Duverger's Law, Penrose's Power Index and the Unity of the UK

Abstract

As predicted by Duverger's Law, the UK has had two‐party competition for long periods in most electoral districts. However, there are different patterns of two‐party competition in different districts and more than two effective parties in the Commons. Since 1874, parliament has always contained parties wishing to modify the Union and contesting seats only outside England. By calculating the Penrose power index for all parties in the House of Commons for all general elections since 1874, we identify when such parties were pivotal. We explain various legislative changes (for example the Crofters Act 1886, the first three Irish Home Rule Bills, the Parliament Act 1911) and non‐changes (for example the failure to enact female suffrage before 1914) by reference to the Penrose index scores. The scores also explain how and why policy towards Scotland, Wales and Northern Ireland changed and did not change in the 1970s.

The Strategic Impact of the Electoral System and the Definition of ‘Good’ Governance

“…5 It has had a profound influence on the architecture and norms of politics by making it hard for new, or minor, parties to win representation (McLean et al, 2005). This mechanical effect, Duverger contended, is reinforced by a psychological effect.…”

Explaining the 2005 Coalition Formation Process in Germany: A Comparison of Power Index and Median Legislator Approaches

“…A priori voting power is policy blind, but is ‘still a useful concept, because it enables us to identify cases where a party may have no power. An a priori power of index of zero means that the actual voting power is also zero’ (McLean, McMillan and Leech, 2005, p. 466). So, this type of descriptive statistic allows a fresh eye to be cast over familiar situations.…”

“…2The Banzhaf index is contested in the literature. McLean, McMillan and Leech (2005) argue for the Penrose Index or normalised Banzhaf index. The standardised Banzhaf index is relative (all values sum to 1) whereas Penrose is an absolute index whose values sum to more than one.…”

“…There are instances when the Euclidean assumption is analytically unhelpful (seeRoemer, 2001, p. 26), but, for the purposes of this article, it is assumed to hold true.2 The Banzhaf index is contested in the literature McLean, McMillan and Leech (2005). argue for the Penrose Index or normalised Banzhaf index.…”

Equitable representation in councils: theory and an application to the United Nations Security Council

“…For instance, some countries have ''Privy'' or ''Executive'' Councils with the right to enact legislation during states of emergency, committees that perform detailed tasks such as voting over proposed new legislation on a clause-by-clause basis prior to final approval by the national legislature, or both. 2 Applications to national legislatures include Miller (2009) and Banzhaf (1968) to the US Electoral College;and McLean et al (2005) and Dunleavy (2010) to the UK Parliament.…”