A group of individuals faces the choice of an alternative out of a set of alternatives. Each member of the group holds an opinion regarding the most suitable (best) alternative for which he or she votes. In this setting, the individual votes are based on their decisional competencies, which hinge on the information to which they are exposed and on their ability to make use of that information. The main question is how to translate the group members’ voting profile to a single collective choice. This chapter studies different aspects of this question in the context of binary voting where the group faces only two alternatives. The selection of an appropriate aggregation rule is a central issue in the fields of social choice, public choice, voting theory, and collective decision making. Since the votes are based on the individual competencies, the applied aggregation rule should take into account not only the voting profile but also the competency profile. In fact, it should also take into consideration any other relevant environmental information such as the asymmetry between the feasible alternatives, the dependence between individual votes, decision-making costs, and the available past record of the voters’ decisions. The chapter focuses on the clarification of the relationship between the performance of binary aggregation rules and the relevant variables and parameters. This has direct normative implications regarding the desirable mode of collective decision making and, in particular, regarding the desirable aggregation rule and the size and the composition of the decision-making body.