Fuzzy measurement of output: A problem of evaluation for health policy

Abstract

In today's economies, a great deal of investment goes into the formation of human capital. But the creation and safeguarding of valuable personal characteristics cannot be measured unambiguously. This paper describes the analysis of linear partial information (LPI analysis) for systematically exploiting fuzzy measurements bearing on personal characteristics like health and education. Specifically, LPI analysis is applied in the evaluation of a measure designed to improve the health of a particular group of people, ergotherapy for the elderly, say. The simple disability index developed by Wright at York serves to illustrate the fuzziness of output measurement. In its ordinal version, it tends to assign elderly individuals to the ‘no change’ category with much higher frequency than in its semi-cardinal version. In a first round, the two versions are assumed to constitute upper and lower bounds for true probabilities of ‘improvement’, ‘no change’, and ‘deterioration’. These bounds, being linear partial information, are used to derive a set of admissible distributions over the three states. The set can be reduced to the finite set of decision-relevant extremal distributions if the decision maker's problem is viewed as a game against Nature. He will then select the alternative resulting in the distribution which guarantees him maximum expected utility. Such a choice amounts to applying the MaxEmin criterion, a natural generalisation of traditional criteria for the case of partial uncertainty rather than risk on the one and complete uncertainty on the other hand. In a second round, the two versions of the York index are treated as two separate sources of information, but of differing reliability. Again, LPI analysis allows knowledge of the type, ‘index A is more dependable than index B’ to be included in the evaluation of the proposed measure. In this particular example, taking the softness of the data into due account adds rather than detracts from the firmness of the recommendation arrived at. In conclusion, it appears that LPI analysis could vastly expand the scope of cost-benefit analysis, particularly in the domain of human resources, where output measurement is fuzzy by its very nature.