UBC Theses and Dissertations
Topological methods of preference and judgment aggregation Jakobsen, Alexander M.
Arrow’s Impossibility Theorem is a classical result in social choice theory (a branch of economic theory), which states that any system of rules for combining (“aggregating”) individual preference relations into a single representative relation results in a “dictatorship” where the combined preference only reflects the wishes of a single individual (provided that the aggregation rule satisfies two basic criteria). Since the 1980s, this result has been reformulated and understood using algebraic topology. The topological approach offers some geometric intuition as to why Arrow’s theorem holds, and can also be used to find alternative hypotheses which may escape the dictatorship outcome. A thorough examination of such topological models constitutes the main body of this thesis. Recently, social choice theory has been generalized (resulting in a field called “judgment aggregation”), and results analogous to Arrow's theorem have been established. The second part of this thesis introduces this field of study, and studies how some of the techniques from topological social choice theory can be extended to understand dictatorship outcomes in the theory of judgment aggregation. Although the analysis is restricted to a rather simple case, it nonetheless highlights the potential for a more general topological model of judgment aggregation, and exposes the main challenges that must be overcome in constructing such a theory.
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