Part 4 of 5: A New MMP Method

Transcription

1 Part 4 of 5: A New MMP Method (draft, 28 March 2008) Markus Schulze Markus.Schulze@Alumn.TU-Berln.de Summary. In ths paper, we explan how proportonal representaton by the sngle transferable vote can be ncorporated nto a mxed member proportonal representaton scheme. Keywords and Phrases: mxed member proportonal representaton, proportonal rankngs, sngle transferable vote JEL Classfcaton Number: D71 Ths paper s the fourth part of a seres of papers that can be downloaded here:

2 Contents 1. Introducton The Dstrct Vote The Dstrcts The Dstrct Ballot The Dstrct Vote Wnners The Party Vote The Party Ballot Allocaton of Seats to Partes Allocaton of the Party Seats to ths Party s Dstrct Organzatons The Party Vote Wnners Vacant Seats Introducton Today, many countres use proportonal representaton by party lsts (PRPL). Ths electon method has two serous problems. Frst, t gves too much power to the party machnes that control the nomnaton processes. Second, t allows proportonalty only accordng to one crteron: party afflatons. A possble way to crcumvent the shortcomngs of PRPL s through proportonal representaton by the sngle transferable vote (STV). Here, each voter gets a complete lst of all canddates and ranks these canddates n order of preference. The ballots are then counted n such a manner that the followng property (Droop proportonalty) s satsfed: Suppose N s the number of voters and M s the number of seats. Then: If N 1 > 0 voters strctly prefer every canddate of a gven set of C 1 canddates to every other canddate, then at least mn { (M+1) N 1 /N - 1; C 1 } canddates of ths set must be elected. To cope wth the large number of canddates who are typcally runnng for a parlament, the electorate s dvded nto dstrcts of e.g. 5 seats each and the same canddate must not run n more than one dstrct. Droop proportonalty s then satsfed only on the dstrct level, so that t can happen that a party wth about 15% of the votes does not wn a sngle seat. 2

3 Therefore, people who promote STV methods n countres that use PRPL are frequently confronted wth the defamaton that they were dshonest and that ther real am was to ncrease the threshold for small partes to gan parlamentary representaton from a legal threshold of typcally about 5% n countres that are usng PRPL to a natural threshold of typcally about 15% n countres that are usng STV. Because of ths reason, t mght be a useful strategy to nclude nto the STV proposal a compensaton of party proportonalty on the natonal level. One way to acheve ths compensaton of party proportonalty s through mxed member proportonal representaton (MMP). Here, each voter gets two ballots: a dstrct ballot and a party ballot. Wth the dstrct ballots, the voters elect ther dstrct representatves. Wth the party ballots, the voters ndcate ther party support. When, on the natonal level, the elected dstrct representatves do not reflect party proportonalty (as ndcated by the party ballots) n an approprate manner, then addtonal representatves are added to the parlament to compensate party proportonalty (so that the total sze of the parlament ncreases). Usually, these addtonal representatves are chosen from canddate lsts that have been submtted by the partes n advance of the electons. The man problem of ths way to choose these addtonal representatves s that, agan, t gves too much power to the party machnes that control the nomnaton processes. One way to avod ths problem of the common way to choose these addtonal representatves s to use MMP wth the best loser method. Here, when a party gets addtonal representatves, then these addtonal representatves are those canddates who performed best n ther respectve dstrcts wthout beng elected. Advantage of the best loser method s that, wth ther dstrct votes, the voters do not only elect ther dstrct representatves, they also decde (n those cases where a party gets addtonal representatves) who these addtonal representatves are. However, to be able to combne STV wth the best loser method, we need a heurstc that tells us how well the canddates performed n ther respectve dstrcts. Here, we propose that, n each dstrct, a proportonal rankng of all canddates should be calculated. A proportonal rankng s a complete rankng (lnear orderng) of all canddates such that, for every Z, the frst Z canddates reflect the voters as proportonally as possble. We propose that the Schulze proportonal rankng should be used, as descrbed n secton 6 of the second paper of ths seres of papers. When a party wns addtonal representatves, then those canddates of ths party are elected who dd not wn a dstrct seat, but who are ranked hghest n the proportonal rankngs of ther respectve dstrcts. 3

