Is majority consistency possible?

The most well-known approaches to decision rules are inspired by “majority-based” and “ranking-based” utilitarianism. The long lasting discussion on the appropriate collective decision mechanism is based on the merits of the rules consistent with these two approaches. Focusing on conformity with qualified majority, we propose single-approval multiple-rejection (SAMR) as a plausible flexible scoring rule narrowing the gap between the two approaches. Given k alternatives, such a mechanism permits approval of a single alternative and rejection of at most $$(k-2)$$ ( k - 2 ) alternatives allowing any relative significance of the approved vs. the rejected alternatives. SAMR is the unique type of rule that spans the whole spectrum of the qualified majority-based utilitarian rules, independent of k. Our first characterization result exposes the relationship between its consistency with any predetermined $$\alpha $$ α -majority based rule, $$\alpha >1/2$$ α > 1 / 2 , and the best/worst (approval/rejection) relative weight p. Our second result establishes that the plurality rule is the unique scoring rule consistent with any $$\alpha $$ α -majority, $$\alpha > 1/2$$ α > 1 / 2 . These results imply the impossibility of universal scoring-rule consistency with any ideal or real $$\alpha $$ α -majority. Copyright Springer-Verlag Berlin Heidelberg 2016