[EM] Proportionality vs utility: redoing 2008 with better units
Kristofer Munsterhjelm
km-elmet at munsterhjelm.no
Wed Sep 11 08:32:43 PDT 2024
On 2024-09-11 14:32, Toby Pereira wrote:
> I have another couple of questions. You said that the zero points are
> what you'd get by picking candidates at random. But does this not depend
> on how the candidates are distributed?
Yes, that's right. All the results depend on the model, which currently
is a very simple binary one.
> Are they just uniformly spread across the voting space?
This is how the model works:
Let n be the number of issues for the issue space for this round. First
draw n random uniform numbers for where the ith number is how likely a
random voter is to hold the "yes" opinion on the ith issue. Call this
the bias vector.
Then assign the voters their issues by flipping biased coins, where the
bias is given by the bias vector.
Calculate the correct proportions of yes opinions across all the voters
and update the bias vector. Since the second step is random, we'll
hardly ever get an exact match to the bias vector proportions from the
first step. The bias vector needs to reflect the proportion of voters
who actually hold the yes position for proportionality calculations to work.
The first k voters are candidates, so the voters and candidates come
from the same distribution. This also means that the candidates
paricipate in the election too.
Random candidate just picks these k candidates at random. They're not
uniformly spread across the voting space since their yes/no opinions are
influenced by the bias vector just like the voters' are.
Each voter rates each candidate according to their Hamming distance,
i.e. number of points equals number of issues that they agree upon, plus
some small amount of noise.
> How did repeatedly electing the plurality loser end up so
> proportional?
I was thinking the reason was something like: if the opinion space is
flat (i.e. some issues are liked by some voters, others are liked by
other voters, with little correlation), then if you were to repeatedly
elect someone hated by a polarizing method, you would be electing
favorites of the "other camp".
But it turned out that wasn't actually the case. What I had called
"Worst Plurality" (electing the Plurality loser) was in fact worst
*Anti*plurality (electing the Antiplurality loser). And I suppose that
since Antiplurality has high VSE awful proportionality, reflecting it
got something that had proportionality but not utility.
That's why review is so important: it helps identify slip-ups and bugs.
Thanks for prompting me to investigate this.
With the bug fixed, I get the following results after 900 rounds, same
parameters:
Prop'ty Utility
-1.0518 -0.64366 Worst Plurality
0.36886 -0.86348 Worst Antiplurality
which makes a lot more sense. (They'll be slightly off compared to the
attached results since I didn't run more rounds, but the quadrants are a
lot more sensible.)
I'm not entirely sure why "elect the loser" flips the sign on both
proportionality and utility, though. You'd expect proportionality to be
more fragile and thus show bad results (VSE < 0) if you go around
electing hated candidates... but apparently not.
> Also would it be possible to post the result as the raw numbers in addition to the graph?
Sure. I've attached the following files:
harmonic.txt: Harmonic voting with different delta values
harmonic_extended.txt: Harmonic voting with delta > 1 (dashed line on graph)
isoelastic.txt: Isoelastic
psi.txt: Psi voting
qpq.txt: QPQ
others.txt: Other methods, for the full graph
selected.txt: Selected methods for the detailed graph
These are with 377k rounds.
I've marked the mistakenly thought to be Plurality loser results #Worst
Antiplurality#, to show that they're really electing Antiplurality losers.
The names in others.txt in particular require some explanation:
Method names containing a question mark have been imported more or less
directly from my old source; I have not fully checked them for bugs.
Maj[base]: Majoritarian/bloc voting using the "base" method. This just
elects the winner, second place, third place, etc. according the base
method.
Maj[Eliminate[base]]: Bloc voting using sequential loser elimination
with "base" as the base method. E.g. Eliminate[Plurality] is IRV,
Eliminate[Antiplurality] is Coombs.
Maj[AVGEliminate[base]]: As above, but eliminates every candidate with
below-average score for the round. Maj[AVGEliminate[Plurality]] is Craig
Carey's IFPP.
Cardinal-20: Range voting with a 0...20 scale. Absolute scale.
Cardinal-20(norm): Same, but normalized scale.
Ext-Minmin: the "max A>B" method: the winner is the one with the
greatest pairwise defeat over someone else.
ReweightA[positional method]: Like reweighted Range voting, but using
the positional method's points instead of ratings. Each voter's weight
is adjusted to be C / (C + Q), where Q is the sum of contributions to
elected candidates, with each contribution normalized so that maximum
number of points is mapped to 1, and minimum to 0; and C is an
adjustable parameter.
ReweightM[positional method]: When someone is elected, each voter's
current weight is multiplied by C / (C + Q), where Q is the sum of
contributions to that candidate.
Range-Auction, Q-Range STV, Linear Range STV, Quota Bucklin, Set PR
Bucklin, Compat-QLTD-PR, M-Set Webster: methods from my 2008 simulator;
I'm not quite sure how they work; they thus need more investigation. Of
these, only the Range STV versions and M-Set Webster seem to be good,
and I can probably throw out the rest unless other simulations show them
to be good.
DHwL[base]: D'Hondt without lists. The base method is used to pick the
next winner according to the modified pairwise matrix.
PSC-CLE: https://electowiki.org/wiki/PSC-CLE. "Quota = x" uses the quota
(num voters)/(num seats + x) instead of the Droop quota.
C-Elim[base]: As PSC-CLE, but using the base method's elimination order.
PSC-CLE is C-Elim[Schulze].
