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Soc Choice Welfare (2002) 19: 113125Walter Bossert1, Marc Fleurbaey21 Departement de Sciences Economiques and C.R.D.E., Universite de Montreal,
C.P. 6128, succursale Centre-ville, Montreal QC H3C 3J7, Canada
(e-mail: [email protected])2 CATT, THEMA, Universite de Pau, Avenue de l'Universite, 64000 Pau, FranceReceived: 27 March 2000/Accepted: 28 August 2000Abstract. We analyze the equity properties of insurance premium schemes
where agents are partitioned into groups with dierent average accident probabilities and each individual has to pay a premium according to the average
probability of the group to which it belongs. In particular, we examine the
question whether choosing ner partitions to dene these groups generates
more equitable situations than coarser groups. Though it turns out that partitioning the agents into ner groups can never be Lorenz dominated by
the coarser partition, it cannot be guaranteed that ner partitions represent
improvements over coarser ones except in very restrictive circumstances.1 IntroductionMuch of the literature on the design of insurance contracts addresses problems of adverse selection and moral hazard. Because insurers typically lack
relevant information regarding the characteristics of insurance buyers (such as
their individual accident probabilities), one of the objectives is to formulate
incentive-compatible contracts such that customers self-select into the appropriate category.In this paper, we examine another issue regarding the design of insurance
premium schemes. Consider, for example, the provision of automobile liability insurance. In most jurisdictions, the purchase of coverage is obligatory,
and the insurance services are often provided by agencies appointed by the
relevant government. In that case, prot maximization may not be the objective of the insurer and, instead, the service is to be provided subject to a zero-We thank two referees for comments and suggestions.99920029Equitable insurance premium schemes114 W. Bossert, M. Fleurbaeyprot constraint. An important question that arises in this context is on what
criteria the premiums charged from dierent individuals should be based. It
seems to be commonly agreed that, on fairness grounds, individuals with
higher accident probabilities should have to pay higher insurance premiums.
Ideally, this objective would be achieved if these probabilities were known
with certainty, in which case individualized schemes could be employed. In
reality, however, this detailed information is not available, and the common
response is to partition the agents into dierent groups (for example, according to age or gender) with...