Votes based on protracted deliberations

We analyze group decision-making in situations in which members discuss the value of a continuous random variable, then take an up-or-down vote based on their assessments of the continuous variable. Applications include jury deliberations and tenure and promotion or partnership votes. We determine conditions under which the group can reach a consensus on the value of the continuous variable, conditions under which the group fails to reach an agreement on the up-or-down vote, and when the outcome of a successful up-or-down vote matches the consensus on the continuous variable. We also consider the impact of unanimous versus nonunanimous voting rules.