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

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.