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Insuring Chaos Theory

In a recent article, Silas Barta has expressed doubts concerning the system of private law that I describe in my pamphlet Chaos Theory. (For those of you unfortunate readers who have not yet purchased your copy, my basic framework is outlined here. If you haven't at least read this article on "Private Law," I encourage you to do so before continuing.) Although I disagree with most of Barta's article, I thank him for expressing his doubts in such a clear fashion, and encourage others to submit negative reviews of my pamphlet, in order that I may educate the class when explaining why your criticisms are unfounded.


Unlike some critics who merely disagree with my predictions concerning law in a market anarchist society, Barta goes further and claims that I am failing to grasp the very nature of insurance itself. To refresh your memory: I propose that under market anarchy, individuals would contractually agree to the penalties they should suffer if they are convicted (by a reputable judge or arbitration agency) of a crime, and that individuals would most likely carry insurance in order for them to pay off the huge penalties associated with crimes such as murder. My proposal is thus completely analogous to our modern system of auto liability; if you crash into someone, you are liable for the damage, and your insurance picks up the tab if you can't afford to.

As I said above, Barta thinks that this approach is completely wrong:

"Such a system…is unnatural in that it fails to recognize the nature of insurance. As Hoppe argues, something is insurable only if the insured has little to no control over the loss or degradation of what he is insuring."

Although Barta doesn't provide citations, I am sure that his characterization of Professor Hoppe's position is correct. Hoppe, in turn, is probably basing his analysis on the distinction between case and class probability offered here by Ludwig von Mises in Human Action.

The basic idea is this: If you can define membership in a definite class according to certain properties, and you know the number of members of this class that possess a certain characteristic X, then you can meaningfully discuss the probability of a member of the class having characteristic X. For example, it makes sense to talk about the probability of rolling a "1" on a die, since we can define the class of all outcomes, and we know that one-sixth of these outcomes match the characteristic in which we're interested.

Case probability, on the other hand, is entirely different. The "case" in question is unique, and we only know certain of the factors influencing it. For this situation, Mises claims, the use of statistical inference is invalid. To say, "There is a 90% chance that Bush will be reelected" is to speak only metaphorically; in truth this statement is meaningless.

If one accepts this distinction by Mises (as Hoppe does), then one can classify certain events as "insurable risks" and others as "uninsurable risks." For example, Hoppe would claim, we can insure against our house burning down, but we cannot take out an insurance policy on the risk of feeling too tired to get out of bed and thus being fired.

Unfortunately, I must disagree with Professor Hoppe. If we accept Mises' distinction, then in fact nothing in human affairs is an "insurable risk." Every moment is a unique "case" that requires understanding (rather than the application of statistical tools). Even a prototypical example of an insurable risk – life insurance – relies on entrepreneurial judgment. There is no fact of the matter regarding the life expectancy of members of a certain class of people. For example, if an insurer offers policies for nonsmoking males aged 30, he cannot know for certain what percentage will survive until 50 years of age. The insurer will certainly resort to statistical data on previous deaths to help in his estimate, but clearly he will not use mortality data from the 19th century, as this information is completely irrelevant. But he also can't merely take, say, the death rate in this class from the last five years as an accurate gauge; there are constant improvements in nutrition and medical techniques to allow people to live longer than members of their "class" who were born twenty years earlier. The concept of "life expectancy" is an entrepreneurial tool, no different in principle from "expected future sales."

(To provide a simple example: The insurers of property and lives lost during the 9/11 attacks still had to pay out on their policies, even though the possibility of such an event probably didn't occur to them. So clearly their estimated probabilities understated the true risks, and consequently these insurers suffered unexpected losses.)

When we consider the situation of actual, real world insurers, we see that the distinction stressed by Barta – that "something is insurable only if the insured has little to no control over the loss or degradation of what he is insuring" – is also not a principled one. People influence whether their house will burn down, and they certainly influence their chance of death. Even such "acts of God" as tornadoes can be somewhat controlled by the victims, to the extent that people choose to build homes in areas prone to earthquakes and tornadoes. (Indeed, one of the arguments against government relief to "disaster victims" is that it allows insurers to charge lower premiums for property insurance in such areas, and thus allows an inefficient number of people to live in areas prone to earthquakes, floods, etc.)

But the ultimate proof that Barta's emphasis on the control of the insuree is unhelpful is the fact that insurance companies in the real world offer policies on things that are almost entirely controllable by the policyholders. For example, many companies treat suicide as a covered risk (after two years)! More generally, Lloyd's of London is famous for offering exotic policies, such as coverage for Liberace's fingers and for the voices of famous singers. I doubt that these companies have overlooked the considerations made by Hoppe and Barta.

