Electoral formula, legal threshold and the number of parties

We exploit a rare natural experiment, a recent reform of local elections in Poland, to study an extension of Duverger’s laws. We analyse party system fragmentation under single-member plurality rule vis-à-vis a proportional representation formula accompanied by a legal threshold. We demonstrate that the presence of a threshold alters Duverger’s ‘psychological’ effect. Proportional representation with a threshold tends to be on a par with single-member plurality as regards restricting the effective number of electoral parties, largely due to the absence of smaller groupings with spatially concentrated support. At the same time, Duverger’s ‘mechanical’ effect takes a rather standard form, single-member plurality being relatively powerful at constraining the effective number of legislative parties.