STV-ME (base): Generalization of BTR-IRV. Let N = (number of seats -
number already elected) + 1. When a candidate needs to be eliminated,
conduct an election between the N candidates with the least first
preference count, using the base method. Eliminate the loser of this
election. Note that STV-ME (Plurality) is not the same thing as plain STV.
R-Birational: Birational with a relative scale. (Just "birational" uses
an absolute scale.)
For positional methods, ER means equal-rank is counted whole, but this
rarely comes into play due to the noise being added to voters' ratings.
/fd means "first differences", i.e. ties for elimination are broken by
the first round where the candidates were not tied.
-km
-------------- next part --------------
-0.02738 0.89931 Cardinal: Harmonic (D'Hondt)
-0.02159 0.89765 Cardinal: Harmonic (delta = 0.99)
-0.01795 0.89674 Cardinal: Harmonic (delta = 0.98)
-0.01432 0.8958 Cardinal: Harmonic (delta = 0.97)
-0.01038 0.89481 Cardinal: Harmonic (delta = 0.96)
-0.00657 0.89381 Cardinal: Harmonic (delta = 0.95)
-0.00306 0.89282 Cardinal: Harmonic (delta = 0.94)
0.00081 0.89171 Cardinal: Harmonic (delta = 0.93)
0.00494 0.89059 Cardinal: Harmonic (delta = 0.92)
0.00904 0.88951 Cardinal: Harmonic (delta = 0.91)
0.01296 0.88832 Cardinal: Harmonic (delta = 0.9)
0.01716 0.88716 Cardinal: Harmonic (delta = 0.89)
0.02141 0.88598 Cardinal: Harmonic (delta = 0.88)
0.0254 0.88484 Cardinal: Harmonic (delta = 0.87)
0.02943 0.88362 Cardinal: Harmonic (delta = 0.86)
0.03373 0.88233 Cardinal: Harmonic (delta = 0.85)
0.0381 0.88108 Cardinal: Harmonic (delta = 0.84)
0.04186 0.87976 Cardinal: Harmonic (delta = 0.83)
0.04637 0.87846 Cardinal: Harmonic (delta = 0.82)
0.05087 0.87706 Cardinal: Harmonic (delta = 0.81)
0.05614 0.87568 Cardinal: Harmonic (delta = 0.8)
0.06089 0.87417 Cardinal: Harmonic (delta = 0.79)
0.0666 0.87235 Cardinal: Harmonic (delta = 0.78)
0.07083 0.87088 Cardinal: Harmonic (delta = 0.77)
0.07607 0.86923 Cardinal: Harmonic (delta = 0.76)
0.08093 0.86754 Cardinal: Harmonic (delta = 0.75)
0.08628 0.86563 Cardinal: Harmonic (delta = 0.74)
0.09115 0.86395 Cardinal: Harmonic (delta = 0.73)
0.09534 0.8624 Cardinal: Harmonic (delta = 0.72)
0.10069 0.86069 Cardinal: Harmonic (delta = 0.71)
0.10612 0.85894 Cardinal: Harmonic (delta = 0.7)
0.11065 0.8572 Cardinal: Harmonic (delta = 0.69)
0.1159 0.85532 Cardinal: Harmonic (delta = 0.68)
0.12154 0.85339 Cardinal: Harmonic (delta = 0.67)
0.12723 0.85125 Cardinal: Harmonic (delta = 0.66)
0.13211 0.84926 Cardinal: Harmonic (delta = 0.65)
0.13695 0.84728 Cardinal: Harmonic (delta = 0.64)
0.14215 0.84522 Cardinal: Harmonic (delta = 0.63)
0.14762 0.84304 Cardinal: Harmonic (delta = 0.62)
0.15353 0.84081 Cardinal: Harmonic (delta = 0.61)
0.15886 0.83862 Cardinal: Harmonic (delta = 0.6)
0.16456 0.83618 Cardinal: Harmonic (delta = 0.59)
0.17044 0.83372 Cardinal: Harmonic (delta = 0.58)
0.1764 0.83127 Cardinal: Harmonic (delta = 0.57)
0.18267 0.82875 Cardinal: Harmonic (delta = 0.56)
0.18831 0.82625 Cardinal: Harmonic (delta = 0.55)
0.19478 0.82344 Cardinal: Harmonic (delta = 0.54)
0.2008 0.82075 Cardinal: Harmonic (delta = 0.53)
0.20685 0.81779 Cardinal: Harmonic (delta = 0.52)
0.21289 0.81489 Cardinal: Harmonic (delta = 0.51)
0.21935 0.81183 Cardinal: Harmonic (Sainte-Laguë)
0.22643 0.8082 Cardinal: Harmonic (delta = 0.49)
0.23258 0.8051 Cardinal: Harmonic (delta = 0.48)
0.23948 0.80159 Cardinal: Harmonic (delta = 0.47)
0.24574 0.79821 Cardinal: Harmonic (delta = 0.46)
0.25337 0.79454 Cardinal: Harmonic (delta = 0.45)
