ABSTRACT
The Arrow-Lind (1970) proposition on risk sharing is the public sector analogy of the well-known proposition of the theory of finance that, as the membership of an insurance syndicate is increased (where each member of the syndicate is risk averse and where his income is uncorrelated with the payoffs of the syndicate) then the syndicate tends to act in a manner that approaches risk neutrality, and that the syndicate acts in a risk neutral manner as the membership tends to infinity. The logic underlying this proposition is relatively easy to grasp. As the population of a syndicate is increased, two opposing effects occur. The first tends to undercut the incentive to take on risks, as the increase in an insurance syndicate’s population dilutes the rewards to each member. The second effect tends to encourage increased risk-taking by the syndicate, as it diminishes the risk faced by each individual and this itself tends to encourage greater risk-taking. Ultimately, as membership rises, the second effect is the stronger because the risk borne by each syndicate member declines at a faster rate than the reduction in each member’s mean income. As a result, larger insurance syndicates are generally able to insure larger corporate risks because the risks faced by individuals within the syndicate are smaller than they are for members of smaller syndicates.
