General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: Abstract. A utility function with risk-aversion as its sole parameter is developed and used to examine the well-known psychological phenomenon, whereby risk averse people adopt behavioural strategies that are extreme and apparently highly risky. The pioneering work of the psychologist, John W. Atkinson, is

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... ed, and utility theory is used to extend his mathematical model. His explanation of the psychology involved is improved by regarding risk-aversion not as a discrete variable with three possible states: risk averse, risk neutral and risk confident, but as continuous and covering a large range. A probability distribution is derived, the "motivational density", to describe the process of selecting tasks of different degrees of difficulty. An assessment is then made of practicable methods for measuring riskaversion. Atkinson needed to devise a mathematical model in order to explain the apparently contradictory behaviour described above. For any task, he saw the "motivation to succeed", as the product of three factors: the incentive to succeed, , the "expectancy" or probability of success, , and the "motive to succeed", . This would be counterbalanced by the "motivation to avoid failure", , found by multiplying the incentive to avoid failure, , by both the "expectancy" ( = probability) of failure, , and the "motive to avoid failure", . The resultant motivation to achieve, , would then be the difference between the motivations to succeed and to avoid failure: s