  Strong lenses are extremely useful probes of the distribution of matter on
galaxy and cluster scales at cosmological distances, but are rare and difficult
to find. The number of currently known lenses is on the order of 1,000. We wish
to use crowdsourcing to carry out a lens search targeting massive galaxies
selected from over 442 square degrees of photometric data from the Hyper
Suprime-Cam (HSC) survey. We selected a sample of $\sim300,000$ galaxies with
photometric redshifts in the range $0.2 < z_{phot} < 1.2$ and photometrically
inferred stellar masses $\log{M_*} > 11.2$. We crowdsourced lens finding on
this sample of galaxies on the Zooniverse platform, as part of the Space Warps
project. The sample was complemented by a large set of simulated lenses and
visually selected non-lenses, for training purposes. Nearly 6,000 citizen
volunteers participated in the experiment. In parallel, we used YattaLens, an
automated lens finding algorithm, to look for lenses in the same sample of
galaxies. Based on a statistical analysis of classification data from the
volunteers, we selected a sample of the most promising $\sim1,500$ candidates
which we then visually inspected: half of them turned out to be possible (grade
C) lenses or better. Including lenses found by YattaLens or serendipitously
noticed in the discussion section of the Space Warps website, we were able to
find 14 definite lenses, 129 probable lenses and 581 possible lenses. YattaLens
found half the number of lenses discovered via crowdsourcing. Crowdsourcing is
able to produce samples of lens candidates with high completeness and purity,
compared to currently available automated algorithms. A hybrid approach, in
which the visual inspection of samples of lens candidates pre-selected by
discovery algorithms and/or coupled to machine learning is crowdsourced, will
be a viable option for lens finding in the 2020s.
