The Condorcet Committee à la Gehrlein (CCG) is a fixed-size subset of
candidates such that each of its members defeats in a pairwise contest any candidate
outside. The Condorcet Committee à la Fishburn (CCF) is a fixed-size subset of
candidates that is preferred to all other subsets of the same size by a majority of voters.
In general, these two types of Condorcet committees may not always exist. Kaymak
and Sanver (Soc Choice Welf 20:477–494, 2003) studied the conditions under which
the CCF exists under a large class of extensions of preferences. We focus here on the
most important members of their class, the lexicographic extension of preferences,
and we define more precisely, the conditions under which these committees coincide
when they exist. Our results depart from the rather optimistic conclusions of Kaymak
and Sanver (Soc Choice Welf 20:477–494, 2003) on the coincidence between the CCG
and the CCF. We exhibit profiles for which the CCF is empty while the CCG exists
and the preferences are all of lexicographic type. Furthermore, we obtain the same
conclusion when we derive preferences on candidates from those on sets of candidates
using the separability assumption.

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• Coincidence of Condorcet committees