4 In secton 2 of ths paper, we ntroduce the detals of the dstrct vote. We explan the creaton of the dstrcts (secton 2.1), the dstrct ballot (secton 2.2), and the determnaton of the dstrct vote wnners (secton 2.3). In secton 3, we explan the detals of the party vote. The party ballot s llustrated n secton 3.1. In sectons 3.2 and 3.3, we show how to determne how many addtonal representatves a gven party gets n a gven dstrct. In secton 3.4, these addtonal representatves are chosen. In secton 4, vacant seats are flled. Where concrete numbers are needed, we use the electons to the Berln House of Representatves (Abgeordnetenhaus von Berln) to llustrate the proposed method. Currently, the electoral law says that the House conssts of at least 130 members. 78 members (= 60%) are elected by frst-past-the-post (FPP) n sngle wnner dstrcts (sngle member pluralty, SMP); at least addtonal 52 members are elected by closed party lsts to compensate party proportonalty. However, as FPP does not lead to proportonal results, usually sgnfcantly more than 52 addtonal members are needed to compensate party proportonalty, so that the House usually has a sze of about 150 members. We recommend that, n future, 115 of the 130 members (about 90%) should be elected by STV n dstrcts of 8 to 22 seats. Ths s possble wthout creatng too many addtonal members, because STV already leads to very proportonal results. 2. The Dstrct Vote 2.1. The Dstrcts Berln s currently dvded nto 12 boroughs (sng.: Bezrk, plur.: Bezrke). borough elgble voters (on 17 Sep. 2006) 1 Mtte 190,550 2 Fredrchshan-Kreuzberg 165,331 3 Pankow 274,380 4 Charlottenburg-Wlmersdorf 216,374 5 Spandau 160,411 6 Stegltz-Zehlendorf 213,787 7 Tempelhof-Schöneberg 231,249 8 Neukölln 193,014 9 Treptow-Köpenck 193, Marzahn-Hellersdorf 201, Lchtenberg 201, Renckendorf 184,143 total: 2,425,480 Table 2.1.1: The 12 Berln boroughs 4

5 Table 2.1.2: The 12 Berln boroughs We recommend that the dstrcts for the electons to the Berln House of Representatves should be the 12 Berln boroughs. When the Hll- Huntngton method s beng used to allocate the 115 dstrct seats to the 12 dstrcts, then we get two 8-seat dstrcts (Fredrchshan-Kreuzberg, Spandau), fve 9-seat dstrcts (Mtte, Neukölln, Treptow-Köpenck, Lchtenberg, Renckendorf), three 10-seat dstrcts (Charlottenburg- Wlmersdorf, Stegltz-Zehlendorf, Marzahn-Hellersdorf), one 11-seat dstrct (Tempelhof-Schöneberg), and one 13-seat dstrct (Pankow). See table Alternatvely, Berln could be dvded nto 6 dstrcts: Central (Mtte and Fredrchshan-Kreuzberg), North (Pankow and Renckendorf), West (Charlottenburg-Wlmersdorf and Spandau), South-West (Stegltz- Zehlendorf and Tempelhof-Schöneberg), South-East (Neukölln and Treptow-Köpenck), and East (Marzahn-Hellersdorf and Lchtenberg). Wth the Hll-Huntngton method, we would then get one 17-seat dstrct (Central), two 18-seat dstrcts (West, South-East), one 19-seat dstrct (East), one 21-seat dstrct (South-West), and one 22-seat dstrct (North). 5