0.26037 0.79105 Cardinal: Harmonic (delta = 0.44)
0.26784 0.78715 Cardinal: Harmonic (delta = 0.43)
0.27438 0.78323 Cardinal: Harmonic (delta = 0.42)
0.28205 0.77917 Cardinal: Harmonic (delta = 0.41)
0.28932 0.77503 Cardinal: Harmonic (delta = 0.4)
0.29757 0.77028 Cardinal: Harmonic (delta = 0.39)
0.305 0.76564 Cardinal: Harmonic (delta = 0.38)
0.31329 0.76073 Cardinal: Harmonic (delta = 0.37)
0.32124 0.75558 Cardinal: Harmonic (delta = 0.36)
0.32908 0.75049 Cardinal: Harmonic (delta = 0.35)
0.33662 0.74525 Cardinal: Harmonic (delta = 0.34)
0.34447 0.73945 Cardinal: Harmonic (delta = 0.33)
0.35277 0.73368 Cardinal: Harmonic (delta = 0.32)
0.36009 0.72766 Cardinal: Harmonic (delta = 0.31)
0.36914 0.72138 Cardinal: Harmonic (delta = 0.3)
0.37808 0.71467 Cardinal: Harmonic (delta = 0.29)
0.38719 0.70756 Cardinal: Harmonic (delta = 0.28)
0.39595 0.70052 Cardinal: Harmonic (delta = 0.27)
0.40561 0.69273 Cardinal: Harmonic (delta = 0.26)
0.41501 0.68476 Cardinal: Harmonic (delta = 0.25)
0.42464 0.67641 Cardinal: Harmonic (delta = 0.24)
0.43428 0.66763 Cardinal: Harmonic (delta = 0.23)
0.44421 0.65837 Cardinal: Harmonic (delta = 0.22)
0.45288 0.64919 Cardinal: Harmonic (delta = 0.21)
0.4631 0.63887 Cardinal: Harmonic (delta = 0.2)
0.47343 0.62789 Cardinal: Harmonic (delta = 0.19)
0.48383 0.61647 Cardinal: Harmonic (delta = 0.18)
0.49527 0.60415 Cardinal: Harmonic (delta = 0.17)
0.50578 0.59143 Cardinal: Harmonic (delta = 0.16)
0.51668 0.57794 Cardinal: Harmonic (delta = 0.15)
0.5275 0.56361 Cardinal: Harmonic (delta = 0.14)
0.53911 0.54809 Cardinal: Harmonic (delta = 0.13)
0.55049 0.53178 Cardinal: Harmonic (delta = 0.12)
0.5617 0.51475 Cardinal: Harmonic (delta = 0.11)
0.57232 0.49644 Cardinal: Harmonic (delta = 0.1)
0.58365 0.47682 Cardinal: Harmonic (delta = 0.09)
0.59484 0.45604 Cardinal: Harmonic (delta = 0.08)
0.60555 0.43383 Cardinal: Harmonic (delta = 0.07)
0.61626 0.41077 Cardinal: Harmonic (delta = 0.06)
0.62699 0.38589 Cardinal: Harmonic (delta = 0.05)
0.63745 0.35986 Cardinal: Harmonic (delta = 0.04)
0.64632 0.33333 Cardinal: Harmonic (delta = 0.03)
0.65466 0.30708 Cardinal: Harmonic (delta = 0.02)
0.66197 0.28345 Cardinal: Harmonic (delta = 0.01)
-------------- next part --------------
-0.0268 0.89934 Cardinal: Harmonic (D'Hondt)
-0.08269 0.91284 Cardinal: Harmonic extended (1.16183)
-0.14134 0.92478 Cardinal: Harmonic extended (1.34986)
-0.19874 0.935 Cardinal: Harmonic extended (1.56831)
-0.2575 0.94406 Cardinal: Harmonic extended (1.82212)
-0.31734 0.95211 Cardinal: Harmonic extended (2.117)
-0.37423 0.95882 Cardinal: Harmonic extended (2.4596)
-0.43104 0.96456 Cardinal: Harmonic extended (2.85765)
-0.48296 0.96936 Cardinal: Harmonic extended (3.32012)
-0.53817 0.97335 Cardinal: Harmonic extended (3.85743)
-0.59081 0.97673 Cardinal: Harmonic extended (4.48169)
-0.63696 0.97946 Cardinal: Harmonic extended (5.20698)
-0.68362 0.98165 Cardinal: Harmonic extended (6.04965)
-0.72727 0.98344 Cardinal: Harmonic extended (7.02869)
-0.76379 0.98481 Cardinal: Harmonic extended (8.16617)
-0.79784 0.98599 Cardinal: Harmonic extended (9.48774)
-0.82832 0.9869 Cardinal: Harmonic extended (11.0232)
-0.85276 0.98763 Cardinal: Harmonic extended (12.8071)
-0.8777 0.98822 Cardinal: Harmonic extended (14.8797)
-0.89782 0.98867 Cardinal: Harmonic extended (17.2878)
-0.91705 0.98906 Cardinal: Harmonic extended (20.0855)
-0.93314 0.98934 Cardinal: Harmonic extended (23.3361)
-0.94642 0.98959 Cardinal: Harmonic extended (27.1126)
-0.95876 0.98973 Cardinal: Harmonic extended (31.5004)