Of course, there is no harm in using the phrase "uninsurable risks" if we merely mean, "risks against which it would not be profitable to insure." As free marketeers, we can still explain to the novice that Social Security isn't really insurance, and that "unemployment insurance" is a State artifact that probably wouldn't exist in an unhampered market. What I am objecting to here is Barta's attempt to rule out my proposal on a priori grounds.


Although Barta's first argument was wrong, it was at least understandable, especially insofar as he based it on the authority of Professor Hoppe. However, Barta then proceeds to get himself into real trouble:

"[R]ecall the basic rule of insurance: you're betting you'll suffer a loss, they're betting you won't. The necessary condition for an insurance transaction, then, is that the insured perceives a greater risk than the insurer."

These comments are completely wrong, and I wonder where Barta picked up this "rule." In fact, most textbook discussions of insurance will point out that it is exactly the opposite of gambling: When you take a gamble, you pay a small sum for certain, in order to create a low chance of winning a much larger sum. When you take out an insurance policy, you pay a small sum for certain, in order to eliminate the low chance of losing a much larger sum (or utility).

Moreover, Barta's "necessary condition" is obviously false. Imagine we have six people, assigned numbers one through six. We roll a die, and whoever's number comes up must pay $600. Now, in this setting, the people might wish to buy insurance against this possible loss. A fair insurer will offer them all policies for $100 each. This example shows the nature and rationale of insurance from the buyer's point of view – most people would prefer a certain loss of $100 than the 1/6 chance of losing $600 – and it also shows that insurance is possible even when everyone agrees on the probability of the "bad event" in question.


After arguing that my proposed system relies on a faulty notion of insurance, Barta goes on to speculate that people in market anarchy would never buy homicide insurance (akin to the current practice of medical malpractice insurance) because most people "quickly realize that they have a zero chance of committing murder."

But this argument completely misses the point: In my vision, property owners require contractual pledges from strangers before allowing them onto their land (or into their buildings). If I'm an employer, it's all well and good if a job applicant swears on his mother's grave that he would never steal from me or kill a co-worker. The sad fact is, most thieves and killers aren't averse to lying.

So to back up the verbal assurances of good faith, most visitors would agree to pay certain penalties for doing naughty things. Now, since some of these pledges would involve sums beyond the means of the visitor – I predict, e.g., that the penalty for murder would exceed $1 million in the present United States – people would need a big agency to guarantee payment. Perhaps it's a bit confusing to label such policies as "homicide insurance," since they're really failure-to-pay-fines-for-homicide insurance. In principle, there is nothing different in my proposal from the current practice of co-signing for a loan or employing the services of a bail bondsman.


Barta goes on to propose an alternative to my ostensibly impractical insurance scheme: Rather than pledge huge monetary payments in the event of criminal behavior, visitors would allow for their execution. To illustrate why people would agree to this, Barta asks his reader to imagine receiving the following offer:

"[I]f you jump within two seconds after accepting this agreement, you get $1 million. If you don't jump in place, you are executed….You can easily accept this offer because you know (are 100% sure) you will jump after accepting the offer, and have complete control over it, even though the penalty for not jumping is death."

I must rush to advise Barta's readers not to accept such an offer, since Barta has not specified who will be the judge of whether or not you have satisfied the agreement. After all, if I'm the judge, then I don't even need to jump to get my money; I can just tell the clerk, "Yeah I jumped; pay up." If, however, the people running the game get to decide, then I would conduct a very extensive review of their previous rulings before entrusting them with my life.

This consideration shows why people might be reluctant to allow for the death penalty in case they are convicted of murder; there is always the possibility that one will be falsely convicted. Mistakes will be made, even in a market anarchist judicial system, but at least if the convict is still alive, he can continue pleading his innocence (and hire others to attempt to win a reversal of the ruling).

I thank Barta for raising this point, however. It's true that I have simply asserted that victims will receive financial restitution under market anarchy. It is entirely possible that, in addition to such monetary compensation, victims would want punitive measures taken against criminals. My system would allow for this (in the contractual pledges), but I did not mention the possibility in my on-line articles or book. (I did however say that extremely violent people, who couldn't obtain an insurance policy because of their past behavior, would be housed in anarchist jails.)


A bit later, Barta argues that "the only workable system of insurance against intentional misbehavior is the straightforward type (insuring against the actions of others to you), rather than Murphy's reverse insurance." Again, Barta simply ignores the fact that current insurance policies cover intentional acts (such as suicide). But now I want to show that my proposal is, at a sufficient degree of abstraction, entirely equivalent to the "straightforward type," but that mine would probably prevail in the real world due to transactions costs.

