Vetoer and tie-making group theorems for indifference-transitive aggregation rules

A binary relation is indifference-transitive if its symmetric part satisfies the transitivity axiom. We investigated the properties of Arrovian aggregation rules that generate acyclic and indifference-transitive social preferences. We proved that there exists unique vetoer in the rule if the number of alternatives is greater than or equal to four. We provided a classification of decisive structures in aggregation rules where the number of alternatives is equal to three. Furthermore, we showed that the coexistence of a vetoer and a tie-making group, which generates social indifference, is inevitable if the rule satisfies the indifference unanimity. The relationship between the vetoer and the tie-making group, i.e., whether the vetoer belongs to the tie-making group or not, determines the power structure of the rule.