en pl
en pl


Show issue
Year 12/2020 
Volume 2020 
Issue 34

Regional Correction of The Flis-Słomczyński-Stolicki Formula: The Case of Turkish Elections

Uğurcan Evci
University of California

12/2020 2020 (34) Decyzje

DOI 10.7206/DEC.1733-0092.145


This paper proposes a correction to the Flis-Słomczyński-Stolicki (2019, 2020) formula for countries with large variation among their districts in terms of political divisions. The Flis-Słomczyński-Stolicki formula (FSS formula) estimates seat allocations under the Jefferson-D’Hondt method by using national vote shares, as well as other parameters that are often readily available. However, the FSS formula does not yield precise estimates in those countries where there are independent candidates, special rights assigned to minority parties, signifi cant variation in district sizes, or an unequal distribution of votes due to ethnic or other regional divisions. Hence, I propose dividing the national distribution of votes into regions that satisfy the assumptions of the FSS formula within their district borders. By applying the FSS formula to regions consisting of historically and politically homogenous districts, I demonstrate that the formula’s estimates become signifi cantly more precise. For instance, by applying the regional correction to the 2018 Turkish Parliamentary elections, as well as other Turkish elections between 2007 and 2015, I show that the formula with the correction in three separate regions improves the Loosemore-Hanby goodness of fi t estimates from 2.1 to 3.41 percentage points (95% CI). Thus, the correction might signifi cantly improve the estimates of the FSS formula in various countries, including Spain, Peru, and Belgium.


