Electoral thresholds and political representation

Some countries allow for exceptions whereby parties can enter the legislature without exceeding the electoral threshold. In Germany, the electoral rule for national elections is a mixed-member proportional representation system with some majoritarian elements, i.e., a fraction of the seats is filled by first-past-the-post elections within constituencies. Parties may thus enter parliament, even if their vote share is less than 5 % t, as long as they win a “direct mandate” in at least three constituencies in the first-past-the-post elections. For more details on different kinds of special rules or criteria used to transform votes into seats, see Lijphart (1994).

In 2014, Germany’s federal constitutional court ruled the 3 % electoral threshold for European Union elections unconstitutional (http://​www.​euractiv.​com/​section/​eu-elections-2014/​news/​germany-s-top-court-annuls-3-threshold-for-eu-election/​). In New Zealand, the Electoral Commission recommended that the party vote share threshold be lowered from 5 to 4 % (http://​www.​nzherald.​co.​nz/​opinion/​news/​article.​cfm?​c_​id=​466&​objectid=​10835116). In Israel, the electoral threshold for the Knesset (national parliament) has risen continually ever since the country was founded; the largest increase occurred as recently as March 2014 (http://​www.​haaretz.​com/​israel-news/​1.​579289).

One exception is Vatter (2003), who uses subnational data at the level of the Swiss Cantons to find that legal electoral thresholds have no effect on the number of parties represented in parliament. Second, Pellicer and Wegner (2014) find significant mechanical and psychological effects of local electoral thresholds in Morocco. However, a limitation of their analysis is that they have data only on seats, but not on votes.

Note, however, that some local parties gain a fairly large vote share within their municipality.

While we lump the various parties into the three aggregate categories for most of our analysis, they of course still compete as individual entities in the local elections.

In particular, the threshold of inclusion is the minimum vote share that enables a party to win a seat, provided that vote shares are distributed among all other parties to the best advantage of the first (Rokkan 1968). Crossing the threshold of inclusion does not guarantee representation.

The threshold of exclusion is the counterpart of the threshold of inclusion. It is defined as the maximum vote share a party may obtain that is still insufficient to gain a seat, owing to the vote distribution among the remaining parties (Rae et al. 1971; Lijphart and Gibberd 1977).

Recall that the threshold of exclusion depends also on the number of parties contesting the elections (Lijphart and Gibberd 1977).

It is difficult to disentangle mechanical and psychological effects. Moser and Scheiner (2012), for example, point out that the psychological effect may mask the size of the perceptible mechanical effect if a substantial number of voters respond to the disproportionality caused by an electoral rule by switching to a less favored larger party. That is, if voters who actually support smaller parties react to, e.g., a high electoral threshold by switching their votes to larger parties, the disproportionality induced by the threshold may seem small because the large parties will have both a large seat and a large vote share. Thus, ultimately mechanical and psychological effects work in concert.

One reason why electoral thresholds were introduced in the first place was the belief that the large number of parties in the Reichstag during the Weimar Republic was inefficient, though the empirical evidence is ambiguous at best (Lehmann 2010).

The fuzziness of the relationship between population size and council size is explained by the legal stipulation that municipalities may choose the (smaller) council size intended for the previous population bracket.

See Grembi et al. (2016) for a more comprehensive discussion of the diff-in-disc design.

For purposes of illustration, take, e.g., Babenhausen, a municipality with about 15,000 inhabitants. It saw a slight increase in the vote share of the large parties in 2001 relative to the previous 1997 election (from around 80 to 82.8 %), but no change in the large parties’ seat share (83.8 %). In the same election, it also saw a reduction in the seat and vote shares of the local parties (the seat share dropped from 5.5 to 2.7 %). The vote share of the medium-sized parties, in turn, declined from 14.5  to 13.7 %, but their seat share increased, from 10.8 to 13.5 %. The effects for the medium parties are driven by the FDP. The FDP did not enter the council in 1997 with a vote share of 3.7 %, but had a vote share of 4.7 % in 2001 and, given the absence of the electoral threshold, a seat share of 5.4 %. By 2011, the seat share—and also vote share—of the large parties had declined considerably, i.e., to 67.5 %. The seat shares of the local parties, in contrast, increased up to 13.5 %. Finally, the medium-sized parties increased their seat share to 19 %. Regarding turnout, the rate dropped to 64.9 % in 1997, to 53.9 % in 2001 and further to 47.9 % in the 2011 elections.

The online appendix reports the results of further tests on the internal validity of the results. In particular, we show that the findings are robust to the use of smaller bandwidths, provide the average effect on the different parties, successfully implement a number of placebo tests and fulfill the criteria on the density of the continuous variable.

Take again the Babenhausen municipality. The number of parties attaining representation increased from four in 1997 to five in 2001 and to six in the 2006 and 2011 elections. The seat share held by the largest party in council, in turn, fell consistently from 46 % in 1997 to 37.5 % in 2011. In contrast, the inverse HHI rose secularly from 63.1 in 1997 to 72.9 in 2011.