-0.97018 0.98988 Cardinal: Harmonic extended (36.5982)
-0.97871 0.98998 Cardinal: Harmonic extended (42.5211)
-0.98588 0.99006 Cardinal: Harmonic extended (49.4024)
-0.99312 0.99015 Cardinal: Harmonic extended (57.3975)
-0.99956 0.9902 Cardinal: Harmonic extended (66.6863)
-1.00367 0.99024 Cardinal: Harmonic extended (77.4785)
-1.0083 0.99028 Cardinal: Harmonic extended (90.0171)
-------------- next part --------------
0.30046 0.01776 Cardinal: Isoelastic (r = -3.26902e+07)
0.30377 0.01903 Cardinal: Isoelastic (r = -2.24676e+07)
0.30879 0.02042 Cardinal: Isoelastic (r = -1.54417e+07)
0.31694 0.02286 Cardinal: Isoelastic (r = -1.06129e+07)
0.32734 0.02593 Cardinal: Isoelastic (r = -7.29416e+06)
0.34374 0.02984 Cardinal: Isoelastic (r = -5.0132e+06)
0.37012 0.03399 Cardinal: Isoelastic (r = -3.44552e+06)
0.40261 0.03755 Cardinal: Isoelastic (r = -2.36807e+06)
0.43782 0.03748 Cardinal: Isoelastic (r = -1.62755e+06)
0.46436 0.03358 Cardinal: Isoelastic (r = -1.1186e+06)
0.4719 0.03027 Cardinal: Isoelastic (r = -768799)
0.47329 0.02904 Cardinal: Isoelastic (r = -528387)
0.47426 0.02843 Cardinal: Isoelastic (r = -363155)
0.47438 0.02823 Cardinal: Isoelastic (r = -249593)
0.47456 0.02824 Cardinal: Isoelastic (r = -171542)
0.47451 0.02829 Cardinal: Isoelastic (r = -117899)
0.47455 0.02837 Cardinal: Isoelastic (r = -81030.8)
0.4746 0.02851 Cardinal: Isoelastic (r = -55691.6)
0.47468 0.02877 Cardinal: Isoelastic (r = -38276.3)
0.47475 0.02926 Cardinal: Isoelastic (r = -26306.9)
0.47584 0.03037 Cardinal: Isoelastic (r = -18080.4)
0.47646 0.03188 Cardinal: Isoelastic (r = -12426.5)
0.47712 0.03456 Cardinal: Isoelastic (r = -8540.59)
0.47778 0.03772 Cardinal: Isoelastic (r = -5869.85)
0.4825 0.04019 Cardinal: Isoelastic (r = -4034.29)
0.49496 0.04753 Cardinal: Isoelastic (r = -2772.72)
0.51746 0.05881 Cardinal: Isoelastic (r = -1905.66)
0.55195 0.07825 Cardinal: Isoelastic (r = -1309.74)
0.57129 0.1013 Cardinal: Isoelastic (r = -900.171)
0.57267 0.11064 Cardinal: Isoelastic (r = -618.678)
0.57158 0.11207 Cardinal: Isoelastic (r = -425.211)
0.57044 0.11237 Cardinal: Isoelastic (r = -292.243)
0.57013 0.11273 Cardinal: Isoelastic (r = -200.855)
0.56997 0.11326 Cardinal: Isoelastic (r = -138.046)
0.57023 0.11449 Cardinal: Isoelastic (r = -94.8774)
0.57174 0.11709 Cardinal: Isoelastic (r = -65.2082)
0.5716 0.12096 Cardinal: Isoelastic (r = -44.8169)
0.56963 0.12838 Cardinal: Isoelastic (r = -30.8022)
0.56808 0.14127 Cardinal: Isoelastic (r = -21.17)
0.56352 0.16282 Cardinal: Isoelastic (r = -14.5499)
0.55366 0.19677 Cardinal: Isoelastic (r = -10)
0.55321 0.19809 Cardinal: Isoelastic (r = -9.9)
0.55294 0.1994 Cardinal: Isoelastic (r = -9.8)
0.55255 0.20072 Cardinal: Isoelastic (r = -9.7)
0.552 0.20201 Cardinal: Isoelastic (r = -9.6)
0.55172 0.20329 Cardinal: Isoelastic (r = -9.5)
0.55121 0.20459 Cardinal: Isoelastic (r = -9.4)
0.5507 0.20612 Cardinal: Isoelastic (r = -9.3)
0.55035 0.20753 Cardinal: Isoelastic (r = -9.2)
0.54971 0.20899 Cardinal: Isoelastic (r = -9.1)
0.54917 0.21051 Cardinal: Isoelastic (r = -9)
0.5487 0.21215 Cardinal: Isoelastic (r = -8.9)
0.54845 0.21367 Cardinal: Isoelastic (r = -8.8)
0.54816 0.21515 Cardinal: Isoelastic (r = -8.7)
0.54753 0.21691 Cardinal: Isoelastic (r = -8.6)
0.54711 0.21847 Cardinal: Isoelastic (r = -8.5)
0.54663 0.22021 Cardinal: Isoelastic (r = -8.4)
0.5461 0.22203 Cardinal: Isoelastic (r = -8.3)
0.54551 0.22387 Cardinal: Isoelastic (r = -8.2)
0.54496 0.2258 Cardinal: Isoelastic (r = -8.1)
0.54415 0.22778 Cardinal: Isoelastic (r = -8)