Let's take the case of an employer looking at a potential job applicant. Assume that the applicant's productivity would justify a salary of $15,000. However, in order to attract workers, the employer not only pays wages, but he also guarantees that anyone who is murdered on the job will have his estate compensated by $10 million. (He would also pledge to compensate workers killed in accidents, but I've ignored this for simplicity.)

Now, suppose that this company is quite large, involving dozens of factories and other buildings and tens of thousands of employees, and that it has been in business for years. Clearly, some people might actually kill others while on the job, and so this pledge must be taken into account by the employer. That is, he occasionally might have to pay out $10 million to the families of murdered employees.

The employer can either cover this risk himself, or he can defer to the expert personnel of an insurance company. Suppose that the actuaries of the insurer estimate that the annual risk of an employee killing another is one in one million. Then, for every employee that he hires, the owner must pay (roughly) $10 more in premiums to the insurance company.

Because each worker generates an additional $10 in expenses, the employer can't pay him the gross marginal productivity, but must deduct this expense. That is, he can only pay the worker $14,990.

But suppose an applicant says to the employer, "I have my own insurance policy, that pledges to pay $10 million to the estate of anyone I murder." Since the employer's own insurance company will never have to pay out if this employee kills a coworker, it won't require a higher premium from the employer. So he could pay such an employee the full $15,000, and have the employee mail in his $10 premium payment to his own insurance company.

So in a world where everyone has the same chance of killing, we see that my proposal is entirely equivalent to the standard anarcho-capitalist system proposed by my critics. However, once we realize that people are different, it is easy to see why an employer might require his employees to carry their own policies: If the employer has his own insurer, then that company must investigate each new applicant afresh. So if Joe Blow interviews at Kodak, Xerox, and IBM, the insurers of each of these companies must conduct a background check on Joe. But if Joe Blow carries his own policy, then his own insurer needs only check up on his criminal record when he first applies; from then on he can just flash his insurance card wherever he applies for work.

The case of murder is the most exotic, and casts my proposal in the worst possible light. I encourage the reader to think through something more mundane, such as a private road, to see the advantages of my approach. I argue that it would be far more practical for owners to require all who use their roads to carry valid policies, rather than for the owner himself to insure everyone who drives on his road. In this respect the system would be the private counterpart of our current arrangement, except that the silly restrictions (not all restrictions, mind you) on licensing required by governments would be absent.

(Incidentally, Barta wonders why I have used "reverse insurance" for visitors who sign contracts before entering property, while I rely on "straightforward insurance" to handle the case of foreign aggressors. The difference is that the former agree to abide by legal codes, while the latter do not. Indeed, I explicitly say in my book that those who unilaterally barge onto another's property may be repelled with force. Barta might just as well have asked why I allow for missiles to be used against invading troops but not against job applicants.)


Before ending, I should make one final point: Critics may object that my above example is wrong because the insurer of the big company could offer lower premiums than the individual's own insurer. In other words, I have merely assumed above that if the big firm's insurer requires $10 more in premiums for each additional employee, then the insurer of the individual employees would also charge them each only $10.

I don't see why this is such a controversial assumption. In both cases the insurer estimates the probability of the person in question committing a crime. There is no reason to think that a person buying his own policy will therefore become more likely to commit murder; that is, there is no danger of moral hazard in this scenario.

Moral hazard refers to the danger of an insured person acting more recklessly than a non-insured one. For example, insurance companies wouldn't want to insure a $100,000 house for $1 million in the event it burns down, because then the owners would have an incentive to start a fire and collect on the policy.

But we don't need to worry about this sort of thing in my setup. The criminal doesn't receive any payment from his insurance company, his victim does. And if the insurance company wants to drive home the point that murder and theft are to be avoided (besides relying on the increase in future premiums following a crime), it can include a huge deductible on these policies, so that e.g. a convicted murderer has to pay $50,000 himself and then let his insurance company pick up the other $9,950,000 (on a ten million dollar policy).


Once again, I thank Silas Barta for his criticism, for it has forced me to clarify my own position. As always, let me state that I am not positive that the market anarchist world will turn out the way I've described it. However, I believe that Barta's particular objections are unfounded, and I hope the above has convinced the reader of the same.

July 1, 2002

Bob Murphy is a graduate student in New York City. He is a columnist for and The Mises Institute, and has a personal website at He is also Senior Editor for

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