In his column on "Mutual Defense," Paul Birch provides an interesting and original analysis of the market for defense in an anarchist society. Specifically, Birch proposes that private individuals could form voluntary militias, in which each member pledges to be liable for his proportional share of the total damage incurred during a war.

This suggestion is compelling, and Birch does an admirable job in listing its virtues. However, Birch is wrong if he believes his system necessarily solves the "free rider" problem that typically plagues market solutions to the threat of foreign invasion. In this Note, I will construct a very simplified scenario to demonstrate the weakness of Birch's proposal in this respect. I will then (briefly) contrast Birch's suggestion with my own thoughts on private defense.

Free Riders and Positive Externalities

Imagine an anarchist society composed of 100,000 households, with each plot of property worth roughly $100,000. Suppose the society is under attack from a statist neighbor, which sends bombers to pound the population into submission. Each bomber, if unmolested, destroys an average of 100 households.

Now, imagine that there are private agencies that will gladly sell surface-to-air missiles to any homeowner. People can buy as many SAMs as they want, and install them in their backyards. (This is anarchy, after all.) Of course, a homeowner has to pay for his missiles; suppose that they each cost $1 million. (Perhaps they are expensive because the enemy's bombers have sophisticated countermeasures.)

With a government, there is no problem. The government buys enough missiles to knock down all incoming bombers, and can tax everyone equally to pay for it. For example, suppose there are 200 bombers on their way. The government fires 200 missiles to knock them down, and passes the $200 million cost onto the taxpayers, meaning each household must pay $2,000. This outcome is considered "efficient" in mainstream economics, since the expenditure of $200 million on missiles prevents $2 billion in property damage (200 bombers x 100 households per bomber x $100,000 per household).

But under anarchy, the conventional argument goes, this outcome won't happen. No one will pay $1 million for a missile in order to protect a house worth only $100,000. It would be wiser to simply abandon the property and move away before the bombs started falling. Specifically (according to mainstream economics) the problem is that defense spending has a "positive externality" or spillover effect: If one person buys a missile, he enjoys a return of at most $100,000 (i.e. he saves his own property), but he doesn't take account of the fact that he also saves the property of 99 other households (since each incoming bomber will destroy 100 total households).

The positive externality in defense spending leads to the familiar free rider problem: Nobody wants to buy missiles himself; it's smarter to hope that other people buy enough to knock down any bombers headed his way. Of course, the tragedy is that this logic applies to everyone, so no one buys any missiles and the anarchist society seems unable to protect itself.

Mutual Defense No Solution

In this setting, Birch's proposal does nothing to ameliorate the problem. To see this, give Birch the fairest possible hearing: Imagine every single household joins the militia, putting all property into a common fund with which to compensate those whose houses are destroyed by bombers.

Nonetheless, the incentives on the margin will not have changed. It will still not be in any individual's interest to purchase a missile. If Joe Smith buys a missile and uses it to knock down a bomber, he has saved 100 households from being destroyed. That means the mutual defense fund (to which Smith contributes) has saved on $10 million in compensation payments.

But Joe Smith doesn't care about the fund's total liability; he just cares about the average member's liability, i.e. his own bill. Since Joe Smith is only one member in a militia composed of 100,000 households, his purchase of the missile will only reduce his total liability to the fund by $100. Since each missile costs $1 million, no one will buy any missiles, just as before.

Thus we see that Birch's proposal does nothing to counteract the free rider problem in this fictitious world. Because no individual faces the full brunt of each bomber's damage, no individual is willing to pay the high price of destroying any bombers.

(Birch could come up with different models in which, say, people in the interior of a region would pay more to defend outer regions from attack, if everyone joined a single militia. However, I believe in such cases the smart thing for these interior residents to do would be to form a smaller militia, excluding the more damage-prone border residents.)

The Insurance Approach

The standard anarcho-capitalist proposal of insurance completely overcomes the externality problem, at least initially. Rather than forming a giant mutual compensation fund, the members of our hypothetical society could simply take out insurance policies on damage from bombers. Then the insurance company would fully internalize every dollar in damage suffered by its clients. Each missile the insurance company buys costs $1 million but saves $10 million in payments to customers, so the insurance company will gladly finance the defense of the region.

The free rider problem kicks in at the next stage in this analysis. After an insurance company pays for an adequate defense, the probability of foreign attack will be greatly diminished. Rival insurance companies will offer cheaper policies and steal away clients from the original firm. These latecomers need not purchase any missiles themselves; they and their customers will free ride off the expenditures of their competitor.

In my book I argue that this subsidiary problem can be mitigated through long-term contracts being offered to the largest property holders. But for now I just wanted to illustrate the manner in which insurance overcomes the free rider problem, at least in the first stage of analysis.

Conclusion

Paul Birch's proposal for private defense is an important and fresh one. If one believes that an anarchist society will defend itself largely through irregular, small-scale operations, they could quite easily be coordinated through mutual defense associations as Birch describes. On the other hand, if one believes that an advanced anarchist society would employ high-tech (and expensive) weaponry to repel statist invaders before they even penetrated the borders, then the insurance approach seems more compelling. Perhaps actual anarchist societies will adopt both mechanisms.

In any event, Birch has yet to convince me that his scheme mitigates the problem of externalities.

November 12, 2002

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