{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T11:30:59Z","timestamp":1750764659176,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":77,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662605547"},{"type":"electronic","value":"9783662605554"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-662-60555-4_1","type":"book-chapter","created":{"date-parts":[[2019,10,31]],"date-time":"2019-10-31T15:09:44Z","timestamp":1572534584000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Probabilistic Model for Detecting Gerrymandering in Partially-Contested Multiparty Elections"],"prefix":"10.1007","author":[{"given":"Dariusz","family":"Stolicki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wojciech","family":"S\u0142omczy\u0144ski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaros\u0142aw","family":"Flis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,11,1]]},"reference":[{"issue":"8","key":"1_CR1","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1016\/S0962-6298(98)00015-8","volume":"17","author":"M Altman","year":"1998","unstructured":"Altman, M.: Modeling the effect of mandatory district compactness on partisan gerrymanders. Polit. Geogr. 17(8), 989\u20131012 (1998). \nhttps:\/\/doi.org\/10.1016\/S0962-6298(98)00015-8","journal-title":"Polit. Geogr."},{"key":"1_CR2","doi-asserted-by":"crossref","unstructured":"Altman, M., Amos, B., McDonald, M.P., Smith, D.A.: Revealing preferences: why gerrymanders are hard to prove, and what to do about it. Technical report, SSRN 2583528, March 2015. \nhttps:\/\/doi.org\/10.2139\/ssrn.2583528","DOI":"10.2139\/ssrn.2583528"},{"issue":"1","key":"1_CR3","first-page":"69","volume":"5","author":"M Altman","year":"2010","unstructured":"Altman, M., McDonald, M.P.: The promise and perils of computers in redistricting. Duke J. Const. Law Public Policy 5(1), 69\u2013159 (2010)","journal-title":"Duke J. Const. Law Public Policy"},{"issue":"9\u201310","key":"1_CR4","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.1016\/j.mcm.2008.05.028","volume":"48","author":"S Ansolabehere","year":"2008","unstructured":"Ansolabehere, S., Leblanc, W.: A spatial model of the relationship between seats and votes. Math. Comput. Model. 48(9\u201310), 1409\u20131420 (2008). \nhttps:\/\/doi.org\/10.1016\/j.mcm.2008.05.028","journal-title":"Math. Comput. Model."},{"key":"1_CR5","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/3-540-35605-3_2","volume-title":"Mathematics and Democracy: Recent Advances in Voting Systems and Collective Choice","author":"N Apollonio","year":"2006","unstructured":"Apollonio, N., Becker, R.I., Lari, I., Ricca, F., Simeone, B.: The sunfish against the octopus: opposing compactness to gerrymandering. In: Simeone, B., Pukelsheim, F. (eds.) Mathematics and Democracy: Recent Advances in Voting Systems and Collective Choice, pp. 19\u201341. Springer, Berlin-Heidelberg (2006). \nhttps:\/\/doi.org\/10.1007\/3-540-35605-3_2"},{"key":"1_CR6","unstructured":"Aras, A., Costantini, M., van Erkelens, D., Nieuweboer, I.: Gerrymandering in three-party elections under various voting rules (2017)"},{"key":"1_CR7","first-page":"31","volume":"4","author":"KB Athreya","year":"1969","unstructured":"Athreya, K.B.: On a characteristic property of Polya\u2019s urn. Stud. Sci. Math. Hung. 4, 31\u201335 (1969)","journal-title":"Stud. Sci. Math. Hung."