  We give a 1.488-approximation for the classic scheduling problem of
minimizing total weighted completion time on unrelated machines. This is a
considerable improvement on the recent breakthrough of $(1.5 -
10^{-7})$-approximation (STOC 2016, Bansal-Srinivasan-Svensson) and the
follow-up result of $(1.5 - 1/6000)$-approximation (FOCS 2017, Li). Bansal et
al. introduced a novel rounding scheme yielding strong negative correlations
for the first time and applied it to the scheduling problem to obtain their
breakthrough, which resolved the open problem if one can beat out the
long-standing $1.5$-approximation barrier based on independent rounding. Our
key technical contribution is in achieving significantly stronger negative
correlations via iterative fair contention resolution, which is of independent
interest. Previously, Bansal et al. obtained strong negative correlations via a
variant of pipage type rounding and Li used it as a black box.
