Actuarially fair insurance has an expected net pay-off of zero. From a consumer's point of view, an insurance contract is actuarially fair if the premiums paid are equal to the expected value of the compensation received. This expected value is, in turn, defined as the probability of the insured-against event occurring multiplied by the compensation received in the event of a loss.
Actuarially fair insurance is not necessarily complete. Complete insurance pays compensation equal to the harm caused by an accident, leaving the person just as well off as he would have been had the accident not occurred. For example, it might take $10,000 to compensate a car lover for the psychological harm caused by someone deliberately scratching the paintwork of his beloved antique MX-6. Complete insurance would cover that $10,000 harm. Actuarially fair insurance may or may not cover that harm, but it is still fair, as long as the premiums paid are equal to the probability of experiencing deliberate scratching of paintwork times the benefits paid out in the event of paintwork scratching.
Economists most frequently define actuarial fairness from the point of view of the consumer. Yet this definition implies that actuarially fair insurance can never exist. As Nicolson and Snyder's Intermediate Micro text informs students, "No insurance company can afford to sell insurance at actuarially fair premiums." Insurance companies have administrative costs. If they paid out everything that they received in premiums in compensation to customers experiencing losses, they could not cover their other costs of doing business.
The reason why economists define actuarial fairness from the consumer's point of view is that it yields useful predictions about consumer behaviour. For example, if actuarially fair insurance is available, a risk averse consumer - one who doesn't like risks - will always purchase complete insurance, insuring herself fully against any losses. True, this type of actuarially fair insurance is an ideal that never exists in the real world. But like that other ideal, the perfectly competitive market, it is analytically convenient (translation: the math is easier), and provides a useful benchmark, a standard against which to judge real-world insurance contracts.
Yet when we define actuarially fair insurance from the consumer's point of view, we have no expression for an insurance contract that is actuarially fair from the insurer's point of view, one where the premiums paid by customers are equal to the expected cost of insurance claims plus administrative costs.
An insurance policy that provides the insurer with an expected payoff of zero has interesting properties. The insurance company makes zero economic profits. No one group of customers subsidizes any other group of customers, which means that the insurance company does not redistribute income ex ante. (Insurance still redistributes income ex post, from those who do not experience a loss to those who do). From a policy point of view, this alternative definition of actuarial fairness - actuarially fair from the point of view of the insurer - is frequently useful. After all, why spend time talking about insurance that is actuarially fair from the consumer's point of view, when we know that such insurance cannot exist?
Some writers do, in fact, define actuarial fairness from the point of view of the insurer. For example, Econport.org writes "for insurance to be actuarially fair, the insurance company should have zero expected profits." University of Toronto philosophy professor Joseph Heath seems to have this same definition in mind in his analysis of the moral implications of subsidies from one group of insurance companies to another. He writes, "it does not really matter whether it is just or unjust to charge actuarially fair premiums, it is necessary for insurers to do so if they wish to remain solvent." The fair-for-insurer definition of actuarial fairness is also implicit in statements such as this one: "An individual with spina bifida might be able to purchase an actuarially fair, albeit expensive insurance policy to provide care for the condition..."
It is surprisingly difficult to find clear definitions of actuarial fairness. There is no Wikipedia entry for "actuarially fair" or "actuarial fairness," perhaps because actuaries themselves appear to prefer betting language, talking about "fair odds". (Thinking about it, from an actuary's point of view, the adjective "actuarial" is redundant.) Where economists talk about actuarial fairness, insurers are more likely to draw a distinction between community rating, where all members of a community pay the same premium, even if some face a greater risk of loss than others, and individual risk rating, which is similar to what I have defined as "actuarially fair from the point of view of insurers."
Economics texts or articles often assume the reader knows what actuarial fairness means, and do not define it. Perhaps this reflects the profession's reluctance to talk about issues of fairness or equity - prices are what they are. The analysis of insurance and pension markets is one the few occasions when economists talk about "fair" prices. Even there, the "fair" price is the one that involves no ex ante redistribution.
This lack of clarity is unfortunate, however, because insurance - for health, or for old age, in the form of pensions - is an issue of critical policy importance. If our language is imprecise, our thinking will be imprecise also.
HT to B., whose question forced me to clarify my own thinking about this topic.