},{"key":"1_CR8","unstructured":"Bachrach, Y., Lev, O., Lewenberg, Y., Zick, Y.: Misrepresentation in district voting. In: Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, pp. 81\u201387 (2016)"},{"issue":"1\u20133","key":"1_CR9","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/BF01589103","volume":"45","author":"ML Balinski","year":"1989","unstructured":"Balinski, M.L., Demange, G.: Algorithms for proportional matrices in reals and integers. Math. Program. 45(1\u20133), 193\u2013210 (1989). \nhttps:\/\/doi.org\/10.1007\/BF01589103","journal-title":"Math. Program."},{"issue":"4","key":"1_CR10","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1287\/moor.14.4.700","volume":"14","author":"ML Balinski","year":"1989","unstructured":"Balinski, M.L., Demange, G.: An axiomatic approach to proportionality between matrices. Math. Oper. Res. 14(4), 700\u2013719 (1989). \nhttps:\/\/doi.org\/10.1287\/moor.14.4.700","journal-title":"Math. Oper. Res."},{"key":"1_CR11","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.electstud.2013.07.004","volume":"34","author":"F Barth\u00e9l\u00e9my","year":"2014","unstructured":"Barth\u00e9l\u00e9my, F., Martin, M., Piggins, A.: The architecture of the Electoral College, the house size effect, and the referendum paradox. Electoral. Stud. 34, 111\u2013118 (2014). \nhttps:\/\/doi.org\/10.1016\/j.electstud.2013.07.004","journal-title":"Electoral. Stud."},{"issue":"2","key":"1_CR12","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1007\/BF00127533","volume":"47","author":"S Berg","year":"1985","unstructured":"Berg, S.: Paradox of voting under an urn model: the effect of homogeneity. Public Choice 47(2), 377\u2013387 (1985). \nhttps:\/\/doi.org\/10.1007\/BF00127533","journal-title":"Public Choice"},{"key":"1_CR13","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1093\/oxfordhb\/9780199270125.003.0033","volume-title":"Oxford Handbook of Political Behavior","author":"A Blais","year":"2007","unstructured":"Blais, A.: Turnout in elections. In: Dalton, R.E., Klingemann, H.D. (eds.) Oxford Handbook of Political Behavior, pp. 621\u2013635. Oxford University Press, Oxford (2007). \nhttps:\/\/doi.org\/10.1093\/oxfordhb\/9780199270125.003.0033"},{"issue":"2","key":"1_CR14","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1111\/j.1467-8497.1959.tb01197.x","volume":"5","author":"RH Brookes","year":"1959","unstructured":"Brookes, R.H.: Electoral distortion in New Zealand. Aust. J. Polit. Hist. 5(2), 218\u2013223 (1959). \nhttps:\/\/doi.org\/10.1111\/j.1467-8497.1959.tb01197.x","journal-title":"Aust. J. Polit. Hist."},{"key":"1_CR15","first-page":"306","volume-title":"The British General Election of 1950","author":"DE Butler","year":"1951","unstructured":"Butler, D.E.: Appendix. In: Nicholas, H.G. (ed.) The British General Election of 1950, pp. 306\u2013333. Macmillan, London (1951)"},{"issue":"02","key":"1_CR16","doi-asserted-by":"publisher","first-page":"320","DOI":"10.2307\/1956652","volume":"79","author":"BE Cain","year":"1985","unstructured":"Cain, B.E.: Assessing the partisan effects of redistricting. Am. Polit. Sci. Rev. 79(02), 320\u2013333 (1985). \nhttps:\/\/doi.org\/10.2307\/1956652","journal-title":"Am. Polit. Sci. Rev."},{"issue":"300","key":"1_CR17","doi-asserted-by":"publisher","first-page":"853","DOI":"10.2307\/2229705","volume":"75","author":"CD Campbell","year":"1965","unstructured":"Campbell, C.D., Tullock, G.: A measure of the importance of cyclical majorities. Econ. J. 75(300), 853 (1965). \nhttps:\/\/doi.org\/10.2307\/2229705","journal-title":"Econ. J."