An approximation problem in computing electoral volatility

This paper is focused on an approximation problem which often arises when volatility is computed from electoral databases. Volatility is a key dimension in studies on electoral change or stability in party systems [M.N. Pedersen, The dynamics of European party systems: changing patterns of electoral volatility, European Journal of Political Research 7 (1979) 1-26]. Though the volatility formula offers no mathematical complexity, its application to real data often presents several problems. The present paper is inspired by the guidelines proposed by Bartolini and Mair [S. Bartolini, P. Mair, Identity, Competition and Electoral Availability: The Stabilization of European Electorates 1885-1985, Cambridge University Press, Cambridge, 1990] for the approximation problem of volatility. Once a general formulation for this problem is provided, Bartolini and Mair's (BM) approach is justified through the analysis of its approximation error. This leads to suggest a class of approximations of volatility whose errors are also analyzed. One of the goals of this paper is to prove that these new approximations are an improvement of the BM approximation. Finally, the performance analysis of the considered approximations is illustrated through examples with data.