6 dstrct elgble voters number of elgble voters dvded by (1 2)... (2 3)... (3 4)... (4 5)... (5 6)... (6 7)... (7 8)... (8 9)... (9 10)... (10 11)... (11 12)... (12 13)... (13 14) Mtte 190, ,739 77,791 55,007 42,608 34,789 29,402 25,463 22,456 20,085 18,168 16,585 15,256 14,124 (21. seat) (34. seat) (46. seat) (58. seat) (72. seat) (83. seat) (97. seat) (109. seat) Fredrchshan- 165, ,906 67,496 47,726 36,969 30,185 25,511 22,093 19,484 17,427 15,763 14,390 13,237 12,255 Kreuzberg (23. seat) (36. seat) (52. seat) (64. seat) (80. seat) (95. seat) (110. seat) Pankow 274, , ,015 79,206 61,353 50,094 42,337 36,665 32,335 28,922 26,161 23,881 21,967 20,338 (13. seat) (25. seat) (31. seat) (41. seat) (49. seat) (59. seat) (67. seat) (76. seat) (85. seat) (92. seat) (102. seat) (112. seat) Charlottenburg- 216, ,999 88,334 62,461 48,382 39,504 33,387 28,914 25,499 22,807 20,630 18,832 17,323 16,038 Wlmersdorf (15. seat) (27. seat) (39. seat) (50. seat) (62. seat) (74. seat) (86. seat) (96. seat) (106. seat) Spandau 160, ,427 65,487 46,306 35,868 29,286 24,751 21,435 18,904 16,908 15,294 13,961 12,843 11,890 (24. seat) (38. seat) (53. seat) (68. seat) (84. seat) (99. seat) (114. seat) Stegltz- 213, ,170 87,278 61,714 47,804 39,031 32,988 28,568 25,195 22,535 20,383 18,607 17,116 15,846 Zehlendorf (16. seat) (28. seat) (40. seat) (51. seat) (63. seat) (75. seat) (87. seat) (98. seat) (108. seat) Tempelhof- 231, ,517 94,407 66,755 51,708 42,220 35,682 30,901 27,252 24,375 22,048 20,127 18,514 17,141 Schöneberg (14. seat) (26. seat) (37. seat) (48. seat) (60. seat) (69. seat) (79. seat) (89. seat) (101. seat) (111. seat) Neukölln 193, ,481 78,797 55,718 43,159 35,239 29,782 25,792 22,746 20,345 18,403 16,799 15,453 14,307 (20. seat) (33. seat) (45. seat) (57. seat) (71. seat) (82. seat) (94. seat) (107. seat) Treptow- 193, ,133 79,174 55,984 43,365 35,407 29,924 25,915 22,855 20,442 18,491 16,879 15,527 14,375 Köpenck (19. seat) (32. seat) (44. seat) (56. seat) (70. seat) (81. seat) (93. seat) (105. seat) Marzahn- 201, ,276 82,143 58,084 44,991 36,735 31,047 26,887 23,712 21,209 19,184 17,512 16,109 14,914 Hellersdorf (17. seat) (29. seat) (42. seat) (54. seat) (65. seat) (77. seat) (90. seat) (103. seat) (115. seat) Lchtenberg 201, ,196 82,097 58,051 44,966 36,714 31,029 26,872 23,699 21,197 19,173 17,503 16,100 14,906 (18. seat) (30. seat) (43. seat) (55. seat) (66. seat) (78. seat) (91. seat) (104. seat) Renckendorf 184, ,208 75,176 53,157 41,175 33,619 28,413 24,607 21,701 19,410 17,557 16,027 14,743 13,649 (22. seat) (35. seat) (47. seat) (61. seat) (73. seat) (88. seat) (100. seat) (113. seat) Table 2.1.3: Allocaton of the 115 dstrct seats to the 12 dstrcts accordng to the Hll-Huntngton method When the Hll-Huntngton method s beng used, then, at the frst stage, each dstrct gets one seat. At the second stage, the numbers of elgble voters of each dstrct are dvded by (1 2), (2 3), (3 4), (4 5), (5 6),... and the remanng seats go to the largest quotents. 6