},{"issue":"3","key":"1_CR18","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1561\/100.00012033","volume":"8","author":"J Chen","year":"2013","unstructured":"Chen, J., Rodden, J.: Unintentional gerrymandering: political geography and electoral bias in legislatures. Q. J. Polit. Sci. 8(3), 239\u2013269 (2013). \nhttps:\/\/doi.org\/10.1561\/100.00012033","journal-title":"Q. J. Polit. Sci."},{"issue":"4","key":"1_CR19","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1089\/elj.2015.0317","volume":"14","author":"J Chen","year":"2015","unstructured":"Chen, J., Rodden, J.: Cutting through the thicket: redistricting simulations and the detection of partisan gerrymanders. Election Law J. Rules Politics Policy 14(4), 331\u2013345 (2015). \nhttps:\/\/doi.org\/10.1089\/elj.2015.0317","journal-title":"Election Law J. Rules Politics Policy"},{"issue":"2","key":"1_CR20","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/S0962-6298(99)00047-5","volume":"19","author":"C Cirincione","year":"2000","unstructured":"Cirincione, C., Darling, T.A., O\u2019Rourke, T.G.: Assessing South Carolina\u2019s 1990s congressional districting. Polit. Geogr. 19(2), 189\u2013211 (2000). \nhttps:\/\/doi.org\/10.1016\/S0962-6298(99)00047-5","journal-title":"Polit. Geogr."},{"key":"1_CR21","volume-title":"Introduction to Mathematical Sociology","author":"JS Coleman","year":"1964","unstructured":"Coleman, J.S.: Introduction to Mathematical Sociology. Free Press, New York (1964)"},{"issue":"4","key":"1_CR22","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1002\/zamm.19230030407","volume":"3","author":"F Eggenberger","year":"1923","unstructured":"Eggenberger, F., P\u00f3lya, G.: \u00fcber die Statistik verketteter Vorg\u00e4nge. Zeitschrift f\u00fcr Angewandte Mathematik und Mechanik 3(4), 279\u2013289 (1923). \nhttps:\/\/doi.org\/10.1002\/zamm.19230030407","journal-title":"Zeitschrift f\u00fcr Angewandte Mathematik und Mechanik"},{"key":"1_CR23","volume-title":"The Spatial Theory of Voting: An Introduction","author":"JM Enelow","year":"1984","unstructured":"Enelow, J.M., Hinich, M.J.: The Spatial Theory of Voting: An Introduction. Cambridge University Press, Cambridge (1984)"},{"issue":"4","key":"1_CR24","doi-asserted-by":"publisher","first-page":"465","DOI":"10.2307\/439420","volume":"2","author":"RL Engstrom","year":"1977","unstructured":"Engstrom, R.L., Wildgen, J.K.: Pruning thorns from the thicket: an empirical test of the existence of racial gerrymandering. Legis. Stud. Q. 2(4), 465\u2013479 (1977). \nhttps:\/\/doi.org\/10.2307\/439420","journal-title":"Legis. Stud. Q."},{"key":"1_CR25","unstructured":"Fifield, B., Higgins, M., Imai, K.: A new automated redistricting simulator using Markov Chain Monte Carlo. Working Paper, Princeton University, Princeton, NJ (2015)"},{"issue":"2","key":"1_CR26","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1017\/psrm.2016.48","volume":"6","author":"F Foos","year":"2018","unstructured":"Foos, F., John, P.: Parties are no civic charities: voter contact and the changing partisan composition of the electorate. Polit. Sci. Res. Methods 6(2), 283\u2013298 (2018). \nhttps:\/\/doi.org\/10.1017\/psrm.2016.48","journal-title":"Polit. Sci. Res. Methods"},{"issue":"1","key":"1_CR27","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1257\/aer.98.1.113","volume":"98","author":"JN Friedman","year":"2008","unstructured":"Friedman, J.N., Holden, R.T.: Optimal gerrymandering: sometimes pack, but never crack. Am. Econ. Rev. 98(1), 113\u2013144 (2008). \nhttps:\/\/doi.org\/10.1257\/aer.98.1.113","journal-title":"Am. Econ. Rev."