0.54356 0.22969 Cardinal: Isoelastic (r = -7.9)
0.54293 0.23161 Cardinal: Isoelastic (r = -7.8)
0.54226 0.23369 Cardinal: Isoelastic (r = -7.7)
0.5418 0.2358 Cardinal: Isoelastic (r = -7.6)
0.5414 0.23796 Cardinal: Isoelastic (r = -7.5)
0.54073 0.24004 Cardinal: Isoelastic (r = -7.4)
0.54017 0.2422 Cardinal: Isoelastic (r = -7.3)
0.53919 0.24469 Cardinal: Isoelastic (r = -7.2)
0.53809 0.247 Cardinal: Isoelastic (r = -7.1)
0.53721 0.24941 Cardinal: Isoelastic (r = -7)
0.53623 0.25187 Cardinal: Isoelastic (r = -6.9)
0.53565 0.25451 Cardinal: Isoelastic (r = -6.8)
0.53485 0.25702 Cardinal: Isoelastic (r = -6.7)
0.53376 0.25973 Cardinal: Isoelastic (r = -6.6)
0.53241 0.2626 Cardinal: Isoelastic (r = -6.5)
0.53157 0.26559 Cardinal: Isoelastic (r = -6.4)
0.53062 0.26849 Cardinal: Isoelastic (r = -6.3)
0.52945 0.27148 Cardinal: Isoelastic (r = -6.2)
0.52843 0.27457 Cardinal: Isoelastic (r = -6.1)
0.52754 0.27786 Cardinal: Isoelastic (r = -6)
0.52635 0.28099 Cardinal: Isoelastic (r = -5.9)
0.52503 0.28447 Cardinal: Isoelastic (r = -5.8)
0.52403 0.28787 Cardinal: Isoelastic (r = -5.7)
0.5229 0.29135 Cardinal: Isoelastic (r = -5.6)
0.52148 0.29476 Cardinal: Isoelastic (r = -5.5)
0.51994 0.29858 Cardinal: Isoelastic (r = -5.4)
0.51855 0.30245 Cardinal: Isoelastic (r = -5.3)
0.51744 0.30643 Cardinal: Isoelastic (r = -5.2)
0.51584 0.31044 Cardinal: Isoelastic (r = -5.1)
0.51398 0.31472 Cardinal: Isoelastic (r = -5)
0.5122 0.31895 Cardinal: Isoelastic (r = -4.9)
0.51081 0.32328 Cardinal: Isoelastic (r = -4.8)
0.50882 0.32806 Cardinal: Isoelastic (r = -4.7)
0.50634 0.33297 Cardinal: Isoelastic (r = -4.6)
0.50462 0.33776 Cardinal: Isoelastic (r = -4.5)
0.50246 0.34286 Cardinal: Isoelastic (r = -4.4)
0.50039 0.34798 Cardinal: Isoelastic (r = -4.3)
0.49817 0.3533 Cardinal: Isoelastic (r = -4.2)
0.49571 0.35867 Cardinal: Isoelastic (r = -4.1)
0.49323 0.36426 Cardinal: Isoelastic (r = -4)
0.49055 0.37008 Cardinal: Isoelastic (r = -3.9)
0.48802 0.37598 Cardinal: Isoelastic (r = -3.8)
0.48517 0.38188 Cardinal: Isoelastic (r = -3.7)
0.48261 0.38794 Cardinal: Isoelastic (r = -3.6)
0.47979 0.39434 Cardinal: Isoelastic (r = -3.5)
0.4761 0.4009 Cardinal: Isoelastic (r = -3.4)
0.47239 0.40769 Cardinal: Isoelastic (r = -3.3)
0.46828 0.4147 Cardinal: Isoelastic (r = -3.2)
0.4642 0.42162 Cardinal: Isoelastic (r = -3.1)
0.46035 0.42898 Cardinal: Isoelastic (r = -3)
0.45596 0.43671 Cardinal: Isoelastic (r = -2.9)
0.45203 0.4444 Cardinal: Isoelastic (r = -2.8)
0.44693 0.45231 Cardinal: Isoelastic (r = -2.7)
0.44273 0.4604 Cardinal: Isoelastic (r = -2.6)
0.43729 0.46875 Cardinal: Isoelastic (r = -2.5)
0.43193 0.4775 Cardinal: Isoelastic (r = -2.4)
0.42629 0.48665 Cardinal: Isoelastic (r = -2.3)
0.42063 0.49581 Cardinal: Isoelastic (r = -2.2)
0.41437 0.50519 Cardinal: Isoelastic (r = -2.1)
0.40813 0.51497 Cardinal: Isoelastic (r = -2)
0.40107 0.5251 Cardinal: Isoelastic (r = -1.9)
0.39393 0.53525 Cardinal: Isoelastic (r = -1.8)
0.38559 0.54579 Cardinal: Isoelastic (r = -1.7)
0.37755 0.55655 Cardinal: Isoelastic (r = -1.6)
0.36802 0.56732 Cardinal: Isoelastic (r = -1.5)
0.35872 0.57835 Cardinal: Isoelastic (r = -1.4)
0.3487 0.58962 Cardinal: Isoelastic (r = -1.3)
0.33869 0.6013 Cardinal: Isoelastic (r = -1.2)
0.32777 0.61316 Cardinal: Isoelastic (r = -1.1)
0.31658 0.62501 Cardinal: Isoelastic (r = -1)
0.30461 0.63718 Cardinal: Isoelastic (r = -0.9)
0.29257 0.64939 Cardinal: Isoelastic (r = -0.8)
0.27932 0.66176 Cardinal: Isoelastic (r = -0.7)
0.26518 0.6742 Cardinal: Isoelastic (r = -0.6)
0.25071 0.68622 Cardinal: Isoelastic (r = -0.5)
