 investigating the frequency with which each method chooses the ideal assignment, we assume that assignment to be the one that is objectively correct or more accurate than the alternative options to be voted on. Even though the nature and extent of the collective decision problems in which there is such an assignment are controversial, there is broad agreement in acknowledging that some public problems are of this kind.21(pp38-47) In developing our approach to examine several voters' preference distributions, we assume that we know what the ideal assignment is –actually, we fix it– and then we compare the performance of the methods. However, the ability of the methods to choose the ideal assignment does not require that someone knows which one it is, but only that such an assignment exists and that the voters' preference distribution (even if their preferences are subjective) surpasses a certain competence threshold in identifying it. We will first define the notation that we use to describe the voting methods: • T = {A, B, C}, the set of "candidates". • A "feasible option" will be any vector with one or three components, each component will be a member of T and each member of T will appear at most once. Thus, each voter will approve or reject a feasible option, with the following interpretation: o (α): Indicates that candidate α (with α ∈ T) is being chosen for the first position. o (α, β, γ): Indicates that candidates α, β, γ (members of T) are being chosen for positions 1, 2, and 3, respectively. • A "conditioned feasible option" will be any vector with three components, one of which will be a member of ?? = {??, ??, ??}, the two remaining components will be different members of T and each member of T will appear at most once. Thus, each voter will approve or reject a FI NA L DR AF T 5 conditioned feasible option, with the following interpretation: o (??, β, γ): Indicates that candidate α (with α ∈ T\{β, γ}) has been fixed in position 1, and β and γ are being chosen for positions