  The observation of gravitational-wave signals from merging black-hole
binaries enables direct measurement of the properties of the black holes. An
individual observation allows measurement of the black-hole masses, but only
limited information about either the magnitude or orientation of the black hole
spins is available, primarily due to the degeneracy between measurements of
spin and binary mass ratio. Using the first six black-hole merger observations,
we are able to constrain the distribution of black-hole spins. We perform model
selection between a set of models with different spin population models
combined with a power-law mass distribution to make inferences about the spin
distribution. We assume a fixed power-law mass distribution on the black holes,
which is supported by the data and provides a realistic distribution of binary
mass-ratio. This allows us to accurately account for selection effects due to
variations in the signal amplitude with spin magnitude, and provides an
improved inference on the spin distribution. We conclude that the first six
LIGO and Virgo observations (Abbott et al. 2016a, 2017a,b,c) disfavour highly
spinning black holes against low spins by an odds-ratio of 15:1; thus providing
strong constraints on spin magnitudes from gravitational-wave observations.
Furthermore, we are able to rule out a population of binaries with completely
aligned spins, even when the spins of the individual black holes are low, at an
odds ratio of 22,000:1, significantly strengthening earlier evidence against
aligned spins (Farr et al. 2017). These results provide important information
that will aid in our understanding on the formation processes of black-holes.
