Balance and Baselines: An Impossibility Theorem And an Axiomatisation of Additive Aggregation

A feature in many multicriteria problems is a preference for “balance”, understood as achieving a desired distribution (e.g., equality or target proportions) of resources across stakeholders or conceptual categories. This paper presents a normative exploration of the implications of balance preferences when baselines are uncertain or contested. We prove an impossibility theorem showing that if a decision maker is strictly outcome-based yet expresses a strict preference for balance over gains whatever the baseline, then an inconsistency arises. We then show that if the balance preference is weakened and combined with standard conditions (such as monotonicity and continuity), the only consistent aggregation rule is a simple additive one. Our results highlight that deliberative decision making necessarily involves reconciling preference intuitions “in the small” (over a fragment of the decision space) and “in the large” (over the whole of that space).