[EM] Proportionality vs individual utility: results
Kristofer Munsterhjelm
km-elmet at munsterhjelm.no
Thu Sep 19 11:48:56 PDT 2024
Here are the results with the Sainte-Laguë index being used properly.
The parameters are as before:
Number of voters per round: 5 ... 260
Number of candidates: 5 ... 11
Number of issue dimensions: 1 ... 11
Number of winners: 3 ... 10.
It still rewards small-opinion methods more than large ones: e.g. QPQ
maximizes proportionality with a parameter of 0.25, not the party-list
unbiased Sainte-Laguë of 0.5. But the feasible region seems more
sensible, and the deliberately bad methods are now seen as bad both in
terms of proportionality and (individual) utility.
The slanted shape of the feasible set has me thinking that maybe there
needs to be "worse" and "better" candidates that pretty much every voter
agrees are worse/or better than others, in order to decouple
proportionality more from individual utility. It might be a thing to
experiment with.
-km
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0.28201 -0.43823 Cardinal: A-Birational ext (0.1)
0.34401 -0.39682 Cardinal: A-Birational ext (0.2)
0.40241 -0.35079 Cardinal: A-Birational ext (0.3)
0.45699 -0.30198 Cardinal: A-Birational ext (0.4)
0.5067 -0.25108 Cardinal: A-Birational ext (0.5)
0.55157 -0.1997 Cardinal: A-Birational ext (0.6)
0.59122 -0.14708 Cardinal: A-Birational ext (0.7)
0.62778 -0.09198 Cardinal: A-Birational ext (0.8)
0.65923 -0.0342 Cardinal: A-Birational ext (0.9)
0.68379 0.02434 Cardinal: A-Birational
0.70176 0.08078 Cardinal: A-Birational ext (1.1)
0.71356 0.13565 Cardinal: A-Birational ext (1.2)
0.72526 0.1887 Cardinal: A-Birational ext (1.3)
0.73484 0.24162 Cardinal: A-Birational ext (1.4)
0.73967 0.29468 Cardinal: A-Birational ext (1.5)
0.74223 0.34714 Cardinal: A-Birational ext (1.6)
0.74055 0.39867 Cardinal: A-Birational ext (1.7)
0.73492 0.44933 Cardinal: A-Birational ext (1.8)
0.72837 0.49874 Cardinal: A-Birational ext (1.9)
0.71959 0.54639 Cardinal: A-Birational ext (2)
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0.33628 -0.2992 Cardinal: R-Birational ext (0.1)
0.47272 -0.11831 Cardinal: R-Birational ext (0.2)
0.5733 0.07207 Cardinal: R-Birational ext (0.3)
0.62939 0.26344 Cardinal: R-Birational ext (0.4)
0.65889 0.46622 Cardinal: R-Birational ext (0.5)
0.63392 0.64813 Cardinal: R-Birational ext (0.6)
0.58422 0.76134 Cardinal: R-Birational ext (0.7)
0.53915 0.82789 Cardinal: R-Birational ext (0.8)
0.5018 0.86951 Cardinal: R-Birational ext (0.9)
0.4715 0.89726 Cardinal: R-Birational
0.44625 0.91577 Cardinal: R-Birational ext (1.1)
0.42513 0.92925 Cardinal: R-Birational ext (1.2)
0.40792 0.93898 Cardinal: R-Birational ext (1.3)
0.39333 0.94639 Cardinal: R-Birational ext (1.4)
0.38111 0.95221 Cardinal: R-Birational ext (1.5)
0.37045 0.95683 Cardinal: R-Birational ext (1.6)
0.36138 0.96042 Cardinal: R-Birational ext (1.7)
0.35313 0.9635 Cardinal: R-Birational ext (1.8)
0.34589 0.9661 Cardinal: R-Birational ext (1.9)
0.33913 0.96842 Cardinal: R-Birational ext (2)
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0.62468 0.28339 Cardinal: Harmonic (delta = 0.01)
0.64232 0.30714 Cardinal: Harmonic (delta = 0.02)
0.65777 0.33351 Cardinal: Harmonic (delta = 0.03)
0.67036 0.35995 Cardinal: Harmonic (delta = 0.04)
0.67955 0.38607 Cardinal: Harmonic (delta = 0.05)
0.68635 0.41092 Cardinal: Harmonic (delta = 0.06)
0.69137 0.43395 Cardinal: Harmonic (delta = 0.07)
0.69464 0.45608 Cardinal: Harmonic (delta = 0.08)
0.69683 0.47693 Cardinal: Harmonic (delta = 0.09)
0.69796 0.49652 Cardinal: Harmonic (delta = 0.1)
0.69837 0.51496 Cardinal: Harmonic (delta = 0.11)