7 2.2. The Dstrct Ballot The same canddate cannot run n more than one dstrct. The same canddate cannot run smultaneously as an ndependent canddate and as a party canddate. The same canddate cannot run for more than one party smultaneously. On the dstrct ballot, the canddates are sorted accordng to ther party afflatons. Canddates wth the same party afflaton are sorted n an order determned by ths party. The ndvdual voter ranks the canddates n order of preference. The ndvdual voter may gve the same preference to more than one canddate.... keep canddates unranked. When a gven voter does not rank all canddates, then ths means (1) that ths voter strctly prefers all ranked canddates to all not ranked canddates and (2) that ths voter s ndfferent between all not ranked canddates.... skp preferences. However, skppng some preferences does not have any mpact on the result of the electons, snce the result of the electons depends only on the order n whch the ndvdual voters ranks the canddates and not on the absolute preferences of the ndvdual voters.... gve preferences to partes. When a gven voter gves a preference to a party, then ths means that each canddate of ths party gets ths preference unless ths voter explctly gves a dfferent preference to ths canddate. Table shows how a cast dstrct ballot could look lke. Table llustrates how ths dstrct ballot would be nterpreted. 7

8 Electons to the Berln House of Representatves on 17. September 2006 Dstrct Ballot for dstrct Fredrchshan-Kreuzberg please rank the canddates n order of preference 01: Socal Democratc Party of Germany (SPD) : Junge-Reyer, Ingeborg : Zackenfels, Stefan : Ktschun, Susanne : Eggert, Björn : Bayram, Canan : Fscher, Slke : Henemann, Sven : Methke, Petra : Kayhan, Sevg : Erdem, Hedye : Klebba, Sgrd : Postler, Lorenz : Hehmke, Andy : Dr. Beckers, Peter : Lorenz, Dort : Borchard, Andreas 02: Chrstan Democratc Unon of Germany (CDU) : Wansner, Kurt : Bleler, Raner : Ruhland, Thomas : Samuray, Sedat : Stry, Ernst-Uwe : Rösner, Helga : Glatzel, Edgar : Schll, Mchael : Müller, Götz : Fretag, Jens-Matthas : Husen, Tmur : Wöhrn, Marna : Taþkýran, Ertan : Przeweslk, Wolfgang : Konschak, Benjamn : Bohl, Danel-Stephan 03: Left Party : Mchels, Martna : Wolf, Udo : Matuschek, Jutta : Zllch, Steffen : Ýzgn, Fgen : Günther, Andreas : Vordenbäumen, Vera : Krüger, Wolfgang : Renauer, Cornela : Bauer, Kerstn : Mldner-Spndler, Knut : Rchter, Clauda : Schüssler, Lothar : Thmm, Helga : Pempel, Joachm : Sommer-Wetter, Regne 04: Allance 90 / The Greens (B 90G) : Ratzmann, Volker : Mutlu, Özcan : Dr. Klotz, Sbyll-Anka : Lux, Benedkt : Herrmann, Clara : Stephan, André : Pohner, Wolfgang : Dr. Altug, Mehmet : Burkert-Eultz, Maranne : Kosche, Hed : Behrendt, Drk : Hauser-Jabs, Chrstne : Schulz, Franz : Kapek, Antje : Wesener, Danel : Çetnkaya, Ýstkbal 13 05: Free Democratc Party of Germany (FDP) : Peters, Frank : Dr. Hansen, Nkolne : Eydner, John : Hohl, Henrch : Salonek, Gumbert-Olaf : Dener, Thomas : Schaefer, Martna : Wolf, Tobas : Dr. Stolz, Peter : Lauf, Sebastan : Paun, Chrstopher : Joecken, Ilka 06: The Republcans (REP) : Dr. Clemens, Björn : Kuhn, Danel : Hnze, Harald Björn Gunnar : Nestmann, Günther 07: Ecologcal Democratc Party (ödp) : Machel-Ebelng, Johannes 08: Cvl Rghts Movement Soldarty (BüSo) : Hnz, Björn 09: Humane Economy Party : Dr. Henrchs, Johannes : Esner, Udo (ndependent) : Stewe, Hauke (ndependent) 20 Table 2.2.1: Dstrct ballot

