National level electoral thresholds: Problems and solutions

Identifying a valid indicator of the electoral barrier is an important concern in many research projects, and Lijphart's Effective Threshold is undoubtedly one of the more popular choices [Lijphart, A., 1994. Electoral Systems and Party Systems – a Study of Twenty-Seven Democracies, 1945–1990. Oxford University Press, Oxford.]. Taagepera has demonstrated that it does not measure what it claims to, however, and has instead suggested the Nationwide Threshold of Representation [Taagepera, R., 2002. Nationwide threshold of representation. Electoral Studies 21, 383–401.]. The problem is that the latter assigns lower thresholds to plurality–majoritarian systems than most PR systems, thus contradicting other standard indicators of the electoral barrier. The arguments and methods involved in national level threshold estimation are therefore subjected to close examination and two main conclusions are drawn. Firstly, the method for centre estimation (using the geometric mean) suggested by Taagepera contains methodological errors that undermine its validity. Secondly, predicting the probability of winning ‘a seat’ with a given vote share is not feasible at the national level as is the case at the district level. Moreover, it is inadequate to capture the electoral barrier of concern to most research projects. To capture this barrier, we must now compare what is required to obtain proportional representation under different rules.