0.69838 0.53184 Cardinal: Harmonic (delta = 0.12)
0.69736 0.54816 Cardinal: Harmonic (delta = 0.13)
0.6956 0.56365 Cardinal: Harmonic (delta = 0.14)
0.69363 0.57788 Cardinal: Harmonic (delta = 0.15)
0.69129 0.59145 Cardinal: Harmonic (delta = 0.16)
0.68882 0.60412 Cardinal: Harmonic (delta = 0.17)
0.68628 0.61643 Cardinal: Harmonic (delta = 0.18)
0.68385 0.62787 Cardinal: Harmonic (delta = 0.19)
0.68113 0.63891 Cardinal: Harmonic (delta = 0.2)
0.67834 0.6491 Cardinal: Harmonic (delta = 0.21)
0.67573 0.65832 Cardinal: Harmonic (delta = 0.22)
0.67269 0.66758 Cardinal: Harmonic (delta = 0.23)
0.66978 0.67638 Cardinal: Harmonic (delta = 0.24)
0.66664 0.68477 Cardinal: Harmonic (delta = 0.25)
0.66348 0.69269 Cardinal: Harmonic (delta = 0.26)
0.6603 0.70044 Cardinal: Harmonic (delta = 0.27)
0.65713 0.70758 Cardinal: Harmonic (delta = 0.28)
0.65385 0.71471 Cardinal: Harmonic (delta = 0.29)
0.65063 0.72141 Cardinal: Harmonic (delta = 0.3)
0.64755 0.72769 Cardinal: Harmonic (delta = 0.31)
0.64456 0.73377 Cardinal: Harmonic (delta = 0.32)
0.64137 0.73954 Cardinal: Harmonic (delta = 0.33)
0.63848 0.7453 Cardinal: Harmonic (delta = 0.34)
0.6355 0.75057 Cardinal: Harmonic (delta = 0.35)
0.63252 0.75568 Cardinal: Harmonic (delta = 0.36)
0.62953 0.76073 Cardinal: Harmonic (delta = 0.37)
0.62638 0.76564 Cardinal: Harmonic (delta = 0.38)
0.6234 0.77027 Cardinal: Harmonic (delta = 0.39)
0.62041 0.77502 Cardinal: Harmonic (delta = 0.4)
0.61748 0.77911 Cardinal: Harmonic (delta = 0.41)
0.61466 0.78317 Cardinal: Harmonic (delta = 0.42)
0.61213 0.78705 Cardinal: Harmonic (delta = 0.43)
0.60934 0.79102 Cardinal: Harmonic (delta = 0.44)
0.60671 0.79454 Cardinal: Harmonic (delta = 0.45)
0.60395 0.79821 Cardinal: Harmonic (delta = 0.46)
0.60136 0.80158 Cardinal: Harmonic (delta = 0.47)
0.59868 0.80508 Cardinal: Harmonic (delta = 0.48)
0.59613 0.80818 Cardinal: Harmonic (delta = 0.49)
0.59357 0.81176 Cardinal: Harmonic (Sainte-Laguë)
0.591 0.81479 Cardinal: Harmonic (delta = 0.51)
0.58853 0.81772 Cardinal: Harmonic (delta = 0.52)
0.58607 0.82068 Cardinal: Harmonic (delta = 0.53)
0.58369 0.82335 Cardinal: Harmonic (delta = 0.54)
0.58125 0.82613 Cardinal: Harmonic (delta = 0.55)
0.57901 0.82865 Cardinal: Harmonic (delta = 0.56)
0.57656 0.83117 Cardinal: Harmonic (delta = 0.57)
0.57435 0.83361 Cardinal: Harmonic (delta = 0.58)
0.57202 0.83607 Cardinal: Harmonic (delta = 0.59)
0.56969 0.83853 Cardinal: Harmonic (delta = 0.6)
0.56755 0.84071 Cardinal: Harmonic (delta = 0.61)
0.56537 0.84296 Cardinal: Harmonic (delta = 0.62)
0.56329 0.84513 Cardinal: Harmonic (delta = 0.63)
0.5613 0.84721 Cardinal: Harmonic (delta = 0.64)
0.5593 0.84924 Cardinal: Harmonic (delta = 0.65)
0.55732 0.85121 Cardinal: Harmonic (delta = 0.66)
0.55521 0.85338 Cardinal: Harmonic (delta = 0.67)
0.55324 0.85528 Cardinal: Harmonic (delta = 0.68)
0.55113 0.85718 Cardinal: Harmonic (delta = 0.69)
0.54926 0.85891 Cardinal: Harmonic (delta = 0.7)
0.54714 0.86068 Cardinal: Harmonic (delta = 0.71)
0.54512 0.86238 Cardinal: Harmonic (delta = 0.72)
0.54337 0.86395 Cardinal: Harmonic (delta = 0.73)
0.54153 0.86562 Cardinal: Harmonic (delta = 0.74)
0.53957 0.86752 Cardinal: Harmonic (delta = 0.75)
0.5377 0.86922 Cardinal: Harmonic (delta = 0.76)
0.5358 0.87089 Cardinal: Harmonic (delta = 0.77)
0.53406 0.87237 Cardinal: Harmonic (delta = 0.78)
0.53186 0.87418 Cardinal: Harmonic (delta = 0.79)
0.53017 0.87568 Cardinal: Harmonic (delta = 0.8)
0.52837 0.87704 Cardinal: Harmonic (delta = 0.81)
0.52675 0.87843 Cardinal: Harmonic (delta = 0.82)
0.52513 0.87975 Cardinal: Harmonic (delta = 0.83)
0.52358 0.88107 Cardinal: Harmonic (delta = 0.84)
0.52193 0.88233 Cardinal: Harmonic (delta = 0.85)
