The Analysis of Distorted Representation in Two-Party Single-Member Elections

Abstract

Lm us ASSUME an election in which every seat is contested by a candidate from each of two major parties, L and N. Suppose that by securing a given proportion (f) of the total vote (V) cast for L and N candidates, L would win x seats of mean size P (i.e. in seats won by L, the total of L and N votes =Px), while with the same proportion of the total vote, N would win y seats of mean size Q (i.e. in seats won by N, the total of L and N votes = Qy). Suppose further that off V votes cast for L, the proportion 1 would be cast in seats won by L, while at the same time, of the (1 -f )V votes cast for N, the proportion u would be cast in seats won by N. Conversely, of f V votes cast for N, the proportion n would be in seats won by N, while of the (1 -f )V votes cast for L the proportion h would be in seats won by L. The two situations may be represented in tabular form thus: Situation 1Votes for(1 -f )V Situation 2

New labour landslide ‐ same old electoral geography?

“…Following Brookes (1960), we define bias as the additional number of seats which one party would have won rather than the other had it obtained the same Downloaded by [UQ Library] at 18:45 02 November 2014 proportion of the national vote, assuming a uniform swing between the two main parties across all constituencies and no change in the performance of other parties or in the level of abstentions (Rossiter et ah, 1997b). At the time of the 1992 election there was a consistent and significant bias favouring the Labour party, when with a lead of some 7.6 per cent over Labour there was a net disadvantage to the Conservatives of 26 seats.…”

Electoral bias at the 2015 general election: reducing Labour’s electoral advantage

“…A method for de-composing bias for a two-party system was developed by Ralph Brookes (1960) and later adapted to take account of party systems with two main parties and a third party winning some seats 2 . Next, a more substantive adaptation permitted bias decomposition for a three-party system (Borisyuk et al 2008;2010).…”

“The electors shall meet in their respective states”: Bias and the US Presidential Electoral College, 1960–2012

“…Grofman et al, 1997;Garand andParent, 1991: Grofman, 1983, demonstrates that most, including the method used here, are 23/04/2014 mathematically equivalent). Here, we employ Brookes' (1959Brookes' ( , 1960 method for analysis of electoral bias in two-party plurality electoral systems, which Grofman (1983, 321) praises for its 'high methodological sophistication'. Originally applied to New Zealand, it has also been used in the United Kingdom (see e.g.…”