  The ELLIS PhD program is a European initiative that supports excellent young
researchers by connecting them to leading researchers in AI. In particular, PhD
students are supervised by two advisors from different countries: an advisor
and a co-advisor. In this work we summarize the procedure that, in its final
step, matches students to advisors in the ELLIS 2020 PhD program. The steps of
the procedure are based on the extensive literature of two-sided matching
markets and the college admissions problem [Knuth and De Bruijn, 1997, Gale and
Shapley, 1962, Rothand Sotomayor, 1992]. We introduce PolyGS, an algorithm for
the case of two-sided markets with quotas on both sides (also known as
many-to-many markets) which we use throughout the selection procedure of
pre-screening, interview matching and final matching with advisors. The
algorithm returns a stable matching in the sense that no unmatched persons
prefer to be matched together rather than with their current partners (given
their indicated preferences). Roth [1984] gives evidence that only stable
matchings are likely to be adhered to over time. Additionally, the matching is
student-optimal. Preferences are constructed based on the rankings each side
gives to the other side and the overlaps of research fields. We present and
discuss the matchings that the algorithm produces in the ELLIS 2020 PhD
program.