0.52024 0.88362 Cardinal: Harmonic (delta = 0.86)
0.51879 0.88483 Cardinal: Harmonic (delta = 0.87)
0.51721 0.88598 Cardinal: Harmonic (delta = 0.88)
0.51573 0.88718 Cardinal: Harmonic (delta = 0.89)
0.51415 0.88836 Cardinal: Harmonic (delta = 0.9)
0.51265 0.88952 Cardinal: Harmonic (delta = 0.91)
0.51116 0.8906 Cardinal: Harmonic (delta = 0.92)
0.50973 0.89172 Cardinal: Harmonic (delta = 0.93)
0.5083 0.89284 Cardinal: Harmonic (delta = 0.94)
0.50684 0.89385 Cardinal: Harmonic (delta = 0.95)
0.50541 0.89485 Cardinal: Harmonic (delta = 0.96)
0.50404 0.89583 Cardinal: Harmonic (delta = 0.97)
0.50268 0.89677 Cardinal: Harmonic (delta = 0.98)
0.50128 0.89769 Cardinal: Harmonic (delta = 0.99)
0.4996 0.89937 Cardinal: Harmonic (D'Hondt)
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0.4996 0.89937 Cardinal: Harmonic (D'Hondt)
0.27741 0.98633 Cardinal: Harmonic extended (10)
0.23062 0.99033 Cardinal: Harmonic extended (100)
0.22679 0.99049 Cardinal: Harmonic extended (1000)
0.22495 0.99067 Cardinal: Harmonic extended (100000)
0.22472 0.99068 Cardinal: Harmonic extended (1e+09)
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0.46078 0.19655 Cardinal: Isoelastic (r = -10)
0.46142 0.19786 Cardinal: Isoelastic (r = -9.9)
0.46217 0.19914 Cardinal: Isoelastic (r = -9.8)
0.46286 0.20043 Cardinal: Isoelastic (r = -9.7)
0.46355 0.20172 Cardinal: Isoelastic (r = -9.6)
0.46419 0.20299 Cardinal: Isoelastic (r = -9.5)
0.4648 0.20431 Cardinal: Isoelastic (r = -9.4)
0.46548 0.20585 Cardinal: Isoelastic (r = -9.3)
0.46634 0.20726 Cardinal: Isoelastic (r = -9.2)
0.46697 0.20874 Cardinal: Isoelastic (r = -9.1)
0.46766 0.21027 Cardinal: Isoelastic (r = -9)
0.46843 0.21186 Cardinal: Isoelastic (r = -8.9)
0.46901 0.21341 Cardinal: Isoelastic (r = -8.8)
0.46967 0.2149 Cardinal: Isoelastic (r = -8.7)
0.47053 0.21666 Cardinal: Isoelastic (r = -8.6)
0.47132 0.21822 Cardinal: Isoelastic (r = -8.5)
0.47215 0.21997 Cardinal: Isoelastic (r = -8.4)
0.47289 0.22177 Cardinal: Isoelastic (r = -8.3)
0.47372 0.22358 Cardinal: Isoelastic (r = -8.2)
0.47469 0.2255 Cardinal: Isoelastic (r = -8.1)
0.47575 0.22753 Cardinal: Isoelastic (r = -8)
0.47674 0.22948 Cardinal: Isoelastic (r = -7.9)
0.4776 0.23137 Cardinal: Isoelastic (r = -7.8)
0.47867 0.23344 Cardinal: Isoelastic (r = -7.7)
0.47974 0.23562 Cardinal: Isoelastic (r = -7.6)
0.48078 0.23781 Cardinal: Isoelastic (r = -7.5)
0.48176 0.23998 Cardinal: Isoelastic (r = -7.4)
0.48282 0.24212 Cardinal: Isoelastic (r = -7.3)
0.48394 0.24459 Cardinal: Isoelastic (r = -7.2)
0.48489 0.24686 Cardinal: Isoelastic (r = -7.1)
0.48603 0.24927 Cardinal: Isoelastic (r = -7)
0.48702 0.25171 Cardinal: Isoelastic (r = -6.9)
0.48828 0.25437 Cardinal: Isoelastic (r = -6.8)
0.48926 0.25694 Cardinal: Isoelastic (r = -6.7)
0.49027 0.25969 Cardinal: Isoelastic (r = -6.6)
0.4914 0.26256 Cardinal: Isoelastic (r = -6.5)
0.49277 0.26552 Cardinal: Isoelastic (r = -6.4)
0.49417 0.26841 Cardinal: Isoelastic (r = -6.3)
0.49531 0.2714 Cardinal: Isoelastic (r = -6.2)
0.49665 0.27456 Cardinal: Isoelastic (r = -6.1)
0.49817 0.27784 Cardinal: Isoelastic (r = -6)
0.49928 0.28106 Cardinal: Isoelastic (r = -5.9)
0.50046 0.28448 Cardinal: Isoelastic (r = -5.8)
0.50158 0.28791 Cardinal: Isoelastic (r = -5.7)
0.5029 0.29142 Cardinal: Isoelastic (r = -5.6)
0.50429 0.29487 Cardinal: Isoelastic (r = -5.5)
0.50572 0.29868 Cardinal: Isoelastic (r = -5.4)
0.50713 0.30253 Cardinal: Isoelastic (r = -5.3)
0.50853 0.3065 Cardinal: Isoelastic (r = -5.2)
0.51017 0.31049 Cardinal: Isoelastic (r = -5.1)
0.51172 0.31475 Cardinal: Isoelastic (r = -5)
0.51333 0.31899 Cardinal: Isoelastic (r = -4.9)