9 Electons to the Berln House of Representatves on 17. September 2006 Dstrct Ballot for dstrct Fredrchshan-Kreuzberg please rank the canddates n order of preference 01: Socal Democratc Party of Germany (SPD) : Junge-Reyer, Ingeborg : Zackenfels, Stefan : Ktschun, Susanne : Eggert, Björn : Bayram, Canan : Fscher, Slke : Henemann, Sven : Methke, Petra : Kayhan, Sevg : Erdem, Hedye : Klebba, Sgrd : Postler, Lorenz : Hehmke, Andy : Dr. Beckers, Peter : Lorenz, Dort : Borchard, Andreas 14 02: Chrstan Democratc Unon of Germany (CDU) : Wansner, Kurt : Bleler, Raner : Ruhland, Thomas : Samuray, Sedat : Stry, Ernst-Uwe : Rösner, Helga : Glatzel, Edgar : Schll, Mchael : Müller, Götz : Fretag, Jens-Matthas : Husen, Tmur : Wöhrn, Marna : Taþkýran, Ertan : Przeweslk, Wolfgang : Konschak, Benjamn : Bohl, Danel-Stephan 25 03: Left Party : Mchels, Martna : Wolf, Udo : Matuschek, Jutta : Zllch, Steffen : Ýzgn, Fgen : Günther, Andreas : Vordenbäumen, Vera : Krüger, Wolfgang : Renauer, Cornela : Bauer, Kerstn : Mldner-Spndler, Knut : Rchter, Clauda : Schüssler, Lothar : Thmm, Helga : Pempel, Joachm : Sommer-Wetter, Regne 15 04: Allance 90 / The Greens (B 90G) : Ratzmann, Volker : Mutlu, Özcan : Dr. Klotz, Sbyll-Anka : Lux, Benedkt : Herrmann, Clara : Stephan, André : Pohner, Wolfgang : Dr. Altug, Mehmet : Burkert-Eultz, Maranne : Kosche, Hed : Behrendt, Drk : Hauser-Jabs, Chrstne : Schulz, Franz : Kapek, Antje : Wesener, Danel : Çetnkaya, Ýstkbal 13 05: Free Democratc Party of Germany (FDP) : Peters, Frank : Dr. Hansen, Nkolne : Eydner, John : Hohl, Henrch : Salonek, Gumbert-Olaf : Dener, Thomas : Schaefer, Martna : Wolf, Tobas : Dr. Stolz, Peter : Lauf, Sebastan : Paun, Chrstopher : Joecken, Ilka 20 06: The Republcans (REP) : Dr. Clemens, Björn : Kuhn, Danel : Hnze, Harald Björn Gunnar : Nestmann, Günther 25 07: Ecologcal Democratc Party (ödp) : Machel-Ebelng, Johannes 18 08: Cvl Rghts Movement Soldarty (BüSo) : Hnz, Björn 22 09: Humane Economy Party : Dr. Henrchs, Johannes : Esner, Udo (ndependent) : Stewe, Hauke (ndependent) 20 Table 2.2.2: Dstrct ballot

