Level-strategyproof belief aggregation mechanisms

21^st April 2021, 13:00
Estelle Varloot
University of Liverpool

Abstract

When aggregating experts probabilistic predictions over an aligned set of outcomes $\Lambda$ (that we model as a Borel measurable subset of the real line $\mathbf{R}$), we introduce level-strategyproofness and prove that it is not only natural but also robust as it implies strategyproofness for a rich domain of single-peakedness preferences on the space of cumulative distributions. Our main results are: (1) the characterization of level-strategyproof probability aggregation mechanisms with or without the combination with other axioms; (2) the determination of four impossibility results when certain axioms are combined or reinforced; and (3) the axiomatization of two new and potentially practical level-strategyproof methods: the middlemost-cumulative and the proportional-cumulative. They are compared with other methods and the proportional-cumulative is applied to extend the approval voting, majority rule, and the more recent majority judgment to situations where voters are uncertain about the quality of the candidates/alternatives to be ranked.