Beyond the Threshold: How Electoral Size-Dependent Uncertainty Affects Majority Determination

The determination of a majority threshold in any voting system can be influenced by voters' attitudes towards uncertainty. Traditionally, a higher majority threshold is associated with a risk-averse attitude, serving as a means to protect against the tyranny of the majority. Moreover, the absence of ex-ante information regarding the likelihood of the voting outcome introduces a further layer of uncertainty, that of ambiguity, which motivates decision-makers to seek increased protection. In this study, we first provide a thorough formalization of this theoretical prediction, relying on a second-order expected utility model with both risk and ambiguity aversion of the voter toward the voting lottery. Second, we experimentally test its predictions by integrating the majority threshold implication into traditional experiments for risk and ambiguity elicitation. Through a series of classroom experiments run on 2020-2023 (about 1,100 subjects in Italy & France), we analyze how individuals, placed under varying conditions of uncertainty, react to the determination of a barrier threshold. We find a strong correlation between the number of voters and the chosen quorum for a majority: as each subject is only aware of her own voting preference, expanding the electoral base results in a more ambiguous probability about the outcome. This favors more conservative behavior and results in an upward adjustment of the majority threshold.