Parliamentary Voting System and Constituencies Bill - Political and Constitutional Reform Committee Contents

Written evidence submitted by Professor Michael Thrasher (PVSCB 11)

  A short note on electoral bias:

  Elections fought under FPTP rules often result in outcomes that are disproportional. This often involves a "winner's bonus" whereby the largest party overall in terms of vote share receives a larger share of seats. FPTP often results in a small bonus for the second placed party also. It is those smaller parties whose votes are broadly rather than narrowly (in terms of geography) distributed that suffer most in the translation of votes into seats.

  Proportionality/disproportionality is not equivalent to electoral bias. Bias occurs when two (or more) parties that obtain similar levels of voter support nevertheless receive markedly different seat shares. There are a number of factors in any electoral outcome that combine together to explain the distribution of bias. In recent elections the bias has favoured the Labour party but this pattern is by no means fixed.

  There is a common misconception that periodic boundary reviews should remove electoral bias. This view is mistaken because such reviews are only concerned with one element that contributes towards bias, viz., unequal electorate size (malapportionment). Other elements are contributing towards overall bias. Apart from malapportionment these remaining elements are, vote distribution (geography); differential turnout (abstention); and the effects produced by competition from smaller parties. There are, in addition, the interaction effects that result from two or more of these components interacting with one another, for example, a party wins its seats in small electorate areas where abstention is also high.

  Using a new method for decomposing bias for three-party systems (Borisyuk, Johnston, Thrasher and Rallings) the following three Tables reveal the size and distribution of the separate bias components for the actual (Table 1) and estimated (Table 2) 2005 general election and finally the recent 2010 general election (Table 3). The total bias (positive and negative) for the three main parties is also shown.

  Table 1 shows the decomposition of electoral bias for the actual 2005 general election. Half of Labour's 83 seat positive bias is a function of its effective vote distribution—effective in the sense that it does not accumulate excessively large numerical majorities and neither does it acquire a large share of votes in seats that it does not win. The rule, "win small, lose big" operates in FPTP systems for parties wishing to optimise vote distributions. Labour is also benefitting relative to its competitors from low turnout. It is also apparent that malapportionment although a significant contributing factor to Labour's bias advantage in 2005 was responsible for only 11 of its 83 (13%) seat advantage. However, it is worth noting that the electoral component accounted for 12 seats of the Conservative 30 seat negative bias (40%).

Table 1


LabourConservative Lib Dem

Geography41-5 -46
Electorate11-12 -3
Abstention16-14 -10
Minor party3-3 -1
Net interactions133 7
Total bias83-30 -52

  Table 2 shows the decomposition of bias following the 5th Periodic Boundary Review. The overall bias advantage to Labour was reduced to 75 seats while the Conservative party benefitted overall. It is most important to note that the Review Process reduced the bias resulting from unequal electorates. Labour's advantage fell from 11 to four seats; the Conservative disadvantage was halved (from -12 to -6). The review process assisted the Liberal Democrats in terms of electorate bias but a spillover effect was an increase in negative bias from a recalibration of its vote distribution. Arguably, if the Review had been able to equalise electorates to an even greater degree then the malapportionment component may have disappeared altogether.

  A crucial point is that the boundary review process takes no account of either turnout (abstention) or, formally speaking, the partisan nature of any constituency re-drawing that takes place. It is not, therefore, impacting directly upon the abstention or geography components.

Table 2


LabourConservative Lib Dem

Geography412 -49
Electorate4-6 2
Abstention17-14 -9
Minor party3-3 0
Net interactions110 4
Total bias75-21 -52

  A major part of the criticism of the boundary review process is that the electorates that are used to calculate the new constituency boundaries are out of date by the time the review is completed and even more so by the time of the election fought on those new boundaries.

  If this criticism is substantiated then we should expect the electorate bias component to feature prominently in the distribution of bias following the 2010 general election result. Table 3 shows that the electorate bias component is indeed larger. In absolute terms there is a two seat greater advantage for Labour, an additional one seat disadvantage for the Conservatives while the two seat positive bias for the Liberal Democrats reduces to one seat. However, most bias is again contributed by the geography and abstention components.

Table 3


LabourConservative Lib Dem

Geography3135 -74
Electorate6-7 1
Abstention13-11 -6
Minor party2-2 -1
Net interactions11-3 4
Total bias6312 -76

  More generally, the overall bias favouring Labour reduces to 63 seats and a negative bias for the Conservatives now becomes a positive one of 12 seats. The bias against the Liberal Democrats rises from -52 to -76 seats, reflecting the party's vote and seat distributions in 2010.

20 July 2010

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Prepared 20 October 2010