1.l. The aim of this paper is to examine a number of issues that arise in decision-making. In particular it seeks to explore the relevance to decision-making of the commonly made polarization as between the so-called objective and subjective approaches to probability. The paper is in three parts. The first concerns utility, and the second various aspects of probability. The third and final part looks at the interplay between these two concepts. Whilst a number of the comments and illustrations refer specifically to the insurance industry, the concepts discussed are broadly set in the wider context of business and commerce as a whole. It is hoped that the paper will thereby provide a basis for discussion on a topic that has acquired increasing importance in recent years.

The development of a ‘law of mortality’, a mathematical expression for the graduation of the age pattern of mortality, has been of interest since the development of the first life tables by John Graunt (1662) and Edmund Halley (1693). Although Abraham De Moivre proposed a very simple law as early as 1725 the best known early contribution is probably that of Benjamin Gompertz (1825). Since World War II mathematical formulae have been used to graduate sections of the English Life Tables, as well as assured lives mortality, and pensioner and annuitant mortality. Reviews of attempts at finding the ‘law of mortality’ have been given by Elston and Benjamin and Haycocks.