  We define several different thresholds for election methods by considering
different scenarios, corresponding to different proportionality criteria that
have been proposed by various authors. In particular, we reformulate the
criteria known as DPC, PSC, JR, PJR, EJR in our setting. We consider
multi-winner election methods of different types, using ballots with unordered
lists of candidates or ordered lists, and for comparison also methods using
only party lists. The thresholds are calculated for many different election
methods. The considered methods include classical ones such as BV, SNTV and STV
(with some results going back to e.g. Droop and Dodgson in the 19th century);
we also study in detail several perhaps lesser known methods by Phragm\'en and
Thiele. There are also many cases left as open problems.