10 2.3. The Dstrct Vote Wnners In each dstrct, a proportonal rankng of all canddates s calculated. For the dstrct Fredrchshan-Kreuzberg, ths proportonal rankng could look as follows: 1. Mutlu (B 90G, canddate ) elected (dstrct vote) 2. Fscher (SPD, canddate ) elected (dstrct vote) 3. Renauer (Left, canddate ) elected (dstrct vote) 4. Junge-Reyer (SPD, canddate ) elected (dstrct vote) 5. Ratzmann (B 90G, canddate ) elected (dstrct vote) 6. İzgn (Left, canddate ) elected (dstrct vote) 7. Klotz (B 90G, canddate ) elected (dstrct vote) 8. Samuray (CDU, canddate ) elected (dstrct vote) 9. Eggert (SPD, canddate ) 10. Henemann (SPD, canddate ) 11. Behrendt (B 90G, canddate ) 12. Wolf (Left, canddate ) 13. Altug (B 90G, canddate ) 14. Bayram (SPD, canddate ) 15. Kosche (B 90G, canddate ) 16. Mchels (Left, canddate ) 17. Bleler (CDU, canddate ) 18. Herrmann (B 90G, canddate ) 19. Zackenfels (SPD, canddate ) 20. Vordenbäumen (Left, canddate ) 21. etc. The dea s: If only the SPD supporters had partcpated, then ths proportonal rankng would have been Fscher, Junge-Reyer, Eggert, Henemann, Bayram, Zackenfels, etc.. If only the B 90G supporters had partcpated, then ths proportonal rankng would have been Mutlu, Ratzmann, Klotz, Behrendt, Altug, Kosche, Herrmann, etc.. If only the Left Party supporters had partcpated, then ths proportonal rankng would have been Renauer, İzgn, Wolf, Mchels, Vordenbäumen, etc.. If only the CDU supporters had partcpated, then ths proportonal rankng would have been Samuray, Bleler, etc.. As Fredrchshan-Kreuzberg s an 8-seat dstrct, the frst 8 canddates of ths proportonal rankng are elected. 3. The Party Vote 3.1. The Party Ballot On the party ballot of a gven dstrct, all those partes are lsted that have nomnated dstrct canddates. The ndvdual voter can vote for one and only one party. Table shows how a cast ballot for dstrct Fredrchshan- Kreuzberg could look lke. 10

11 Electons to the Berln House of Representatves on 17. September 2006 for dstrct Fredrchshan-Kreuzberg Party Ballot please vote for one and only one party X 01: Socal Democratc Party of Germany (SPD) 02: Chrstan Democratc Unon of Germany (CDU) 03: Left Party 04: Allance 90 / The Greens (B 90G) 05: Free Democratc Party of Germany (FDP) X 06: The Republcans (REP) 07: Ecologcal Democratc Party (ödp) 08: Cvl Rghts Movement Soldarty (BüSo) 09: Humane Economy Party Table 3.1.1: Party ballot

12 3.2. Allocaton of Seats to Partes Suppose X s the number of dstrct seats won by ndependent canddates. Suppose D s the number of dstrct seats won by party. Suppose P s the number of party votes for party. Suppose S s the number of seats that wll have been allocated to party durng the allocaton process. We recommend that the rules to allocate the seats to the partes should have the followng propertes: The seats are allocated accordng to the Sante-Laguë method wth 0.75 as frst dvsor. That means: The numbers of party votes for each party are dvded by 0.75, 1.5, 2.5, 3.5, 4.5, 5.5,... and the seats go to the largest quotents. When a gven party wns more dstrct seats than t deserves seats accordng to ts number of party votes, then ths party keeps all these dstrct seats, so that the total sze of the Berln House of Representatves ncreases (overhang seats). The other partes then also get addtonal seats to preserve party proportonalty, so that the total sze of the House ncreases further (compensaton seats). However, the total sze of the House should not be larger than absolutely necessary to preserve party proportonalty, because every addtonal seat compromses the dea that the House should be elected by proportonal representaton by the sngle transferable vote. However, to guarantee that the sze of the House does not vary too much from one electon to the other electon, the mnmum sze s set to 131 members and the maxmum sze s set to 179 members. Therefore, we get 131 X + Σ j S j 179. The consttuton of Berln says that a party has qualfed f and only f t has receved at least 5% of the vald party votes or has won at least one dstrct seat. If a party has not qualfed, then t must not get any seats (threshold clause). Suppose P qual : = Σ j ( P j party j has qualfed ). In Germany, t s tradton that, f party has qualfed and has receved more than half of the votes of the qualfed partes, then party must also get more than half of the seats that are allocated to qualfed partes (majorty clause). Therefore, we get: If party has qualfed and P > P qual / 2, then S > ( Σ j S j ) / 2. The total number of seats X + Σ j S j should be odd (stalemate clause). 12

