  We study the extent to which it is possible to approximate the optimal value
of a Unique Games instance in Fixed-Point Logic with Counting (FPC). We prove
two new FPC-inexpressibility results for Unique Games: the existence of a (1/2,
1/3 + delta)-inapproximability gap, and inapproximability to within any
constant factor. Previous recent work has established similar
FPC-inapproximability results for a small handful of other problems. Our
construction builds upon some of these ideas, but contains a novel technique.
While most FPC-inexpressibility results are based on variants of the
CFI-construction, ours is significantly different.
