  To convert a fractional solution to an instance of a constraint satisfaction
problem into a solution, a rounding scheme is needed, which can be described by
a collection of symmetric operations with one of each arity. An intriguing
possibility, raised in a recent paper by Carvalho and Krokhin, would imply that
any clone of operations on a set $D$ which contains symmetric operations of
arities $1, 2, \ldots, \lvert D \rvert$ contains symmetric operations of all
arities in the clone. If true, then it is possible to check whether any given
family of constraint satisfaction problems is solved by its linear programming
relaxation.
  We characterize all idempotent clones containing symmetric operations of
arities $1, 2, \ldots, \lvert D \rvert$ for all sets $D$ with size at most four
and prove that each one contains symmetric operations of every arity, proving
the conjecture above for $\lvert D \rvert \leq 4$.
