The fuzzy set approach to modeling thick indifference can accommodate highly irregular shaped indifference curves, even those that are concave or multi-modal. We show that its ability to do so owes to a homomorphism that permits a region of interest (spatial model) to be mapped to a simpler region with a suitable and natural partial ordering where the results are determined and then faithfully transferred back to the original region of interest. We then prove that in all but a limited number of cases, spatial models of individual preferences of thick indifference result in an empty majority rule maximal set if and only if the Pareto set contains a union of cycles.

majority rule maximal set, thick indifference, Pareto set, homomorphism.