},{"issue":"3","key":"1_CR28","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1086\/661511","volume":"54","author":"RG Fryer","year":"2011","unstructured":"Fryer, R.G., Holden, R.: Measuring the compactness of political districting plans. J. Law Econ. 54(3), 493\u2013535 (2011). \nhttps:\/\/doi.org\/10.1086\/661511","journal-title":"J. Law Econ."},{"key":"1_CR29","doi-asserted-by":"publisher","unstructured":"Garand, J.C., Parent, T.W.: Representation, swing, and bias in U.S. Presidential Elections, 1872\u20131988. Am. J. Polit. Sci. 35(4), 1011 (1991). \nhttps:\/\/doi.org\/10.2307\/2111504","DOI":"10.2307\/2111504"},{"issue":"505","key":"1_CR30","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1080\/01621459.2013.842173","volume":"109","author":"G Geenens","year":"2014","unstructured":"Geenens, G.: Probit transformation for kernel density estimation on the unit interval. J. Am. Stat. Assoc. 109(505), 346\u2013358 (2014). \nhttps:\/\/doi.org\/10.1080\/01621459.2013.842173","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"1_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01725789","volume":"26","author":"WV Gehrlein","year":"1976","unstructured":"Gehrlein, W.V., Fishburn, P.C.: Condorcet\u2019s paradox and anonymous preference profiles. Public Choice 26(1), 1\u201318 (1976). \nhttps:\/\/doi.org\/10.1007\/BF01725789","journal-title":"Public Choice"},{"issue":"410","key":"1_CR32","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1080\/01621459.1990.10476199","volume":"85","author":"A Gelman","year":"1990","unstructured":"Gelman, A., King, G.: Estimating the electoral consequences of legislative redistricting. J. Am. Stat. Assoc. 85(410), 274\u2013282 (1990)","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"1_CR33","doi-asserted-by":"publisher","first-page":"514","DOI":"10.2307\/2111417","volume":"38","author":"A Gelman","year":"1994","unstructured":"Gelman, A., King, G.: A unified method of evaluating electoral systems and redistricting plans. Am. J. Polit. Sci. 38(2), 514\u2013554 (1994)","journal-title":"Am. J. Polit. Sci."},{"issue":"3","key":"1_CR34","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1111\/j.1751-5823.2002.tb00178.x","volume":"70","author":"AL Gibbs","year":"2002","unstructured":"Gibbs, A.L., Su, F.E.: On choosing and bounding probability metrics. Int. Stat. Rev. 70(3), 419\u2013435 (2002). \nhttps:\/\/doi.org\/10.1111\/j.1751-5823.2002.tb00178.x","journal-title":"Int. Stat. Rev."},{"issue":"3","key":"1_CR35","first-page":"295","volume":"9","author":"B Grofman","year":"1983","unstructured":"Grofman, B.: Measures of bias and proportionality in seats-votes relationships. Polit. Methodol. 9(3), 295\u2013327 (1983)","journal-title":"Polit. Methodol."},{"issue":"1","key":"1_CR36","first-page":"77","volume":"33","author":"B Grofman","year":"1985","unstructured":"Grofman, B.: Criteria for districting: a social science perspective. UCLA Law Rev. 33(1), 77\u2013184 (1985)","journal-title":"UCLA Law Rev."},{"key":"1_CR37","doi-asserted-by":"publisher","unstructured":"Grofman, B., King, G.: The future of partisan symmetry as a judicial test for partisan gerrymandering after LULAC v. Perry. Election Law J. Rules Polit. Policy 6(1), 2\u201335 (2007). \nhttps:\/\/doi.org\/10.1089\/elj.2006.6002","DOI":"10.1089\/elj.2006.6002"},{"key":"1_CR38","volume-title":"Seats, Votes, and the Spatial Organisation of Elections","author":"G Gudgin","year":"1979","unstructured":"Gudgin, G., Taylor, P.J.: Seats, Votes, and the Spatial Organisation of Elections. Pion, London (1979)"},{"issue":"2","key":"1_CR39","doi-asserted-by":"publisher","first-page":"593","DOI":"10.2307\/1342611","volume":"116","author":"S Issacharoff","year":"2002","unstructured":"Issacharoff, S.: Gerrymandering and political cartels. Harvard Law Rev. 116(2), 593\u2013648 (2002). \nhttps:\/\/doi.org\/10.2307\/1342611","journal-title":"Harvard Law Rev."