Abstract
We consider methods for aggregating preferences based on discrete optimization. The preferences are represented by arbitrary binary relations (possibly weighted) or matrices of paired comparisons (possibly incomplete). The case of incomplete preferences remains practically unexplored so far. We examine properties of several known methods and propose one new method. Some results are established that characterize solutions of the related optimization problems. Necessary conditions of a new axiom called Self-Consistent Monotonicity are proved. The generalized row sum method is shown to satisfy Self-Consistent Monotonicity. The results suggest that there are general limitations of the discrete optimization approach to preference aggregation.
This work was supported by the Russian Foundation for Basic Research. Partial research support from the European Community under Grant No. ACE-91-R02 is also gratefully acknowledged.
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Chebotarev, P.Y., Shamis, E. (1997). Constructing an Objective Function for Aggregating Incomplete Preferences. In: Tangian, A., Gruber, J. (eds) Constructing Scalar-Valued Objective Functions. Lecture Notes in Economics and Mathematical Systems, vol 453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48773-6_8
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