0.23602 0.69912 Cardinal: Isoelastic (r = -0.4)
0.21859 0.71189 Cardinal: Isoelastic (r = -0.3)
0.20064 0.72493 Cardinal: Isoelastic (r = -0.2)
0.18159 0.73765 Cardinal: Isoelastic (r = -0.1)
0.16184 0.75016 Cardinal: Isoelastic (r = -1.87905e-14)
0.14094 0.76235 Cardinal: Isoelastic (r = 0.1)
0.11761 0.775 Cardinal: Isoelastic (r = 0.2)
0.09434 0.78712 Cardinal: Isoelastic (r = 0.3)
0.06893 0.79909 Cardinal: Isoelastic (r = 0.4)
0.04409 0.81075 Cardinal: Isoelastic (r = 0.5)
0.01686 0.82226 Cardinal: Isoelastic (r = 0.6)
-0.01227 0.83428 Cardinal: Isoelastic (r = 0.7)
-0.04336 0.84756 Cardinal: Isoelastic (r = 0.8)
-0.0779 0.86154 Cardinal: Isoelastic (r = 0.9)
-0.16069 0.89184 Cardinal: Isoelastic (r = 1.1)
-0.21091 0.90761 Cardinal: Isoelastic (r = 1.2)
-0.26753 0.92338 Cardinal: Isoelastic (r = 1.3)
-0.33452 0.93886 Cardinal: Isoelastic (r = 1.4)
-0.41378 0.95324 Cardinal: Isoelastic (r = 1.5)
-0.50785 0.96575 Cardinal: Isoelastic (r = 1.6)
-0.61852 0.97588 Cardinal: Isoelastic (r = 1.7)
-0.75033 0.98332 Cardinal: Isoelastic (r = 1.8)
-0.89538 0.98809 Cardinal: Isoelastic (r = 1.9)
-1.03353 0.99067 Cardinal: Isoelastic (r = 2)
-1.11183 0.99144 Cardinal: Isoelastic (r = 2.1)
-1.17097 0.99141 Cardinal: Isoelastic (r = 2.2)
-1.22365 0.99067 Cardinal: Isoelastic (r = 2.3)
-1.27026 0.98939 Cardinal: Isoelastic (r = 2.4)
-1.30824 0.98781 Cardinal: Isoelastic (r = 2.5)
-1.34287 0.9859 Cardinal: Isoelastic (r = 2.6)
-1.37397 0.98387 Cardinal: Isoelastic (r = 2.7)
-1.40206 0.98173 Cardinal: Isoelastic (r = 2.8)
-1.42793 0.97938 Cardinal: Isoelastic (r = 2.9)
-1.45035 0.97698 Cardinal: Isoelastic (r = 3)
-1.47373 0.9743 Cardinal: Isoelastic (r = 3.1)
-1.49607 0.97164 Cardinal: Isoelastic (r = 3.2)
-1.51351 0.96893 Cardinal: Isoelastic (r = 3.3)
-1.52953 0.96622 Cardinal: Isoelastic (r = 3.4)
-1.5422 0.96342 Cardinal: Isoelastic (r = 3.5)
-1.55532 0.96075 Cardinal: Isoelastic (r = 3.6)
-1.56636 0.95801 Cardinal: Isoelastic (r = 3.7)
-1.57837 0.95529 Cardinal: Isoelastic (r = 3.8)
-1.58916 0.95248 Cardinal: Isoelastic (r = 3.9)
-1.59838 0.94952 Cardinal: Isoelastic (r = 4)
-1.60853 0.94664 Cardinal: Isoelastic (r = 4.1)
-1.61867 0.94381 Cardinal: Isoelastic (r = 4.2)
-1.62789 0.94094 Cardinal: Isoelastic (r = 4.3)
-1.63596 0.93809 Cardinal: Isoelastic (r = 4.4)
-1.6446 0.93526 Cardinal: Isoelastic (r = 4.5)
-1.65057 0.93227 Cardinal: Isoelastic (r = 4.6)
-1.65702 0.92943 Cardinal: Isoelastic (r = 4.7)
-1.66329 0.92665 Cardinal: Isoelastic (r = 4.8)
-1.66987 0.92366 Cardinal: Isoelastic (r = 4.9)
-1.67423 0.9209 Cardinal: Isoelastic (r = 5)
-1.68054 0.91792 Cardinal: Isoelastic (r = 5.1)
-1.68511 0.915 Cardinal: Isoelastic (r = 5.2)
-1.68849 0.91215 Cardinal: Isoelastic (r = 5.3)
-1.69212 0.90925 Cardinal: Isoelastic (r = 5.4)
-1.69681 0.90631 Cardinal: Isoelastic (r = 5.5)
-1.70064 0.9034 Cardinal: Isoelastic (r = 5.6)
-1.7047 0.90046 Cardinal: Isoelastic (r = 5.7)
-1.70851 0.89767 Cardinal: Isoelastic (r = 5.8)
-1.71208 0.89472 Cardinal: Isoelastic (r = 5.9)
-1.71484 0.89173 Cardinal: Isoelastic (r = 6)
-1.71711 0.88875 Cardinal: Isoelastic (r = 6.1)
-1.71974 0.88582 Cardinal: Isoelastic (r = 6.2)
-1.7224 0.88302 Cardinal: Isoelastic (r = 6.3)
-1.72341 0.88017 Cardinal: Isoelastic (r = 6.4)
-1.72474 0.87726 Cardinal: Isoelastic (r = 6.5)
-1.72694 0.87436 Cardinal: Isoelastic (r = 6.6)
-1.72841 0.87135 Cardinal: Isoelastic (r = 6.7)
-1.72989 0.86816 Cardinal: Isoelastic (r = 6.8)
-1.73104 0.86531 Cardinal: Isoelastic (r = 6.9)
-1.73322 0.86236 Cardinal: Isoelastic (r = 7)
