Application of the Variable Choice Logit Model to the British General Election of 2010

The chapter aims to estimate the modification of the classic spatial electoral model and to evaluate the convergence of the electoral system at the origin for the case when the assumption of irrelevant alternatives (IIA) is violated, and, hence, the standard multinomial logistic model is inapplicable. The work looks at the General British Election of 2010, in which the voters from Scotland and Wales could vote for Scottish National Party and Plaid Cymru, respectively, in addition to the parties common with the voters of England. To account properly for the presence of these additional parties, the theoretical model of Yamamoto (2011) for the varying choice logit (VCL) is implemented by applying Gibbs sampling. For the convenience of the analysis, the set of common parties is restricted to the three major parties, the Conservatives, Labour, and Liberal Democrats, that are of our main interest. In the end, we find that the electoral system diverges, because of the saddle location of Plaid Cymru. Meanwhile, conditional on the insignificance of this party, the system converges. A separate study of Scotland is particularly relevant because of the referendum on Scottish independence in September, 2014. The method deployed here is also relevant in many countries in Europe where there are regional parties, including Spain, Belgium, and Italy.