0.51491 0.32329 Cardinal: Isoelastic (r = -4.8)
0.51648 0.32812 Cardinal: Isoelastic (r = -4.7)
0.51788 0.33299 Cardinal: Isoelastic (r = -4.6)
0.51953 0.33778 Cardinal: Isoelastic (r = -4.5)
0.52115 0.34282 Cardinal: Isoelastic (r = -4.4)
0.52299 0.34794 Cardinal: Isoelastic (r = -4.3)
0.52463 0.3532 Cardinal: Isoelastic (r = -4.2)
0.5262 0.35865 Cardinal: Isoelastic (r = -4.1)
0.52774 0.36414 Cardinal: Isoelastic (r = -4)
0.52915 0.36994 Cardinal: Isoelastic (r = -3.9)
0.53073 0.3758 Cardinal: Isoelastic (r = -3.8)
0.53206 0.38177 Cardinal: Isoelastic (r = -3.7)
0.53379 0.38792 Cardinal: Isoelastic (r = -3.6)
0.53551 0.39439 Cardinal: Isoelastic (r = -3.5)
0.5371 0.40082 Cardinal: Isoelastic (r = -3.4)
0.53861 0.40764 Cardinal: Isoelastic (r = -3.3)
0.54021 0.41472 Cardinal: Isoelastic (r = -3.2)
0.54167 0.42167 Cardinal: Isoelastic (r = -3.1)
0.5432 0.42904 Cardinal: Isoelastic (r = -3)
0.54474 0.43675 Cardinal: Isoelastic (r = -2.9)
0.54618 0.44445 Cardinal: Isoelastic (r = -2.8)
0.5476 0.45237 Cardinal: Isoelastic (r = -2.7)
0.54934 0.46043 Cardinal: Isoelastic (r = -2.6)
0.55045 0.46876 Cardinal: Isoelastic (r = -2.5)
0.55177 0.47762 Cardinal: Isoelastic (r = -2.4)
0.553 0.48676 Cardinal: Isoelastic (r = -2.3)
0.55393 0.49585 Cardinal: Isoelastic (r = -2.2)
0.55495 0.50516 Cardinal: Isoelastic (r = -2.1)
0.55591 0.51487 Cardinal: Isoelastic (r = -2)
0.55656 0.52504 Cardinal: Isoelastic (r = -1.9)
0.55704 0.53518 Cardinal: Isoelastic (r = -1.8)
0.55771 0.5457 Cardinal: Isoelastic (r = -1.7)
0.55806 0.55642 Cardinal: Isoelastic (r = -1.6)
0.55759 0.56728 Cardinal: Isoelastic (r = -1.5)
0.55712 0.57835 Cardinal: Isoelastic (r = -1.4)
0.55673 0.58964 Cardinal: Isoelastic (r = -1.3)
0.55628 0.60134 Cardinal: Isoelastic (r = -1.2)
0.55555 0.61309 Cardinal: Isoelastic (r = -1.1)
0.55433 0.62503 Cardinal: Isoelastic (r = -1)
0.55275 0.63721 Cardinal: Isoelastic (r = -0.9)
0.55092 0.64953 Cardinal: Isoelastic (r = -0.8)
0.54849 0.66191 Cardinal: Isoelastic (r = -0.7)
0.54561 0.67439 Cardinal: Isoelastic (r = -0.6)
0.54231 0.68641 Cardinal: Isoelastic (r = -0.5)
0.53853 0.69943 Cardinal: Isoelastic (r = -0.4)
0.53422 0.71215 Cardinal: Isoelastic (r = -0.3)
0.52939 0.72525 Cardinal: Isoelastic (r = -0.2)
0.52378 0.73795 Cardinal: Isoelastic (r = -0.1)
0.51795 0.75044 Cardinal: Isoelastic (r = -1.87905e-14)
0.51177 0.76263 Cardinal: Isoelastic (r = 0.1)
0.50416 0.7752 Cardinal: Isoelastic (r = 0.2)
0.49649 0.78726 Cardinal: Isoelastic (r = 0.3)
0.48801 0.79924 Cardinal: Isoelastic (r = 0.4)
0.4789 0.811 Cardinal: Isoelastic (r = 0.5)
0.46968 0.82258 Cardinal: Isoelastic (r = 0.6)
0.46043 0.83456 Cardinal: Isoelastic (r = 0.7)
0.45132 0.84778 Cardinal: Isoelastic (r = 0.8)
0.44142 0.86175 Cardinal: Isoelastic (r = 0.9)
0.41925 0.89184 Cardinal: Isoelastic (r = 1.1)
0.40599 0.90757 Cardinal: Isoelastic (r = 1.2)
0.39012 0.92337 Cardinal: Isoelastic (r = 1.3)
0.37136 0.93888 Cardinal: Isoelastic (r = 1.4)
0.35006 0.95327 Cardinal: Isoelastic (r = 1.5)
0.32673 0.96579 Cardinal: Isoelastic (r = 1.6)
0.30187 0.97585 Cardinal: Isoelastic (r = 1.7)
0.27571 0.98332 Cardinal: Isoelastic (r = 1.8)
0.24932 0.98809 Cardinal: Isoelastic (r = 1.9)
0.22472 0.99068 Cardinal: Isoelastic (r = 2)
0.20597 0.99144 Cardinal: Isoelastic (r = 2.1)
0.19025 0.99141 Cardinal: Isoelastic (r = 2.2)
0.17537 0.99067 Cardinal: Isoelastic (r = 2.3)
0.16165 0.98939 Cardinal: Isoelastic (r = 2.4)
0.14849 0.9878 Cardinal: Isoelastic (r = 2.5)
0.13588 0.98588 Cardinal: Isoelastic (r = 2.6)
0.12477 0.98384 Cardinal: Isoelastic (r = 2.7)
0.1144 0.98169 Cardinal: Isoelastic (r = 2.8)
0.10414 0.97933 Cardinal: Isoelastic (r = 2.9)
0.09479 0.97691 Cardinal: Isoelastic (r = 3)
