Exploring estimation of social welfare functions for consensus

Consensus is critical for problems ranging from policy decision-making to expert elicitation, yet research is lacking on methods for helping small groups come to consensus. We take advantage of a proof by Roberts (1980) that the level sets of cardinal fully comparable social welfare functions are cones with vertices at the equal utility point, where the angle of the cone can change depending on the region of the space of utility orders. We propose an approach that leverages an assumption about the relationship between the social welfare function across the n! regions. Specifically, we assume that the social welfare function's local behavior will be similar if the ordering of the utilities is similar across two regions of the order space. We compare the approach against alternative non-parametric and parametric approaches.