How proportional is proportional representation? (Q1089286)

In a very popular way the author discusses the problem of division of seats in some assembly between parties provided the number of votes received by these parties at the elections is known. The author shows why the proportional distribution is not adequate and discusses different quota methods, e.g. D'Hondt's rule, Droop quota etc. and their properties. Finally he proposes an algorithm of seats allocation and proves in a theorem that this algorithm ''results in each party receiving at least its Droop minimum of seats, unless every party has an exact number of Droop quotas of votes''.