0.08554 0.97425 Cardinal: Isoelastic (r = 3.1)
0.07689 0.97157 Cardinal: Isoelastic (r = 3.2)
0.06873 0.96886 Cardinal: Isoelastic (r = 3.3)
0.06099 0.96613 Cardinal: Isoelastic (r = 3.4)
0.05404 0.96334 Cardinal: Isoelastic (r = 3.5)
0.0474 0.96066 Cardinal: Isoelastic (r = 3.6)
0.04112 0.95794 Cardinal: Isoelastic (r = 3.7)
0.03515 0.95525 Cardinal: Isoelastic (r = 3.8)
0.02929 0.95244 Cardinal: Isoelastic (r = 3.9)
0.02309 0.94942 Cardinal: Isoelastic (r = 4)
0.01788 0.94661 Cardinal: Isoelastic (r = 4.1)
0.01247 0.94374 Cardinal: Isoelastic (r = 4.2)
0.00757 0.9409 Cardinal: Isoelastic (r = 4.3)
0.00279 0.93802 Cardinal: Isoelastic (r = 4.4)
-0.00167 0.93518 Cardinal: Isoelastic (r = 4.5)
-0.00616 0.93216 Cardinal: Isoelastic (r = 4.6)
-0.01033 0.92932 Cardinal: Isoelastic (r = 4.7)
-0.01434 0.92655 Cardinal: Isoelastic (r = 4.8)
-0.01871 0.92356 Cardinal: Isoelastic (r = 4.9)
-0.02226 0.92081 Cardinal: Isoelastic (r = 5)
-0.02622 0.91784 Cardinal: Isoelastic (r = 5.1)
-0.02982 0.91493 Cardinal: Isoelastic (r = 5.2)
-0.03303 0.91209 Cardinal: Isoelastic (r = 5.3)
-0.03607 0.90914 Cardinal: Isoelastic (r = 5.4)
-0.03917 0.90623 Cardinal: Isoelastic (r = 5.5)
-0.04253 0.90339 Cardinal: Isoelastic (r = 5.6)
-0.04539 0.90043 Cardinal: Isoelastic (r = 5.7)
-0.04811 0.89758 Cardinal: Isoelastic (r = 5.8)
-0.05102 0.89464 Cardinal: Isoelastic (r = 5.9)
-0.05384 0.8917 Cardinal: Isoelastic (r = 6)
-0.05619 0.88871 Cardinal: Isoelastic (r = 6.1)
-0.05902 0.88575 Cardinal: Isoelastic (r = 6.2)
-0.06151 0.88292 Cardinal: Isoelastic (r = 6.3)
-0.06325 0.88007 Cardinal: Isoelastic (r = 6.4)
-0.06547 0.8772 Cardinal: Isoelastic (r = 6.5)
-0.0676 0.87433 Cardinal: Isoelastic (r = 6.6)
-0.0699 0.87126 Cardinal: Isoelastic (r = 6.7)
-0.07232 0.8681 Cardinal: Isoelastic (r = 6.8)
-0.07442 0.8652 Cardinal: Isoelastic (r = 6.9)
-0.07663 0.86223 Cardinal: Isoelastic (r = 7)
-0.07875 0.85931 Cardinal: Isoelastic (r = 7.1)
-0.08035 0.85659 Cardinal: Isoelastic (r = 7.2)
-0.08182 0.85357 Cardinal: Isoelastic (r = 7.3)
-0.08327 0.85075 Cardinal: Isoelastic (r = 7.4)
-0.08493 0.84789 Cardinal: Isoelastic (r = 7.5)
-0.08665 0.84487 Cardinal: Isoelastic (r = 7.6)
-0.08815 0.84202 Cardinal: Isoelastic (r = 7.7)
-0.08935 0.8391 Cardinal: Isoelastic (r = 7.8)
-0.09049 0.83631 Cardinal: Isoelastic (r = 7.9)
-0.09171 0.83334 Cardinal: Isoelastic (r = 8)
-0.09285 0.83061 Cardinal: Isoelastic (r = 8.1)
-0.09429 0.82781 Cardinal: Isoelastic (r = 8.2)
-0.09557 0.82503 Cardinal: Isoelastic (r = 8.3)
-0.09674 0.82223 Cardinal: Isoelastic (r = 8.4)
-0.0981 0.81945 Cardinal: Isoelastic (r = 8.5)
-0.0991 0.81667 Cardinal: Isoelastic (r = 8.6)
-0.10022 0.81367 Cardinal: Isoelastic (r = 8.7)
-0.10144 0.8109 Cardinal: Isoelastic (r = 8.8)
-0.10242 0.8082 Cardinal: Isoelastic (r = 8.9)
-0.10362 0.80544 Cardinal: Isoelastic (r = 9)
-0.10485 0.80265 Cardinal: Isoelastic (r = 9.1)
-0.10595 0.7999 Cardinal: Isoelastic (r = 9.2)
-0.10686 0.79734 Cardinal: Isoelastic (r = 9.3)
-0.10785 0.79473 Cardinal: Isoelastic (r = 9.4)
-0.10906 0.79185 Cardinal: Isoelastic (r = 9.5)
-0.10982 0.78918 Cardinal: Isoelastic (r = 9.6)
-0.11076 0.78657 Cardinal: Isoelastic (r = 9.7)
-0.11165 0.78385 Cardinal: Isoelastic (r = 9.8)
-0.11261 0.78116 Cardinal: Isoelastic (r = 9.9)
-0.11328 0.77864 Cardinal: Isoelastic (r = 10)
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0.45931 0.83178 Cardinal: Psi (delta = 0)
0.45859 0.83332 Cardinal: Psi (delta = 0.01)
0.45833 0.83546 Cardinal: Psi (delta = 0.02)
0.45831 0.83805 Cardinal: Psi (delta = 0.03)
0.45799 0.84079 Cardinal: Psi (delta = 0.04)
0.45759 0.84332 Cardinal: Psi (delta = 0.05)