},{"issue":"1","key":"1_CR40","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/0022-0531(72)90119-6","volume":"5","author":"D Jamison","year":"1972","unstructured":"Jamison, D., Luce, E.: Social homogeneity and the probability of intransitive majority rule. J. Econ. Theory 5(1), 79\u201387 (1972)","journal-title":"J. Econ. Theory"},{"key":"1_CR41","volume-title":"Urn Models and Their Applications: An Approach to Modern Discrete Probability Theory","author":"NL Johnson","year":"1977","unstructured":"Johnson, N.L., Kotz, S.: Urn Models and Their Applications: An Approach to Modern Discrete Probability Theory. Wiley, New York (1977)"},{"issue":"1","key":"1_CR42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0962-6298(01)00070-1","volume":"21","author":"R Johnston","year":"2002","unstructured":"Johnston, R.: Manipulating maps and winning elections: measuring the impact of malapportionment and gerrymandering. Polit. Geogr. 21(1), 1\u201331 (2002). \nhttps:\/\/doi.org\/10.1016\/S0962-6298(01)00070-1","journal-title":"Polit. Geogr."},{"key":"1_CR43","unstructured":"Johnston, R.J.: Political, Electoral, and Spatial Systems: An Essay in Political Geography. Contemporary Problems in Geography. Clarendon Press; Oxford University Press, Oxford; New York (1979)"},{"issue":"2","key":"1_CR44","doi-asserted-by":"publisher","first-page":"947","DOI":"10.1016\/j.csda.2005.09.014","volume":"51","author":"J Karvanen","year":"2006","unstructured":"Karvanen, J.: Estimation of quantile mixtures via L-moments and trimmed L-moments. Comput. Stat. Data Anal. 51(2), 947\u2013959 (2006). \nhttps:\/\/doi.org\/10.1016\/j.csda.2005.09.014","journal-title":"Comput. Stat. Data Anal."},{"issue":"1","key":"1_CR45","doi-asserted-by":"publisher","first-page":"15","DOI":"10.2307\/2585758","volume":"93","author":"JN Katz","year":"1999","unstructured":"Katz, J.N., King, G.: A statistical model for multiparty electoral data. Am. Polit. Sci. Rev. 93(1), 15\u201332 (1999). \nhttps:\/\/doi.org\/10.2307\/2585758","journal-title":"Am. Polit. Sci. Rev."},{"issue":"3","key":"1_CR46","doi-asserted-by":"publisher","first-page":"183","DOI":"10.2307\/588113","volume":"1","author":"MG Kendall","year":"1950","unstructured":"Kendall, M.G., Stuart, A.: The law of the cubic proportion in election results. Br. J. Sociol. 1(3), 183\u2013196 (1950). \nhttps:\/\/doi.org\/10.2307\/588113","journal-title":"Br. J. Sociol."},{"issue":"4","key":"1_CR47","doi-asserted-by":"publisher","first-page":"1251","DOI":"10.2307\/1962588","volume":"81","author":"G King","year":"1987","unstructured":"King, G., Browning, R.X.: Democratic representation and partisan bias in Congressional elections. Am. Polit. Sci. Rev. 81(4), 1251 (1987). \nhttps:\/\/doi.org\/10.2307\/1962588","journal-title":"Am. Polit. Sci. Rev."},{"issue":"6","key":"1_CR48","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.2307\/1914217","volume":"42","author":"K Kuga","year":"1974","unstructured":"Kuga, K., Nagatani, H.: Voter antagonism and the paradox of voting. Econometrica 42(6), 1045\u20131067 (1974). \nhttps:\/\/doi.org\/10.2307\/1914217","journal-title":"Econometrica"},{"issue":"1","key":"1_CR49","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.mathsocsci.2011.04.006","volume":"62","author":"D Lepelley","year":"2011","unstructured":"Lepelley, D., Merlin, V., Rouet, J.L.: Three ways to compute accurately the probability of the referendum paradox. Math. Soc. Sci. 62(1), 28\u201333 (2011). \nhttps:\/\/doi.org\/10.1016\/j.mathsocsci.2011.04.006","journal-title":"Math. Soc. Sci."