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    Dictatorial domains in preference aggregation
    (Springer, 2007) Ozdemir, Ugur; Sanver, M. Remzi
    We call a domain of preference orderings dictatorial if there exists no Arrovian (Pareto optimal, IIA and non-dictatorial) social welfare function defined over that domain. In a finite world of alternatives where indifferences are ruled out, we identify a condition which implies the dictatoriality of a domain. This condition, to which we refer as being essentially saturated, is fairly weak. In fact, independent of the number of alternatives, there exists an essentially saturated ( hence dictatorial) domain which consists of precisely six orderings. Moreover, this domain exhibits the superdictatoriality property, i.e., every superdomain of it is also dictatorial. Thus, given m alternatives, the ratio of the size of a superdictatorial domain to the size of the full domain may be as small as 6/m!, converging to zero as m increases.
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    Measuring democracy: axiomatic foundations for aggregating characteristics
    (Springer, 2025) Ozdemir, Ugur; Sanver, M. Remzi; Yazgan, M. Ege
    The determination of appropriate criteria for the selection of an aggregation rule for composite indices represents a nuanced area of inquiry. This study embarks on an axiomatic exploration of the aggregation methodology employed by the Economist Intelligence Unit (EIU) in the formulation of its Democracy Index. We introduce two axiomatic precepts and demonstrate that while the EIU's additive aggregation rule satisfies one axiom, it does not uphold the other. In contrast, we suggest the implementation of the Borda count for the aggregation of identical indicator categories and reveal that this method adheres to the axiom contravened by the additive rule but does not fulfill the axiom that the additive rule meets. Moreover, we scrutinize the empirical ramifications of applying diverse aggregation rules across the span from 2006 to 2020. It is observed that the two aggregation approaches yield markedly divergent outcomes, particularly among nations with lower democratic rankings. The insights garnered from this investigation underscore the pivotal role of the selection of aggregation rules in the constitution of indices and advocate for a more profound examination of the axiomatic principles that undergird such choices.