This work introduces a multimodal data aggregation methodology featuring optimization models and algorithms for jointly aggregating heterogenous ordinal and cardinal evaluation inputs into a consensus evaluation. Mathematical modeling components are derived to enforce three types of logical couplings between the collective ordinal and cardinal evaluations: Rating and ranking preferences, numerical and ordinal estimates, and rating and approval preferences. The methodology is tailored for use with axiomatic distances rooted in social choice theory, and it is equipped to adequately deal with highly incomplete evaluations, tied values, and other challenging aspects of distributed decision-making contexts. The practicality of the proposed methodology for group decision-making is illustrated on a case study involving an academic student paper competition. These considerations and computational aspects are further explored via synthetic instances sampled from distributions parameterized by ground truths and varying noise levels. The results show that multimodal aggregation is effective at extracting a collective truth from noisy information sources and at capturing the distinctive evaluation qualities of ordinal and cardinal evaluations in group decision-making.
A. R. Escobedo, E. Moreno-Centeno, R. Yasmin, An axiomatic distance methodology for aggregating multimodal evaluations'', Unpublished, December 2020.