13 Therefore, we propose the followng method to allocate the seats to the partes: s s the number of seats already allocated to party. We wll concentrate on the qualfed partes. Partes, that have not qualfed, wll be gnored n the followng allocaton procedure. If no party has qualfed, then no seats wll be allocated on the cty-wde level. Stage 1: Stage 2: For each party, we start wth s : = D. r : = P / ( D ) for each party wth D > 1. r : = P / 0.75 for each party wth D = 1. r : = for each party wth D = 0. Y : = mn r. [The dea s: As soon as the next quotent T, that wll be rewarded wth a seat, s equal to or strctly smaller than Y, party proportonalty has been acheved, so that the allocaton procedure can stop. Addng more seats would not mprove proportonalty accordng to party afflatons any further, but would worsen proportonalty accordng to whchever other crtera the voters consdered mportant when choosng the dstrct wnners by STV.] 13

14 Stage 3: Repeat ( untl at least one of the termnaton condtons s satsfed ): t : = P / ( s ) for each party wth s > 0. t : = P / 0.75 for each party wth s = 0. T : = max t. U : = max { D t = T }. If at least one of the followng two condtons s satsfed, then the allocaton procedure termnates. Condton #1: The followng four statements are satsfed: Condton #2: (a) X + Σ j s j 131. (b) X + Σ j s j s odd. (c) T Y. (d) There s no party wth P > P qual / 2 and s ( Σ j s j ) / 2. X + Σ j s j = 179. If none of these two condtons s satsfed, then we proceed as follows: If there s a party wth P > P qual / 2 and s ( 1 + Σ j s j ) / 2, then the next seat goes to party. Otherwse: The next seat goes to party wth t = T and D = U. If there s more than one party wth t = T and D = U, then we decde randomly whch party wth t = T and D = U gets the next seat. 14

15 3.3. Allocaton of the Party Seats to ths Party s Dstrct Organzatons As canddates run on the dstrct level and not on a cty-wde level, we now have to allocate the seats of a party to ths party s dstrct organzatons. We recommend that ths allocaton procedure should have the followng propertes: The seats are allocated accordng to the Sante-Laguë method wth 0.75 as frst dvsor. Each dstrct organzaton must get at least as many seats as t has won dstrct seats. Therefore, we propose the followng method to allocate the seats of party to ths party s dstrct organzatons: Suppose D j s the number of dstrct seats won by party n dstrct j. Suppose P j s the number of party votes for party n dstrct j. Suppose S s the number of seats that have been allocated to party as descrbed n secton 3.2. s j s the number of seats already allocated to the dstrct organzaton of party n dstrct j. Stage 1: Stage 2: For each j, we start wth s j : = D j. Repeat ( untl Σ j s j = S ): t j : = P j / ( s j ) for each dstrct organzaton j of party wth s j > 0. t j : = P j / 0.75 for each dstrct organzaton j of party wth s j = 0. T : = max j t j. U : = max j { D j t j = T }. The next seat goes to dstrct organzaton j wth t j = T and D j = U. If there s more than one dstrct organzaton wth t j = T and D j = U, then we decde randomly whch dstrct organzaton wth t j = T and D j = U gets the next seat. 15