},{"issue":"3","key":"1_CR50","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1093\/pan\/mps017","volume":"20","author":"DA Linzer","year":"2012","unstructured":"Linzer, D.A.: The relationship between seats and votes in multiparty systems. Polit. Anal. 20(3), 400\u2013416 (2012). \nhttps:\/\/doi.org\/10.1093\/pan\/mps017","journal-title":"Polit. Anal."},{"key":"1_CR51","unstructured":"Mattingly, J.C., Vaughn, C.: Redistricting and the will of the people. Technical report, \narXiv: 1410.8796\n\n [physics.soc-ph], October 2014"},{"issue":"3","key":"1_CR52","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1111\/j.1540-5907.2006.00213.x","volume":"50","author":"SD McClurg","year":"2006","unstructured":"McClurg, S.D.: The electoral relevance of political talk: examining disagreement and expertise effects in social networks on political participation. Am. J. Polit. Sci. 50(3), 737\u2013754 (2006). \nhttps:\/\/doi.org\/10.1111\/j.1540-5907.2006.00213.x","journal-title":"Am. J. Polit. Sci."},{"issue":"1","key":"1_CR53","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1111\/lsq.12033","volume":"39","author":"E McGhee","year":"2014","unstructured":"McGhee, E.: Measuring partisan bias in single-member district electoral systems: measuring partisan bias. Legis. Stud. Q. 39(1), 55\u201385 (2014). \nhttps:\/\/doi.org\/10.1111\/lsq.12033","journal-title":"Legis. Stud. Q."},{"issue":"3","key":"1_CR54","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1080\/105846099198659","volume":"16","author":"JM Mcleod","year":"1999","unstructured":"Mcleod, J.M., Scheufele, D.A., Moy, P.: Community, communication, and participation: the role of mass media and interpersonal discussion in local political participation. Polit. Commun. 16(3), 315\u2013336 (1999). \nhttps:\/\/doi.org\/10.1080\/105846099198659","journal-title":"Polit. Commun."},{"issue":"1","key":"1_CR55","doi-asserted-by":"publisher","first-page":"23","DOI":"10.2307\/2110786","volume":"28","author":"S Merrill","year":"1984","unstructured":"Merrill, S.: A comparison of efficiency of multicandidate electoral systems. Am. J. Polit. Sci. 28(1), 23\u201348 (1984). \nhttps:\/\/doi.org\/10.2307\/2110786","journal-title":"Am. J. Polit. Sci."},{"key":"1_CR56","first-page":"185","volume":"33","author":"RG Niemi","year":"1985","unstructured":"Niemi, R.G.: Relationship between votes and seats: the ultimate question in political gerrymandering. UCLA Law Rev. 33, 185\u2013212 (1985)","journal-title":"UCLA Law Rev."},{"issue":"4","key":"1_CR57","doi-asserted-by":"publisher","first-page":"1304","DOI":"10.2307\/1954541","volume":"72","author":"RG Niemi","year":"1978","unstructured":"Niemi, R.G., Deegan, J.: A theory of political districting. Am. Polit. Sci. Rev. 72(4), 1304\u20131323 (1978). \nhttps:\/\/doi.org\/10.2307\/1954541","journal-title":"Am. Polit. Sci. Rev."},{"issue":"1","key":"1_CR58","doi-asserted-by":"publisher","first-page":"75","DOI":"10.2307\/439910","volume":"11","author":"RG Niemi","year":"1986","unstructured":"Niemi, R.G., Fett, P.: The swing ratio: an explanation and an assessment. Legis. Stud. Q. 11(1), 75\u201390 (1986). \nhttps:\/\/doi.org\/10.2307\/439910","journal-title":"Legis. Stud. Q."