Sannolikhets-, statistik- och kombinatorikseminarium: The hiring problem

  • Datum:
  • Plats: Ångströmlaboratoriet
  • Föreläsare: Svante Janson
  • Kontaktperson: Fiona Skerman
  • Seminarium

The hiring problem

The hiring problem is a variant of the well-known secretary problem, where
the aim is to hire many persons. Candidates are interviewed one by one, and
the employer has to decide whether to hire them or not immediately, before
the next candidate is interviewed. (We assume that each candidate has a
value that is revealed during the interview. The values are supposed to be
i.i.d. random variables.)

Different hiring strategies are possible, and the mathematical problem is to
analyze them, in particular to find the asymptotic distribution of the
number hired out of n candidates. For example, 
one interesting strategy is to hire everyone that is better than the median
of the ones already hired. More generally, one can use any fixed quantile of
the ones already hired as a threshold. An extreme strategy is to hire only
those that are better than everyone seen so far, i.e. the record values.

These strategies have been analysed previously by several authors. 
Nevertheless, I will present a new method of analysis, which seems to
be both simpler and more general than previous work.