Simple decision rules in small groups: Collegial rule vs. rotational rule

I analyze the decision by ex ante identical group members with private preferences who must choose between two simple power-sharing schemes: collegial rule and rotational rule. Under collegial rule, members simultaneously express their preferred decisions, and the final decision takes the form of a simple compromise: the average of expressed decisions. Under rotational rule, one member is given the full authority to make decisions for a period of time, but this role (potentially) rotates among members. I identify the trade off between preference aggregation and information aggregation, and its interaction with group size and the extent of preference alignment among members.