Pot and ladle: a formula for estimating the distribution of seats under the Jefferson–D’Hondt method

Abstract

We propose a simple yet new formula for estimating national seat shares and quantifying seat biases in elections employing the Jefferson-D'Hondt (JDH) method for seat allocation. It is based solely on the national vote shares and fixed parameters of the given electoral system. The proposed formula clarifies the relationship between seat bias on the one hand, and the number of parties and the number of districts on the other. We demonstrate that the formula provides a good estimate of seat allocations in real-life elections even in the case of minor violations of the underlying assumptions. With that aim in mind, we have tested it for all nine EU countries that employ the JDH method in parliamentary elections. Moreover, we discuss the applications of the formula for modeling the effects of vote swings, coalition formation and breakup, spoiler effects, electoral engineering, artificial thresholds and political gerrymandering. By not requiring district-level vote shares, our formula simplifies electoral simulations using the JDH method.

Show issue Year 12/2012 Volume 2020 Issue 34 Regional Correction of The Flis-Słomczyński-Stolicki Formula: The Case of Turkish Elections

“…All essential simulations using the FSS formula in this paper can be replicated using the data found in Table 5. All three regions reasonably satisfy the assumptions put forward by Flis et al (2020), as they do not present a large variation in voter distribution among themselves. The third correction to the FSS formula is much better at estimating the distribution of seats in real elections (see Table 6).…”

“…Therefore, the FSS formula overestimates the number of seats for the stronger parties -the AKP and the CHP -while underestimating the number of seats for a regional party -the HDP. The LH index is 4.09%, which is worse than 80 out of the 84 European election cases that Flis, Słomczyński, and Stolicki (2018)…”

“…Here, the estimates are better than the estimates in the fi rst scenario because the HDP receives more seats and the AKP receives fewer seats. However, their fi t is still not satisfactory since the LH index is 1.75%, which is better than the LH-score of 36 out of 84 cases in Flis et al (2018). Although the difference in the number of AKP seats is relatively small, one critical problem is that the formula predicts a majority rule for the AKP in the Parliament.…”

“…Thus, this variant seems to overcome the problems related to the existence of regional parties. In Flis et al (2018), the largest value of the LH index is for Spain's 1979 election, where the LH is 6.2%. Out of the 84 elections that they analyze, the value of LH is larger than 4% in only four elections.…”

“…The LH is as small as 0.4% (Netherlands 1956 election), and the average LH in all 84 post-1945 parliamentary elections in eight European countries is 1.9%. It is important to note that the analysis by Flis et al (2018) includes data from nations with regional voter distributions, such as Spain, where the formula does not work as well as it does in other countries. The fi rst scenario analyzed in this paper presents an LH value of 4.09%; therefore, the estimates are poor compared to Flis et al (2018).…”