Constructing Quadratic and Polynomial Objective Functions

A model for constructing quadratic and polynomial objective functions in n target variables from interviewing an expert is considered. The person interviewed is presented a set of incomplete alternatives (vectors of target variables with one coordinate not fixed) and is asked to complete these alternatives (to adjust these coordinates) to the end of making the given alternatives equivalent in preference to some reference vector. Then an indifference hypersurface is fitted to the equivalent vectors, thus determining the objective function on the whole of ℝn. The data required for the construction are ordinal, simplest, and minimal. It is proved that the resulting ordinal preference is independent of the cardinal utility scale used in intermediate computations. Besides formal properties of the model and its regression-like extensions, computer experiments on constructing an objective function of German economic policy in four target variables (inflation, unemployment, GNP growth, and public debt) are briefly reported for illustration.

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