16 3.4. The Party Vote Wnners If S j > D j, then ( n addton to those canddates who have already been elected by the dstrct votes ) those S j - D j canddates of ths party are elected who are ranked hghest n the proportonal rankng of ths dstrct. Example: D FK SPD = 2 and S FK SPD = 3; then one ( = S FK SPD - D FK SPD ) addtonal SPD canddate must be elected n the dstrct Fredrchshan-Kreuzberg; ths addtonal canddate s Eggert, because he s the hghest ranked SPD canddate n the proportonal rankng of ths dstrct who has not yet been elected. D FK FK FK Left = 2 and S Left = 3; then one ( = S Left - D FK Left ) addtonal Left canddate must be elected n the dstrct Fredrchshan-Kreuzberg; ths addtonal canddate s Wolf, because he s the hghest ranked Left canddate n the proportonal rankng of ths dstrct who has not yet been elected. D FK '90G B = 3 and S FK B '90G = 5; then two ( = S FK B '90G - D FK B '90G ) addtonal B 90G canddates must be elected n the dstrct Fredrchshan-Kreuzberg; these addtonal canddates are Behrendt and Altug, because they are the hghest ranked B 90G canddates n the proportonal rankng of ths dstrct who have not yet been elected. Therefore, we get: 1. Mutlu (B 90G, canddate ) elected (dstrct vote) 2. Fscher (SPD, canddate ) elected (dstrct vote) 3. Renauer (Left, canddate ) elected (dstrct vote) 4. Junge-Reyer (SPD, canddate ) elected (dstrct vote) 5. Ratzmann (B 90G, canddate ) elected (dstrct vote) 6. İzgn (Left, canddate ) elected (dstrct vote) 7. Klotz (B 90G, canddate ) elected (dstrct vote) 8. Samuray (CDU, canddate ) elected (dstrct vote) 9. Eggert (SPD, canddate ) elected (party vote) 10. Henemann (SPD, canddate ) 11. Behrendt (B 90G, canddate ) elected (party vote) 12. Wolf (Left, canddate ) elected (party vote) 13. Altug (B 90G, canddate ) elected (party vote) 14. Bayram (SPD, canddate ) 15. Kosche (B 90G, canddate ) 16. Mchels (Left, canddate ) 17. Bleler (CDU, canddate ) 18. Herrmann (B 90G, canddate ) 19. Zackenfels (SPD, canddate ) 20. Vordenbäumen (Left, canddate ) 21. etc. If the lst of canddates of ths party s exhausted, then ths seat stays vacant. 16

17 4. Vacant Seats When a seat gets vacant, then ths seat goes to that canddate of ths party who s ranked hghest n the proportonal rankng of ths dstrct. If the lst of canddates of ths party s exhausted or f ths seat was the seat of an ndependent canddate, then ths seat stays vacant. Example: The seat of Klotz gets vacant. Then ths seat goes to Kosche. Therefore we get: 1. Mutlu (B 90G, canddate ) elected (dstrct vote) 2. Fscher (SPD, canddate ) elected (dstrct vote) 3. Renauer (Left, canddate ) elected (dstrct vote) 4. Junge-Reyer (SPD, canddate ) elected (dstrct vote) 5. Ratzmann (B 90G, canddate ) elected (dstrct vote) 6. İzgn (Left, canddate ) elected (dstrct vote) 7. Klotz (B 90G, canddate ) elected (dstrct vote) 8. Samuray (CDU, canddate ) elected (dstrct vote) 9. Eggert (SPD, canddate ) elected (party vote) 10. Henemann (SPD, canddate ) 11. Behrendt (B 90G, canddate ) elected (party vote) 12. Wolf (Left, canddate ) elected (party vote) 13. Altug (B 90G, canddate ) elected (party vote) 14. Bayram (SPD, canddate ) 15. Kosche (B 90G, canddate ) elected (successor of Klotz) 16. Mchels (Left, canddate ) 17. Bleler (CDU, canddate ) 18. Herrmann (B 90G, canddate ) 19. Zackenfels (SPD, canddate ) 20. Vordenbäumen (Left, canddate ) 21. etc. 17