What was fair in actuarial fairness?

The concept of acturial fairness stems from an Aristotelian tradition in which fairness requires equality between the goods exchanged. When dealing with aleatory contracts, this principle evolved, among medieval scholars, into equality in risk: benefits and losses should be proportional to the risks undertaken. The formalization of this principle gave rise to the concept of mathematical expectation, first implemented in the calculation of the fair price of gambles. The concept of an actuarial fair price was first theoretically articulated in the 17th century as an implementation of this same Aristotelian principle in the field of life insurance. For a practical estimation of fair actuarial prices it was necessary to build mortality tables, assuming that the major risk factor was age. Yet, in the 18th and 19th centuries, we find no agreement among proto-actuaries about the proper construction of these tables. Among the obstacles they found, we want to highlight their early awareness of the possibility of adverse selection: buyers and sellers could manipulate the risk assessment for their own private interests, in a way that would either make fair companies collapse or fair customers be cheated. The paradox in the concept of actuarial fairness is that as soon as it was formally articulated, markets made clear it could never be implemented in actual pricing