Can we aggregate voters’ perceptions of political parties’ left–right positions? Formal and probabilistic tests of the left–right scale as a unidimensional common space on cross-national and longitudinal data

The left–right scale is widely assumed to be a common space, a joint yardstick that facilitates political communication. Aggregate voter perceptions of party positions on the left–right scale are widely used by scholars, a.o. to test models of voting behaviour, assess voter-elite congruence, or study party system change. Remarkably, while these models hinge on the longstanding assumption that voters have a joint understanding of the ordering of political parties on the left–right scale, this assumption has not been put to a systematic test. This paper introduces formal and a probabilistic tests of the formal demands of a common space: individual transitivity and collective transitivity. Cross-national analyses of election survey data (36 countries in the CSES) and longitudinal analyses in Germany (1983–2021), Great Britain (1997–2019), and the Netherlands (1981–2021) test whether the left–right dimension meets these demands. The outcomes are sobering. They cast serious doubt on the interpretation of the left–right scale as a common scale among voters, except under specific circumstances. We discuss the far-reaching implications of these findings.