},{"key":"1_CR59","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03782-9","volume-title":"Voting Paradoxes and How to Deal with Them","author":"H Nurmi","year":"1999","unstructured":"Nurmi, H.: Voting Paradoxes and How to Deal with Them. Springer, New York (1999). \nhttps:\/\/doi.org\/10.1007\/978-3-662-03782-9"},{"issue":"2","key":"1_CR60","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1111\/j.1467-8306.1982.tb01817.x","volume":"72","author":"J O\u2019Loughlin","year":"1982","unstructured":"O\u2019Loughlin, J.: The identification and evaluation of racial gerrymandering. Ann. Assoc. Am. Geogr. 72(2), 165\u2013184 (1982). \nhttps:\/\/doi.org\/10.1111\/j.1467-8306.1982.tb01817.x","journal-title":"Ann. Assoc. Am. Geogr."},{"key":"1_CR61","volume-title":"On the Objective Study of Crowd Behaviour","author":"LS Penrose","year":"1952","unstructured":"Penrose, L.S.: On the Objective Study of Crowd Behaviour. H.K. Lewis, London (1952)"},{"issue":"2","key":"1_CR62","first-page":"301","volume":"9","author":"DD Polsby","year":"1991","unstructured":"Polsby, D.D., Popper, R.D.: The third criterion: compactness as a procedural safeguard against partisan gerrymandering. Yale Law Policy Rev. 9(2), 301\u2013353 (1991)","journal-title":"Yale Law Policy Rev."},{"issue":"2","key":"1_CR63","first-page":"117","volume":"1","author":"G P\u00f3lya","year":"1930","unstructured":"P\u00f3lya, G.: Sur quelques points de la th\u00e9orie des probabilit\u00e9s. Ann. l\u2019inst. Henri Poincar\u00e9 1(2), 117\u2013161 (1930)","journal-title":"Ann. l\u2019inst. Henri Poincar\u00e9"},{"issue":"1","key":"1_CR64","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/s10479-013-1468-3","volume":"215","author":"F Pukelsheim","year":"2014","unstructured":"Pukelsheim, F.: Biproportional scaling of matrices and the iterative proportional fitting procedure. Ann. Oper. Res. 215(1), 269\u2013283 (2014). \nhttps:\/\/doi.org\/10.1007\/s10479-013-1468-3","journal-title":"Ann. Oper. Res."},{"key":"1_CR65","volume-title":"Behavioral Social Choice: Probabilistic Models, Statistical Inference, and Applications","author":"M Regenwetter","year":"2006","unstructured":"Regenwetter, M., Grofman, B., Tsetlin, I., Marley, A.: Behavioral Social Choice: Probabilistic Models, Statistical Inference, and Applications. Cambridge University Press, Cambridge (2006)"},{"key":"1_CR66","doi-asserted-by":"publisher","unstructured":"Sano, F., Hisakado, M., Mori, S.: Mean field voter model of election to the House of Representatives in Japan. In: APEC-SSS2016, p. 011016. Journal of the Physical Society of Japan (2017). \nhttps:\/\/doi.org\/10.7566\/JPSCP.16.011016","DOI":"10.7566\/JPSCP.16.011016"},{"key":"1_CR67","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/S0167-5060(08)70866-5","volume":"8","author":"RG Stanton","year":"1980","unstructured":"Stanton, R.G.: A result of Macmahon on electoral predictions. Ann. Discrete Math. 8, 163\u2013167 (1980). \nhttps:\/\/doi.org\/10.1016\/S0167-5060(08)70866-5","journal-title":"Ann. Discrete Math."},{"issue":"4","key":"1_CR68","doi-asserted-by":"publisher","first-page":"684","DOI":"10.2307\/2045462","volume":"88","author":"T Steerneman","year":"1983","unstructured":"Steerneman, T.: On the total variation and hellinger distance between signed measures; an application to product measures. Proc. Am. Math. Soc. 88(4), 684\u2013688 (1983). \nhttps:\/\/doi.org\/10.2307\/2045462","journal-title":"Proc. Am. Math. Soc."},{"issue":"2","key":"1_CR69","first-page":"831","volume":"82","author":"NO Stephanopoulos","year":"2015","unstructured":"Stephanopoulos, N.O., McGhee, E.M.: Partisan gerrymandering and the efficiency gap. Univ. Chicago Law Rev. 82(2), 831\u2013900 (2015)","journal-title":"Univ. Chicago Law Rev."