Policy-making and policy assessments with partially ordered alternatives

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The present work collects three essays on social choice and decision-making in the presence of multiple objectives and severe informational limitations. When feasible alternatives must be ordered according to their performance under various criteria, it is typically necessary to make use of a specific functional relation and assume the implied rates of substitution between scores in different criteria. In the special case of collective choice and voting, rather than having proper rates of substitution, each individually preferred ordering of the alternatives is usually weighted according to its frequency in the population. Both decision frameworks imply the availability of extensive information about such functional relation and the proper weights of each criterion or must acknowledge a vast and arbitrary discretion to those in charge of resolving the decision process. The alternative approach herein discussed consists in applying the Pareto criterion to identify Pareto-superior alternatives in each pairwise comparison, a procedure that easily produces an incomplete ordering. Then, applying a tool of Order Theory, a complete ordering is identified from the linear extensions of the partially ordered set derived from the Pareto criterion. The claim is that this method highlights conflicts in value judgements and in incomparable criteria, allowing to search for a conflict-mitigating solution that doesn't make assumptions on the reciprocal importance of criteria or judgements. The method is actually a combination of existing but unrelated approaches in Social Choice Theory and in Order Theory and provides outcomes with interesting properties. The essays present, respectively, an axiomatic discussion of the properties of this approach and two applications to policy issues.

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