Paradoxes of voting in list systems of proportional representation

Mathematical Aspects of Electoral Systems

“…In this paper we consider a description of a proportional electoral system and a number of electoral paradoxes. The latter are mathematically correct and sometimes practically possible results of elections which contradict our intuition, see also [1,2,3].…”

Election Inversions, Coalitions and Proportional Representation: Examples from Danish Elections

“…Van Deemen 1993;Kurrild-Klitgaard 2008). In this case, we are just focusing on government coalitions as alternatives rather than individual parties.…”

“…2 Most such studies have dealt with voting on legislative proposals or elections in plurality/majority systems (cf., e.g., Riker 1982;Nurmi 1987). However, recent work has also turned the attention to the types of voting paradoxes that may occur in systems of proportional representation (e.g., Van Deemen 1993;Van Deemen and Vergunst 1998;Härd 2000;Kurrild-Klitgaard 2008). Common for these studies is the identification of the potential discrepancy between the voters' preferences and the election outcomes.…”

Untitled

“…It can be shown that each of these paradoxes may occur in the Dutch system of proportional representation (Van Deemen, 1993). However, do they occur in reality?…”

“…We also investigate the occurrence of other paradoxes related to the plurality rule and the majority rule. These so-called majority-plurality paradoxes are presented in Van Deemen (1993). The first paradox of this kind occurs when a party is preferred by a majority of the electorate to another party and yet receives less seats than that other party.…”