0.45707 0.84576 Cardinal: Psi (delta = 0.06)
0.4566 0.8481 Cardinal: Psi (delta = 0.07)
0.45605 0.85041 Cardinal: Psi (delta = 0.08)
0.45554 0.85263 Cardinal: Psi (delta = 0.09)
0.4547 0.85492 Cardinal: Psi (delta = 0.1)
0.45406 0.85696 Cardinal: Psi (delta = 0.11)
0.45324 0.85891 Cardinal: Psi (delta = 0.12)
0.45248 0.8608 Cardinal: Psi (delta = 0.13)
0.45175 0.86276 Cardinal: Psi (delta = 0.14)
0.45078 0.86465 Cardinal: Psi (delta = 0.15)
0.4498 0.86642 Cardinal: Psi (delta = 0.16)
0.44888 0.86817 Cardinal: Psi (delta = 0.17)
0.44814 0.86975 Cardinal: Psi (delta = 0.18)
0.44727 0.87147 Cardinal: Psi (delta = 0.19)
0.44632 0.87304 Cardinal: Psi (delta = 0.2)
0.44542 0.8746 Cardinal: Psi (delta = 0.21)
0.44444 0.87619 Cardinal: Psi (delta = 0.22)
0.44351 0.87769 Cardinal: Psi (delta = 0.23)
0.44246 0.87911 Cardinal: Psi (delta = 0.24)
0.44146 0.8806 Cardinal: Psi (delta = 0.25)
0.44046 0.88192 Cardinal: Psi (delta = 0.26)
0.4395 0.88327 Cardinal: Psi (delta = 0.27)
0.43874 0.88456 Cardinal: Psi (delta = 0.28)
0.43786 0.88587 Cardinal: Psi (delta = 0.29)
0.43701 0.8872 Cardinal: Psi (delta = 0.3)
0.43628 0.88835 Cardinal: Psi (delta = 0.31)
0.43532 0.88963 Cardinal: Psi (delta = 0.32)
0.43451 0.89076 Cardinal: Psi (delta = 0.33)
0.43366 0.89206 Cardinal: Psi (delta = 0.34)
0.43278 0.89317 Cardinal: Psi (delta = 0.35)
0.432 0.89417 Cardinal: Psi (delta = 0.36)
0.4312 0.89529 Cardinal: Psi (delta = 0.37)
0.43035 0.89633 Cardinal: Psi (delta = 0.38)
0.42943 0.89737 Cardinal: Psi (delta = 0.39)
0.42847 0.89845 Cardinal: Psi (delta = 0.4)
0.42767 0.89929 Cardinal: Psi (delta = 0.41)
0.4268 0.90026 Cardinal: Psi (delta = 0.42)
0.42587 0.90127 Cardinal: Psi (delta = 0.43)
0.42514 0.90217 Cardinal: Psi (delta = 0.44)
0.42427 0.90305 Cardinal: Psi (delta = 0.45)
0.42342 0.90401 Cardinal: Psi (delta = 0.46)
0.42261 0.90488 Cardinal: Psi (delta = 0.47)
0.42185 0.90572 Cardinal: Psi (delta = 0.48)
0.42107 0.90658 Cardinal: Psi (delta = 0.49)
0.41987 0.90805 Cardinal: Psi (Sainte-Laguë)
0.41897 0.90888 Cardinal: Psi (delta = 0.51)
0.41808 0.90965 Cardinal: Psi (delta = 0.52)
0.41726 0.91041 Cardinal: Psi (delta = 0.53)
0.4165 0.91121 Cardinal: Psi (delta = 0.54)
0.41585 0.91199 Cardinal: Psi (delta = 0.55)
0.41497 0.91275 Cardinal: Psi (delta = 0.56)
0.41414 0.91348 Cardinal: Psi (delta = 0.57)
0.41336 0.91414 Cardinal: Psi (delta = 0.58)
0.4127 0.91483 Cardinal: Psi (delta = 0.59)
0.41182 0.91565 Cardinal: Psi (delta = 0.6)
0.41112 0.91629 Cardinal: Psi (delta = 0.61)
0.41044 0.91695 Cardinal: Psi (delta = 0.62)
0.40967 0.91762 Cardinal: Psi (delta = 0.63)
0.40894 0.91828 Cardinal: Psi (delta = 0.64)
0.40809 0.91899 Cardinal: Psi (delta = 0.65)
0.40733 0.91963 Cardinal: Psi (delta = 0.66)
0.40661 0.92045 Cardinal: Psi (delta = 0.67)
0.40595 0.92102 Cardinal: Psi (delta = 0.68)
0.40521 0.92164 Cardinal: Psi (delta = 0.69)
0.40453 0.92221 Cardinal: Psi (delta = 0.7)
0.40386 0.92278 Cardinal: Psi (delta = 0.71)
0.4031 0.92336 Cardinal: Psi (delta = 0.72)
0.40233 0.92398 Cardinal: Psi (delta = 0.73)
0.40167 0.92454 Cardinal: Psi (delta = 0.74)
0.40099 0.92527 Cardinal: Psi (delta = 0.75)
0.4004 0.92578 Cardinal: Psi (delta = 0.76)
0.39979 0.9263 Cardinal: Psi (delta = 0.77)
0.39914 0.92681 Cardinal: Psi (delta = 0.78)
0.39845 0.92734 Cardinal: Psi (delta = 0.79)
0.39767 0.92799 Cardinal: Psi (delta = 0.8)
0.39708 0.92842 Cardinal: Psi (delta = 0.81)
0.39644 0.92888 Cardinal: Psi (delta = 0.82)
0.39577 0.92939 Cardinal: Psi (delta = 0.83)
0.39503 0.92996 Cardinal: Psi (delta = 0.84)
0.39438 0.93044 Cardinal: Psi (delta = 0.85)
0.39372 0.93094 Cardinal: Psi (delta = 0.86)
0.39291 0.93143 Cardinal: Psi (delta = 0.87)
