Impacts on resource allocations when the relative importance of allocation criteria is changed, with reference to Australian universities

In 1998, the West report on higher education in Australia considered possible changes to the monies allocated to universities on the basis of research. One method of doing this, and its implications, were discussed by David Phillips in an article in The Australian. The questions raised are treated here as an abstract resource allocation problem, and the discussion is not neccesarily restricted to universities. Using simple mathematics, the situation is analysed in somewhat more generality than in the article of Phillips, and the qualitative implications assessed. There is also a discussion of how, depending upon the circumstances, the parameters of the general procedure may be adjusted to avoid unacceptable outcomes, or to achieve ones considered desirable. The formulation of resource allocation problems in general mathematical terms potentially provides a greater understanding of the strengths and deficiencies of particular procedures and an appreciation of possible alternatives. In Australian public policy mathematics is generally seen as a secondary tool for data accumulation and associated arithmetical calculations. It is hoped that this paper may serve to show the potential for mathematical thinking to contribute to obtaining broad, qualitative insights into questions of public policy, while nevertheless maintaining the rigour and intellectual clarity associated with the discipline.