Numerical Judgment Aggregation: Towards a General Framework
Tisja Irene Smits

Abstract:
This thesis introduces and develops the framework of Numerical Judgment Aggregation (NJA), extending classical judgment aggregation to settings where agents express numerical judgments over general variables. Unlike traditional models, NJA allows for more expressive inputs and outputs, accommodating real-world scenarios where uncertainty, gradation, or nuance play a central role.
Several classes of aggregation rules are defined and analyzed: calculation-based (e.g., mean), ordinal (e.g., median), and support-based (e.g., majority). The normative behavior of these rules is axiomatically evaluated by means of properties such as anonymity, unanimity, independence, autonomy, and monotonicity. A central result is the axiomatic characterization of support quota rules via the concept of winning coalitions, generalizing results from classical judgment aggregation.
To ensure well-structured outputs (e.g., as intervals or points), repair operations are introduced and studied in terms of their effects on axiomatic properties. The framework also accommodates the use of integrity constraints to formalize dependencies between issues, structural coherence, or domain-specific consistency requirements. The expressive power and flexibility of NJA are further illustrated through applications to preference aggregation, binary judgment aggregation, and societal trade-off modeling.
Overall, this thesis offers a unified and general approach to aggregating numerical judgments under structural constraints, providing both theoretical insight and practical relevance.