[Séminaire CREM] The Condorcet Loser Criterion in Committee Selection

**Abstract:** Some proposed solution concepts in committee selection are based on the Condorcet majority principle: Condorcet Committee of Gehrlein (CCG) and Condorcet Committee of Fishburn (CCF). These solution concepts are based on an extension of the Condorcet winner criterion. Even when they exist, these committees are not always elected. In some cases, the aggregation of preferences may lead to the existence of a committee such that each of its members is defeated in majority duels by each of the external candidates. We call this committee the "Condorcet Loser Committee" (CLC). The CLC is indeed an extension of Condorcet loser criterion to committee selection; when it exists, it is unique. The quasi-consensus of the literature on single-winner elections is that the election of a Condorcet loser is not desirable. Should the election of the CLC be tolerated? Do the popular vote rules prevent the election of the CLC when it exists? One of the ambitions of this paper is to provide answers to these questions. It appears that, of the large family of voting rules used for committee selection, only a limited number of them always prevent the election of the CLC. Thus, we managed to identify among the rules of committee selection, those that never elect the CLC when it exists.

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