On party-proportional representation under district distortions

Abstract

The paper presents the problem of choosing the representatives in an assembly when the whole electoral region is subdivided into electoral districts. Because of the two dimensions, geographical (districts) and political (parties), the problem is called bi-apportionment. Often the allocation of seats to districts is predetermined and furthermore distorted-meaning that the ratios of the number of assigned seats to population size vary significantly across districts. The paper surveys proposed bi-apportionment methods with a focus on the conflict that may arise between partyproportional representation and district distortions.

The cost of proportional representations in electoral system design

“…It is important to note that the scenario described in Corollary 1, involving 'no split-ticket voting' essentially mirrors a single-vote system. Thus, this outcome is not a novel finding and aligns with the results observed in previous studies of singlevote systems, notably Balinski and Demange (1989b) and Demange (2012). In fact, without resorting to Theorem 1, one could deduce that setting s i j = v i j v x L for all (i, j) ∈ N × M suffices as a solution to the linear system.…”

“…The foundational work of Balinski and Demange (1989b) introduced the biproportional divisor methods, see also Balinski and Demange (1989a). Additionally, Demange (2012) delved into the challenge of achieving party proportionality, assuming a pre-determined allocation of seats to districts are distorted. Later, Demange 1 Countries using compensatory systems include Germany, South Korea, Italy, Hungary, Bolivia, etc.…”

On Allocating Seats to Parties and Districts: Apportionments

“…Furthermore, if party-proportional representation is the goal, a simple fact is that party-proportionality cannot be achieved by allocating seats district per district when there are distortions in the district apportionment. This result is independent of any integer requirement (see Demange [2011]). This difficulty is at the root of complex additional features in electoral rules that aim at achieving party-proportionality.…”

New Electoral Systems and Old Referendums

“…For experiments conducted in the 2017 presidential election, see 'Voter autrement' https://vote.imag.fr/ and http://www.jugementmajoritaire2017.com/.3 For a recent account of bi-apportionment problems, seeDemange (2012); for a review of electoral systems in various countries, seeSimeone and Pukelsheim (2006).4 The bi-divisor methods could be applied in other contexts than the political one.…”