  Danilov, Karzanov and Koshevoy (2012) geometrically introduced an interesting
operation of composition on tiling Condorcet domains and using it they
disproved a long-standing problem of Fishburn about the maximal size of
connected Condorcet domains. We give an algebraic definition of this operation
and investigate its properties. We give a precise formula for the cardinality
of composition of two Condorcet domains and improve the Danilov, Karzanov and
Koshevoy result showing that Fishburn's alternating scheme does not always
define a largest peak-pit Condorcet domain.
