On allocating seats to parties and districts

Gabrielle Demange

This paper focuses on the electoral rules whose aim is to achieve a proportional representation of political parties. If no rules can satisfy all desirable properties, some give rise to paradoxes or unacceptable bugs (a party is given more seats if the votes in its favor fall: Italy in 2005, Germany in 2006...). These paradoxes are difficult to anticipate when elections are conducted in geographical entities of different sizes (cantons in Switzerland, states in the UE...). Indeed, the number of seats allocated a priori to these entities is far from being in proportion to their population, which makes the representation of parties all the more difficult and leads to complex electoral rules.
The article discusses, through a general model, the various solutions that can be implemented. These solutions require to determine the representation of the assembly (e.g. the parliamentary groups in the European Parliament) taking into account simultaneously the votes obtained by parties in each geographical entity and those obtained at the aggregate level, country or union. As a result, the representation cannot be easily computed by hand. Despite this complexity, such a solution is currently experimented in the cantonal elections in Switzerland, thereby shedding new light to this debate
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Original title of the article: On allocating seats to parties and districts
Published in : International Game Theory, Sept 2013, Vol. 15, Issue 03, Sept. 2013, p1-14
Download : http://www.worldscientific.com/doi/abs/10.1142/S0219198913400148
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