Boundary properties of the inconsistency of pairwise comparisons in group decisions

•We study the inconsistency of pairwise comparisons in group decision making.•We study the effect of the aggregation of pairwise comparisons on their consistency.•We derive general results and provide a complete study for well-known inconsistency indices.•We start a discussion on the meaning of inconsistency of aggregated preferences. This paper proposes an analysis of the effects of consensus and preference aggregation on the consistency of pairwise comparisons. We define some boundary properties for the inconsistency of group preferences and investigate their relation with different inconsistency indices. Some results are presented on more general dependencies between properties of inconsistency indices and the satisfaction of boundary properties. In the end, given three boundary properties and nine indices among the most relevant ones, we will be able to present a complete analysis of what indices satisfy what properties and offer a reflection on the interpretation of the inconsistency of group preferences.