-1.73375 0.85946 Cardinal: Isoelastic (r = 7.1)
-1.73446 0.85674 Cardinal: Isoelastic (r = 7.2)
-1.73471 0.85373 Cardinal: Isoelastic (r = 7.3)
-1.73517 0.85098 Cardinal: Isoelastic (r = 7.4)
-1.73508 0.84801 Cardinal: Isoelastic (r = 7.5)
-1.73618 0.84502 Cardinal: Isoelastic (r = 7.6)
-1.73664 0.8422 Cardinal: Isoelastic (r = 7.7)
-1.73676 0.83931 Cardinal: Isoelastic (r = 7.8)
-1.73608 0.83647 Cardinal: Isoelastic (r = 7.9)
-1.73596 0.83357 Cardinal: Isoelastic (r = 8)
-1.73523 0.83088 Cardinal: Isoelastic (r = 8.1)
-1.73469 0.82807 Cardinal: Isoelastic (r = 8.2)
-1.7342 0.82534 Cardinal: Isoelastic (r = 8.3)
-1.73461 0.82251 Cardinal: Isoelastic (r = 8.4)
-1.73454 0.81973 Cardinal: Isoelastic (r = 8.5)
-1.73372 0.81695 Cardinal: Isoelastic (r = 8.6)
-1.7327 0.81397 Cardinal: Isoelastic (r = 8.7)
-1.73182 0.81123 Cardinal: Isoelastic (r = 8.8)
-1.73132 0.80848 Cardinal: Isoelastic (r = 8.9)
-1.73063 0.80576 Cardinal: Isoelastic (r = 9)
-1.73012 0.80301 Cardinal: Isoelastic (r = 9.1)
-1.73006 0.80025 Cardinal: Isoelastic (r = 9.2)
-1.7293 0.79771 Cardinal: Isoelastic (r = 9.3)
-1.72869 0.79513 Cardinal: Isoelastic (r = 9.4)
-1.72828 0.79226 Cardinal: Isoelastic (r = 9.5)
-1.72691 0.78957 Cardinal: Isoelastic (r = 9.6)
-1.72641 0.78696 Cardinal: Isoelastic (r = 9.7)
-1.7264 0.78419 Cardinal: Isoelastic (r = 9.8)
-1.7264 0.78152 Cardinal: Isoelastic (r = 9.9)
-1.72508 0.779 Cardinal: Isoelastic (r = 10)
-------------- next part --------------
-1.61679 0.95099 Maj[Eliminate-[ER-Antiplurality]/fd]
-1.40797 0.94104 Maj[AVGEliminate-[ER-Antiplurality]/fd]
-1.24178 0.98719 Cardinal: Log-penalty (K = 1000)
-1.20759 0.89398 ReweightA[ER-Antiplurality]
-1.1997 0.89932 Maj[ER-Antiplurality]
-1.1997 0.89932 ReweightM[ER-Antiplurality]
-1.13952 0.46683 -- Random dictator --
-1.1151 0.9852 Cardinal: Log-penalty (K = 10)
-1.11111 0.99998 Maj[Cardinal-20]
-1.08219 0.98757 Maj[Schulze(wv)]
-1.07381 0.98886 Maj[Ext-Minmin(margins)]
-1.06715 0.99985 Range-Auction(?? Ordinary)
-1.03167 0.99008 Maj[Cardinal-20(norm)]
-0.9911 0.98129 Maj[Eliminate-[ER-VoteForAgainst]/fd]
-0.96976 0.99052 Maj[ER-Borda]
-0.96388 0.99073 Maj[AVGEliminate-[ER-Borda]/fd]
-0.94529 0.98949 Maj[Eliminate-[ER-Borda]/fd]
-0.92982 0.98211 ReweightA[ER-Borda]
-0.83645 0.96695 Maj[AVGEliminate-[ER-VoteForAgainst]/fd]
-0.77986 0.99494 ?Linear Range STV
-0.72211 0.97955 Range-Auction(?? Cumul)
-0.71905 0.93486 Maj[Ext-Minmax(margins)]
-0.69755 0.96327 Cardinal: Log-penalty (K = 1)
-0.65632 0.98809 ??Q-Range STV
-0.65185 0.97489 Maj[ER-Baseball MVP]
-0.64671 0.96189 Quota Bucklin(restart, Hare)
-0.64671 0.96189 Quota Bucklin(static, Hare)
-0.60388 0.93271 Maj[ER-VoteForAgainst]
-0.60084 0.96484 ReweightA[ER-Baseball MVP]
-0.58543 0.96352 PSC-CLE (Hare)
-0.57964 0.91704 ReweightA[ER-VoteForAgainst]
-0.52378 0.96446 Maj[AVGEliminate-[ER-Baseball MVP]/fd]
-0.49861 0.93023 Quota Bucklin(restart, Droop)
-0.49861 0.93023 Quota Bucklin(static, Droop)
-0.49229 0.93951 Maj[Eliminate-[ER-Heisman Trophy]/fd]
-0.47065 0.95118 PSC-CLE (Quota = 0.5)
-0.40764 0.95073 ReweightM[ER-Borda]
-0.3852 0.91833 Maj[AVGEliminate-[ER-Heisman Trophy]/fd]
-0.37264 0.91441 ReweightM[ER-VoteForAgainst]
-0.35933 0.93565 PSC-CLE
-0.33304 0.90553 Maj[ER-Heisman Trophy]
-0.29291 0.89928 Cardinal: LPV0+
-0.27468 0.94722 Maj[Eliminate-[ER-Baseball MVP]/fd]
-0.27178 0.91793 Maj[ER-Nauru Borda]
-0.25152 0.89137 ReweightA[ER-Heisman Trophy]
-0.22507 0.917 Maj[AVGEliminate-[ER-Nauru Borda]/fd]
-0.20481 0.90493 ReweightA[ER-Nauru Borda]