0.39231 0.93188 Cardinal: Psi (delta = 0.88)
0.39164 0.93238 Cardinal: Psi (delta = 0.89)
0.39103 0.93282 Cardinal: Psi (delta = 0.9)
0.39046 0.93328 Cardinal: Psi (delta = 0.91)
0.38991 0.93369 Cardinal: Psi (delta = 0.92)
0.38935 0.93413 Cardinal: Psi (delta = 0.93)
0.38874 0.93459 Cardinal: Psi (delta = 0.94)
0.38811 0.93501 Cardinal: Psi (delta = 0.95)
0.38746 0.93543 Cardinal: Psi (delta = 0.96)
0.38681 0.93582 Cardinal: Psi (delta = 0.97)
0.38621 0.93619 Cardinal: Psi (delta = 0.98)
0.38573 0.93655 Cardinal: Psi (delta = 0.99)
0.3847 0.93753 Cardinal: Psi (D'Hondt)
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0.47257 -0.03006 QPQ(div 0.002, multiround)
0.4787 -0.02571 QPQ(div 0.004, multiround)
0.48664 -0.02047 QPQ(div 0.006, multiround)
0.49452 -0.01492 QPQ(div 0.008, multiround)
0.50216 -0.00961 QPQ(div 0.01, multiround)
0.51004 -0.0035 QPQ(div 0.012, multiround)
0.51818 0.00281 QPQ(div 0.014, multiround)
0.5259 0.00906 QPQ(div 0.016, multiround)
0.53345 0.01479 QPQ(div 0.018, multiround)
0.54048 0.02075 QPQ(div 0.02, multiround)
0.54722 0.02697 QPQ(div 0.022, multiround)
0.55413 0.03306 QPQ(div 0.024, multiround)
0.56033 0.03889 QPQ(div 0.026, multiround)
0.56706 0.04487 QPQ(div 0.028, multiround)
0.57231 0.05038 QPQ(div 0.03, multiround)
0.57848 0.05618 QPQ(div 0.032, multiround)
0.58368 0.06174 QPQ(div 0.034, multiround)
0.58929 0.06722 QPQ(div 0.036, multiround)
0.59468 0.07246 QPQ(div 0.038, multiround)
0.59977 0.07787 QPQ(div 0.04, multiround)
0.60515 0.08371 QPQ(div 0.042, multiround)
0.60908 0.0887 QPQ(div 0.044, multiround)
0.61303 0.09396 QPQ(div 0.046, multiround)
0.6178 0.09952 QPQ(div 0.048, multiround)
0.62197 0.10443 QPQ(div 0.05, multiround)
0.62604 0.10938 QPQ(div 0.052, multiround)
0.62993 0.11409 QPQ(div 0.054, multiround)
0.6343 0.11956 QPQ(div 0.056, multiround)
0.6376 0.12413 QPQ(div 0.058, multiround)
0.64118 0.12866 QPQ(div 0.06, multiround)
0.64456 0.13317 QPQ(div 0.062, multiround)
0.64838 0.13819 QPQ(div 0.064, multiround)
0.65126 0.14244 QPQ(div 0.066, multiround)
0.65523 0.14745 QPQ(div 0.068, multiround)
0.65832 0.15169 QPQ(div 0.07, multiround)
0.66155 0.1563 QPQ(div 0.072, multiround)
0.6641 0.16034 QPQ(div 0.074, multiround)
0.6669 0.16492 QPQ(div 0.076, multiround)
0.6697 0.16941 QPQ(div 0.078, multiround)
0.67231 0.17372 QPQ(div 0.08, multiround)
0.67489 0.17794 QPQ(div 0.082, multiround)
0.67865 0.18358 QPQ(div 0.084, multiround)
0.68091 0.18765 QPQ(div 0.086, multiround)
0.68299 0.19138 QPQ(div 0.088, multiround)
0.68525 0.19551 QPQ(div 0.09, multiround)
0.68769 0.19967 QPQ(div 0.092, multiround)
0.69002 0.2038 QPQ(div 0.094, multiround)
0.69213 0.20788 QPQ(div 0.096, multiround)
0.6939 0.2115 QPQ(div 0.098, multiround)
0.69609 0.21581 QPQ(div 0.1, multiround)
0.70495 0.23437 QPQ(div 0.11, multiround)
0.71258 0.25263 QPQ(div 0.12, multiround)
0.71948 0.27026 QPQ(div 0.13, multiround)
0.7251 0.28618 QPQ(div 0.14, multiround)
0.72969 0.30147 QPQ(div 0.15, multiround)
0.73347 0.31641 QPQ(div 0.16, multiround)
0.73796 0.33276 QPQ(div 0.17, multiround)
0.74042 0.34602 QPQ(div 0.18, multiround)
0.7427 0.35939 QPQ(div 0.19, multiround)
0.74432 0.37263 QPQ(div 0.2, multiround)
0.74584 0.38502 QPQ(div 0.21, multiround)
0.74673 0.39688 QPQ(div 0.22, multiround)
0.7477 0.40847 QPQ(div 0.23, multiround)
0.74784 0.41919 QPQ(div 0.24, multiround)
0.74821 0.43095 QPQ(div 0.25, multiround)
0.74826 0.44183 QPQ(div 0.26, multiround)
0.7477 0.45136 QPQ(div 0.27, multiround)
0.74719 0.46082 QPQ(div 0.28, multiround)
0.74651 0.47012 QPQ(div 0.29, multiround)
0.74594 0.47877 QPQ(div 0.3, multiround)
0.7453 0.48709 QPQ(div 0.31, multiround)