  1. Bakke, E., & Sitter, N. (2005). Patterns of stability: Party competition and strategy in central Europe since 1989. Party Politics, 11(2), 243–263. [Google Scholar]
  2. Balinski, M.L., & Young, H.P. (1978). Stability, coalitions, and schisms in proportional representation systems. The American Political Science Review, 72(3) 848–858. [Google Scholar]
  3. Blau, A. (2001). Partisan bias in British general elections. British Elections & Parties Review, 11(1), 46–65. [Google Scholar]
  4. Bochsler, D. (2010). Who gains from apparentments under D’Hondt? Electoral Studies, 29(4), 617–627. [Google Scholar]
  5. Calvo, E., & Rodden, J. (2015). The Achilles heel of plurality systems: Geography and representation in multiparty democracies. American Journal of Political Science, 59(4), 789–805. [Google Scholar]
  6. Cox, G.W. (1997). Making votes count: Strategic coordination in the world’s electoral systems. Cambridge University Press. [Google Scholar]
  7. Evci, U., Kaminski, M.M. (2020). Shot in the foot: unintended political consequences of electoral engineering in the Turkish parliamentary elections in 2018. Turkish Studies. DOI:1080/14683849.2020.1843443. [Google Scholar]
  8. Evci, U., Kaminski, M.M. (2021). Strzał w stopę. Niezamierzone konsekwencje polityczne manipulacji wyborczej w tureckich wyborach parlamentarnych w 2018 roku. Decyzje, 34, 49-65. [Google Scholar]
  9. Flis, J., Słomczyński, W., & Stolicki, D. (2018). Pot and ladle: Seat allocation and seat bias under the Jefferson-D’Hondt method. arXiv preprint arXiv:1805.08291. [Google Scholar]
  10. Flis, J., Słomczyński, W., & Stolicki, D. (2019). Kociołek i chochelka: Formuła szacowania rozkładu mandatów metodą Jeffersona-D’Hondta. Decyzje, 32, 5–40. [Google Scholar]
  11. Flis, J., Słomczyński, W., & Stolicki, D. (2020). Pot and ladle: A formula for estimating the distribution of seats under the Jefferson–D’Hondt method. Public Choice, 182(1-2), 201–227. [Google Scholar]
  12. Grigoriadis, I.N. (2016). The Peoples’ Democratic Party (HDP) and the 2015 elections. Turkish Studies, 17(1), 39–46. [Google Scholar]
  13. Gudgin, G., & Taylor, P. J. (2012). Seats, votes, and the spatial organisation of elections. ECPR Press. Haberturk. (2018). Bolgelere gore secim sonuclari. https://www.haberturk.com/secim/secim2018/ genel-secim/bolgeler [Google Scholar]
  14. Janson, S. (2014). Asymptotic bias of some election methods. Annals of Operations Research, 215(1), 89–136. [Google Scholar]
  15. Kaminski, M.M. (2018a). Spoiler effects in proportional representation systems: Evidence from eight Polish parliamentary elections, 1991–2015. Public Choice, 176(3-4), 441–460. [Google Scholar]
  16. Kaminski, M.M. (2018b). Spoilery w systemach reprezentacji proporcjonalnej: Analiza ośmiu polskich wyborów parlamentarnych, 1991–2015. Decyzje, 30, 5–32. [Google Scholar]
  17. Kaminski, M.M. (2001). Coalitional stability of multi-party systems: Evidence from Poland. American Journal of Political Science, 45(2). 294–312. [Google Scholar]
  18. Kaminski, M.M. (2002). Do parties benefi t from electoral manipulation? Electoral laws and heresthetics in Poland, 1989-93. Journal of Theoretical Politics, 14(3), 325–358. [Google Scholar]
  19. Karpov, A. (2015). Alliance incentives under the D’Hondt method. Mathematical Social Sciences, 74, 1–7. [Google Scholar]
  20. Katz, J.N., & King, G. (1999). A statistical model for multiparty electoral data. American Political Science Review, 93(1) 15–32. [Google Scholar]
  21. Konda. (2018). Temmuz ’18 Barometresi. https://konda.com.tr/wp-content/uploads/2018/07/1807_KONDA_24HaziranSecimleriSandikAnalizi.pdf [Google Scholar]
  22. Latner, M., & McGann, A. (2005). Geographical representation under proportional representation: The cases of Israel and the Netherlands. Electoral Studies, 24(4), 709–734 [Google Scholar]
  23. Leutgäb, P., & Pukelsheim, F. (2009). List apparentements in local elections: A lottery. Homo Oeconomicus, 26(3/4), 489–500. [Google Scholar]
  24. Linzer, D.A. (2012). The relationship between seats and votes in multiparty systems. Political Analysis, 20(3). 400–416. [Google Scholar]
  25. Loosemore, J., & Hanby, V. J. (1971). The theoretical limits of maximum distortion: Some analytic expressions for electoral systems. British Journal of Political Science, 1(4), 467–477. [Google Scholar]
  26. Maps of World. (2017). Map of Turkey Geographical Regions. Retrieve From: https://www.mapsofworld.com/turkey/geography/ [Google Scholar]
  27. McLean, I. (1991). Forms of representation and systems of voting. In D. Held (Ed.), Political Theory Today (pp. 172–196). Stanford University Press. [Google Scholar]
  28. Ministerio del Interior. [Spain.] (2019). Consulta de Resultados Electorales. http://www.infoelectoral.mir.es/min/busquedaAvanzadaAction.html vuelta=1&codTipoEleccion=2&codPeriodo=201904&codEstado=99&codComunidad=10&codProvincia=0&codMunicipio=0&codDistrito=0&codSeccion=0&codMesa=0 [Google Scholar]
  29. Norton, P. (1997). The case for fi rst-past-the-post. Representation, 34(2), 84–88. Özbudun, E. (1996). Democratization in the Middle East: Turkey—How far from consolidation? Journal of Democracy, 7(3), 123–138. [Google Scholar]
  30. Sayarı, S. (1992). Politics and economic policy-making in Turkey, 1980-1988. In T.F. Nas and M. Odekon (Ed.), Economics and Politics of Turkish Liberalization, (pp. 26-43). Lehigh University Press. [Google Scholar]
  31. Taagepera, R., & Shugart, M. S. (1989). Seats and votes: The effects and determinants of electoral systems. Yale University Press.Taagepera, R., & Shugart, M. S. (1989). Seats and votes: The effects and determinants of electoral systems. Yale University Press. [Google Scholar]
  32. Yeğen, M. (2004). Citizenship and ethnicity in Turkey. Middle Eastern Studies, 40(6), 51–66. [Google Scholar]
  33. Yeğen, M. (2009). “Prospective-Turks” or “Pseudo-Citizens”: Kurds in Turkey. The Middle East Journal, 63(4), 597–615. [Google Scholar]
  34. Yüksek Seçim Kurulu. [Supreme Election Council.] (2020). YSK web portal. http://www.ysk.gov.tr/ [Google Scholar]

Full metadata record

Cite this record

APA style

Evci, Uğurcan (2020). Regional Correction of The Flis-Słomczyński-Stolicki Formula: The Case of Turkish Elections. (2020). Regional Correction of The Flis-Słomczyński-Stolicki Formula: The Case of Turkish Elections. Decyzje, 2020(34), 29-48. https://doi.org/10.7206/DEC.1733-0092.145 (Original work published 12/2020AD)

MLA style

Evci, Uğurcan. “Regional Correction Of The Flis-Słomczyński-Stolicki Formula: The Case Of Turkish Elections”. 12/2020AD. Decyzje, vol. 2020, no. 34, 2020, pp. 29-48.

Chicago style

Evci, Uğurcan. “Regional Correction Of The Flis-Słomczyński-Stolicki Formula: The Case Of Turkish Elections”. Decyzje, Decyzje, 2020, no. 34 (2020): 29-48. doi:10.7206/DEC.1733-0092.145.