},{"key":"1_CR70","unstructured":"Szufa, S.: Optimal gerrymandering for simplified districts. Working Paper, Jagiellonian Center for Quantitative Research in Political Science, Krak\u00f3w (2019)"},{"key":"1_CR71","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/978-3-642-20441-8_9","volume-title":"Electoral Systems. Paradoxes, Assumptions, and Procedures","author":"TN Tideman","year":"2012","unstructured":"Tideman, T.N., Plassmann, F.: Modeling the outcomes of vote-casting in actual elections. In: Felsenthal, D.S., Machover, M. (eds.) Electoral Systems. Paradoxes, Assumptions, and Procedures, pp. 217\u2013251. Springer, Heidelberg (2012). \nhttps:\/\/doi.org\/10.1007\/978-3-642-20441-8_9"},{"issue":"1","key":"1_CR72","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1093\/pan\/10.1.66","volume":"10","author":"M Tomz","year":"2002","unstructured":"Tomz, M., Tucker, J.A., Wittenberg, J.: An easy and accurate regression model for multiparty electoral data. Polit. Anal. 10(1), 66\u201383 (2002). \nhttps:\/\/doi.org\/10.1093\/pan\/10.1.66","journal-title":"Polit. Anal."},{"issue":"2","key":"1_CR73","doi-asserted-by":"publisher","first-page":"540","DOI":"10.2307\/1958782","volume":"67","author":"ER Tufte","year":"1973","unstructured":"Tufte, E.R.: The relationship between seats and votes in two-party systems. Am. Polit. Sci. Rev. 67(2), 540\u2013554 (1973). \nhttps:\/\/doi.org\/10.2307\/1958782","journal-title":"Am. Polit. Sci. Rev."},{"issue":"3","key":"1_CR74","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1017\/S0007123400004257","volume":"15","author":"G Upton","year":"1985","unstructured":"Upton, G.: Blocks of voters and the cube \u2018law\u2019. Br. J. Polit. Sci. 15(3), 388\u2013398 (1985). \nhttps:\/\/doi.org\/10.1017\/S0007123400004257","journal-title":"Br. J. Polit. Sci."},{"issue":"3","key":"1_CR75","doi-asserted-by":"publisher","first-page":"423","DOI":"10.2307\/439554","volume":"5","author":"JK Wildgen","year":"1980","unstructured":"Wildgen, J.K., Engstrom, R.L.: Spatial distribution of partisan support and the seats\/votes relationship. Legis. Stud. Q. 5(3), 423\u2013435 (1980). \nhttps:\/\/doi.org\/10.2307\/439554","journal-title":"Legis. Stud. Q."},{"key":"1_CR76","unstructured":"Yamamoto, T.: A multinomial response model for varying choice sets, with application to partially contested multiparty elections. Working Paper, Massachusetts Institute of Technology, Cambridge, MA (2014)"},{"issue":"1","key":"1_CR77","doi-asserted-by":"publisher","first-page":"105","DOI":"10.2307\/439947","volume":"13","author":"HP Young","year":"1988","unstructured":"Young, H.P.: Measuring the compactness of legislative districts. Legis. Stud. Q. 13(1), 105\u2013115 (1988). \nhttps:\/\/doi.org\/10.2307\/439947","journal-title":"Legis. Stud. Q."}],"container-title":["Lecture Notes in Computer Science","Transactions on Computational Collective Intelligence XXXIV"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-60555-4_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,28]],"date-time":"2020-04-28T10:04:31Z","timestamp":1588068271000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-60555-4_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783662605547","9783662605554"],"references-count":77,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-60555-4_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"1 November 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}