0.74394 0.49495 QPQ(div 0.32, multiround)
0.74301 0.50253 QPQ(div 0.33, multiround)
0.74255 0.51258 QPQ(div 0.34, multiround)
0.74177 0.51987 QPQ(div 0.35, multiround)
0.74083 0.52695 QPQ(div 0.36, multiround)
0.73968 0.53408 QPQ(div 0.37, multiround)
0.73876 0.54105 QPQ(div 0.38, multiround)
0.73774 0.5475 QPQ(div 0.39, multiround)
0.73707 0.55392 QPQ(div 0.4, multiround)
0.73563 0.56064 QPQ(div 0.41, multiround)
0.73426 0.56708 QPQ(div 0.42, multiround)
0.73326 0.57416 QPQ(div 0.43, multiround)
0.73205 0.57998 QPQ(div 0.44, multiround)
0.73063 0.58635 QPQ(div 0.45, multiround)
0.72915 0.59223 QPQ(div 0.46, multiround)
0.72782 0.59792 QPQ(div 0.47, multiround)
0.72612 0.60357 QPQ(div 0.48, multiround)
0.72417 0.60921 QPQ(div 0.49, multiround)
0.72193 0.61611 QPQ(div Sainte-L, multiround)
0.71977 0.62414 QPQ(div 0.51, multiround)
0.71765 0.62963 QPQ(div 0.52, multiround)
0.71559 0.63511 QPQ(div 0.53, multiround)
0.71428 0.6403 QPQ(div 0.54, multiround)
0.71264 0.64578 QPQ(div 0.55, multiround)
0.71108 0.651 QPQ(div 0.56, multiround)
0.70948 0.65595 QPQ(div 0.57, multiround)
0.70788 0.66162 QPQ(div 0.58, multiround)
0.70629 0.66676 QPQ(div 0.59, multiround)
0.70482 0.67193 QPQ(div 0.6, multiround)
0.70313 0.67839 QPQ(div 0.61, multiround)
0.70107 0.68332 QPQ(div 0.62, multiround)
0.6989 0.6887 QPQ(div 0.63, multiround)
0.69654 0.69372 QPQ(div 0.64, multiround)
0.69452 0.6987 QPQ(div 0.65, multiround)
0.69214 0.7033 QPQ(div 0.66, multiround)
0.68934 0.71058 QPQ(div 0.67, multiround)
0.68721 0.71484 QPQ(div 0.68, multiround)
0.68451 0.71947 QPQ(div 0.69, multiround)
0.68183 0.72406 QPQ(div 0.7, multiround)
0.67936 0.7281 QPQ(div 0.71, multiround)
0.67682 0.73254 QPQ(div 0.72, multiround)
0.67419 0.73658 QPQ(div 0.73, multiround)
0.67177 0.74036 QPQ(div 0.74, multiround)
0.66915 0.74449 QPQ(div 0.75, multiround)
0.6661 0.7502 QPQ(div 0.76, multiround)
0.66348 0.75369 QPQ(div 0.77, multiround)
0.66079 0.75706 QPQ(div 0.78, multiround)
0.65819 0.76027 QPQ(div 0.79, multiround)
0.65547 0.76398 QPQ(div 0.8, multiround)
0.65319 0.76693 QPQ(div 0.81, multiround)
0.65079 0.76988 QPQ(div 0.82, multiround)
0.64847 0.77255 QPQ(div 0.83, multiround)
0.64581 0.77579 QPQ(div 0.84, multiround)
0.64364 0.77816 QPQ(div 0.85, multiround)
0.6413 0.78101 QPQ(div 0.86, multiround)
0.63918 0.78325 QPQ(div 0.87, multiround)
0.63703 0.78556 QPQ(div 0.88, multiround)
0.63483 0.78783 QPQ(div 0.89, multiround)
0.63266 0.78991 QPQ(div 0.9, multiround)
0.63059 0.792 QPQ(div 0.91, multiround)
0.62849 0.794 QPQ(div 0.92, multiround)
0.62647 0.79589 QPQ(div 0.93, multiround)
0.62435 0.79787 QPQ(div 0.94, multiround)
0.62244 0.79969 QPQ(div 0.95, multiround)
0.62065 0.80137 QPQ(div 0.96, multiround)
0.61886 0.80306 QPQ(div 0.97, multiround)
0.61718 0.80457 QPQ(div 0.98, multiround)
0.61547 0.80601 QPQ(div 0.99, multiround)
0.6129 0.80926 QPQ(div D'Hondt, multiround)
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-0.09576 0.46675 -- Random dictator --
0.19516 0.98757 Maj[Schulze(wv)]
0.22519 0.99009 Maj[Cardinal-20(norm)]
0.23491 0.99051 Maj[ER-Borda]
0.25641 0.99493 ?Linear Range STV
0.30385 0.93477 Maj[Ext-Minmax(margins)]
0.32473 0.93574 PSC-CLE
0.37428 0.89933 Cardinal: LPV0+
0.39476 0.32593 Random ballots
0.4715 0.89726 Cardinal: R-Birational
0.4859 0.90777 DHwL(Schulze(wv))
0.5872 0.83002 STV-ME (Schulze)
0.62401 0.80046 Meek STV
0.62747 0.79062 STV
0.62749 0.79642 Warren STV
0.63065 0.65719 Maj[ER-Plurality]
0.64325 0.67215 C-Elim[ER-Plurality]
0.64737 0.68169 Schulze STV
0.67901 0.68584 Maj[Eliminate-[ER-Plurality]/fd]
0.68379 0.02434 Cardinal: A-Birational
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