Duverger’s Law, Penrose’s Power Index and the unity of the United Kingdom

As predicted by Duverger’s Law, the UK has two-party competition in each electoral district. However, there can be different patterns of two-party competition in different districts (currently there are five), so that there have usually been more than two effective parties in the Commons. Since 1874 it has always contained parties fighting seats in only one of the non-English parts of the Union. These parties wish to change the Union by strengthening, weakening, or dissolving it. By calculating the Penrose power index for all parties in the House of Commons for all General Elections since 1874, we identify the occasions on which a party that wished to modify the Union was pivotal. We explain various acts (e.g, the Crofters Act 1886; the first three Irish Home Rule Bills; the Parliament Act 1911) and non-acts (e.g. the failure to enact female suffrage before 1914) by reference to the Penrose indices of the non-English parties. The indices also explain how and why policy towards Scotland, Wales and Northern Ireland changed, and did not change, in the 1970s.