that the US will intervene if Nicaragua or Panama invade. Our tour guide even bragged about how smart the Costa Ricans are for having a no-cost military protection plan.

However, if Costa Rica wasn't the second-oldest democracy, and wasn't friendly to the US, then it would need to pay for its national defense: the neighbors are not friendly.

Eric H writes:

"National" defense for "all" people is a contradiction. No government musters an army to satisfy a public desire to pre-emptively protect unwitting "others" whether they be Trobrianders, Kiwis or Azerbijanis. No country sets up its own defense force for all people. A nation represents a select group of people. We can totally argue whether that select group of people is lame or stupid or arbitrary or whatever, but a nation is a nation. It's not all people.

How would Brian's proof fare if one country, Country USA, for example, wanted to defend itself against the rest of a completely non-threatening, pacifist world? Would it really be bad for the world--all the people in the world--if that paranoid country wanted to defend itself against phantoms? Let's go even further down the rabbit hole and assume that in this scenario there is absolutely zero chance of there ever being conflict--though no one but us knows this--just so we as observers can be absolutely certain of Country USA's paranoia. The public bads in such a case would be 1)the rest of the world having to put up with the social awkwardness of Country USA's paranoia and 2)the net drain to world resources of country USA's spending billions and billions on ultimately useless national defense. But is it really useless if the citizens of Country USA on average experience net personal utility gains from believing their fearless leaders were prepared for any circumstance? And what about the bonus Country USA confers upon the rest of the world by using its resources to that end? It offers the rest of the world chances to exploit the shortages it experiences from diverting resources towards national defense.

If one is to consider national defense not a public good for all people, one should first presume that either no nations exist or one nation exists. Crafting such a proof within a framework of 2,3 or 193 nations makes no sense.

Lindsey writes:

I believe that your fear is correct. I know that I am a young college student who is naive in many ways but, the last time I checked, our national defense allows you the privilege of writing this article. I understand and recognize that the definition of national defense does not match up with the definition of a public good. And I do agree with your viewpoint that if there was not National Defense, people’s security would be higher. But that does not mean that the national defense does not serve us or others. Day after day, men and women sacrifice themselves so that we, as citizens, are allow walk, talk, and use sidewalk chalk as we please. I know that I feel honored to live in a country where others are willing to lose their life to protect mime. It is a shame that soldiers, fireman, policeman, and even medical personal are often “thrown under the bus” or even forgot about. Yes, I know that they are not always our best buddies, but how lucky we are to have a National Defense that does just that.
Our National Defense may not be as cost efficient, but what would our country look like twenty years down the road if we did not have a National Defense. Would we, the United States of America, still be a country? Personally, I am willing to pay higher taxes or whatnot to make sure that we have a country in twenty years. I may not say that twenty years from now; but at this point in my life, I am.


Swimmy writes:

Eric H writes: "No country sets up its own defense force for all people."

And no country sets up its roads to be used by all people, but the increased opportunites for trade they provide are a benefit to people across the globe all the same. Something I should have made more clear--if roads are a public good for Americans and nobody else in the world cares at all, they count as valid public goods. All that matters is that the net social benefits are positive.

Your example of a paranoid national defense is a valid one--it could be a public good. The key is willingness to pay. If there are social benefits worldwide, it's a public good. If there are social costs worldwide that outweigh the American benefit, it's a public bad. If it provides solace for the American people and everyone else is neutral, it's a public good, because the American social benefit is not offset. We're looking at the total willingness to pay for all people. Bryan's proof still fares just fine, because he's talking about militaries that are used for killing people, a social cost.

Likewise if we mixed the blood and body parts of foreigners into our pavement, roads would no longer be a public good, even though they still helped Americans get around.

Ryan Vann writes:

I agree with the spirit of your argument, and would even take it a step forward. National Defense isn't really a good or service at all.

William writes:

If "National Defense" was set up to actually defend the nation and not used as a euphemism for all things military it might be a public good. Unfortunately fighting unnecessary and illegal wars and spending exorbitant amounts of money on exotic weapons systems cannot truly be defined as national defense.

Follow this link for a deeper analysis of whether defense is a public good...

Ndubu Moses Mbah writes:

I write to challenge the view that national defense is public goods.
Consider the analysis below to best understand my point.

Assume an econoy where there is no national defense. In this regards, the strong will loot thwe weak. The weak not being secure of enjoying the proceed of their action will cease from producing and at the end the strong will have nothing to loot from the weak.

On the contrary if the weak are secure, they will be willing to pay for their security which will be use to conpensate the strong that looted them and all will be better off.

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