  This paper studies the strategic manipulation of set-valued social choice
functions according to Kelly's preference extension, which prescribes that one
set of alternatives is preferred to another if and only if all elements of the
former are preferred to all elements of the latter. It is shown that
set-monotonicity---a new variant of Maskin-monotonicity---implies
Kelly-strategyproofness in comprehensive subdomains of the linear domain.
Interestingly, there are a handful of appealing Condorcet extensions---such as
the top cycle, the minimal covering set, and the bipartisan set---that satisfy
set-monotonicity even in the unrestricted linear domain, thereby answering
questions raised independently by Barber\`a (1977) and Kelly (1977).