-0.18806 0.86316 Set PR Bucklin
-0.13252 0.92062 ReweightM[ER-Baseball MVP]
-0.11422 0.91432 Maj[Eliminate-[ER-Nauru Borda]/fd]
-0.10956 0.90776 DHwL(Schulze(wv))
-0.08229 0.90724 DHwL(Ext-Minmin(margins))
-0.07524 0.87113 DHwL(Ext-Minmax(margins))
-0.06104 0.89726 Cardinal: R-Birational
0.11023 0.84305 ReweightM[ER-Heisman Trophy]
0.13685 0.08265 Compat-QLTD-PR
0.14113 0.84429 ReweightM[ER-Nauru Borda]
0.17557 0.82993 STV-ME (Schulze)
0.21223 0.361 Set Webster
0.21371 0.81155 STV-ME (Plurality)
0.23069 0.32589 Random ballots
0.25191 0.80054 Meek STV
0.26192 0.79069 STV
0.26474 0.79642 Warren STV
0.28495 0.65722 Maj[ER-Plurality]
0.28495 0.65722 ReweightM[ER-Plurality]
0.29889 0.70759 M-Set Webster (640, EXP, 1, complx)
0.31024 0.64387 ReweightA[ER-Plurality]
0.3104 0.70195 M-Set Webster (640, EXP, 3, complx)
0.31991 0.66487 Maj[AVGEliminate-[ER-Plurality]/fd]
0.32799 0.65875 C-Elim[ER-Plurality] (Hare)
0.33388 0.67222 C-Elim[ER-Plurality]
0.33822 0.66217 C-Elim[ER-Plurality] (Quota = 0.5)
0.36976 -0.83915 Maj[ER-#Worst Antiplurality#]
0.36976 -0.83915 ReweightM[ER-#Worst Antiplurality#]
0.38075 0.68178 Schulze STV
0.39606 0.66624 M-Set Webster (c37, EXP, 0, simple, unlimit)
0.39678 0.68592 Maj[Eliminate-[ER-Plurality]/fd]
0.42465 -0.83841 Maj[AVGEliminate-[ER-#Worst Antiplurality#]/fd]
0.49265 -0.82571 ReweightA[ER-#Worst Antiplurality#]
0.64245 -0.83168 Maj[Eliminate-[ER-#Worst Antiplurality#]/fd]
0.87565 0.02416 Cardinal: Birational
-------------- next part --------------
-0.32125 0.93748 Cardinal: Psi (D'Hondt)
-0.3167 0.9365 Cardinal: Psi (delta = 0.99)
-0.31452 0.93613 Cardinal: Psi (delta = 0.98)
-0.3127 0.93577 Cardinal: Psi (delta = 0.97)
-0.31022 0.93539 Cardinal: Psi (delta = 0.96)
-0.30782 0.93496 Cardinal: Psi (delta = 0.95)
-0.3058 0.93453 Cardinal: Psi (delta = 0.94)
-0.30352 0.93406 Cardinal: Psi (delta = 0.93)
-0.30163 0.93362 Cardinal: Psi (delta = 0.92)
-0.29944 0.93322 Cardinal: Psi (delta = 0.91)
-0.29743 0.93274 Cardinal: Psi (delta = 0.9)
-0.29561 0.9323 Cardinal: Psi (delta = 0.89)
-0.29337 0.9318 Cardinal: Psi (delta = 0.88)
-0.29111 0.93135 Cardinal: Psi (delta = 0.87)
-0.28831 0.93085 Cardinal: Psi (delta = 0.86)
-0.28587 0.93035 Cardinal: Psi (delta = 0.85)
-0.28353 0.92987 Cardinal: Psi (delta = 0.84)
-0.28069 0.92929 Cardinal: Psi (delta = 0.83)
-0.27812 0.92878 Cardinal: Psi (delta = 0.82)
-0.27558 0.92833 Cardinal: Psi (delta = 0.81)
-0.27402 0.92789 Cardinal: Psi (delta = 0.8)
-0.27108 0.92726 Cardinal: Psi (delta = 0.79)
-0.26847 0.92675 Cardinal: Psi (delta = 0.78)
-0.26585 0.92624 Cardinal: Psi (delta = 0.77)
-0.26354 0.92571 Cardinal: Psi (delta = 0.76)
-0.26097 0.92519 Cardinal: Psi (delta = 0.75)
-0.258 0.92445 Cardinal: Psi (delta = 0.74)
-0.25579 0.92389 Cardinal: Psi (delta = 0.73)
-0.25266 0.92326 Cardinal: Psi (delta = 0.72)
-0.2497 0.92269 Cardinal: Psi (delta = 0.71)
-0.2476 0.92212 Cardinal: Psi (delta = 0.7)
-0.24491 0.92156 Cardinal: Psi (delta = 0.69)
-0.24279 0.92095 Cardinal: Psi (delta = 0.68)
-0.24033 0.92039 Cardinal: Psi (delta = 0.67)
-0.2376 0.91959 Cardinal: Psi (delta = 0.66)
-0.23487 0.91894 Cardinal: Psi (delta = 0.65)
-0.2318 0.91824 Cardinal: Psi (delta = 0.64)
-0.22931 0.91758 Cardinal: Psi (delta = 0.63)
-0.2266 0.9169 Cardinal: Psi (delta = 0.62)
-0.22369 0.91624 Cardinal: Psi (delta = 0.61)
-0.22132 0.91559 Cardinal: Psi (delta = 0.6)
-0.21823 0.91477 Cardinal: Psi (delta = 0.59)
-0.21586 0.91409 Cardinal: Psi (delta = 0.58)
-0.21283 0.91343 Cardinal: Psi (delta = 0.57)
-0.20968 0.9127 Cardinal: Psi (delta = 0.56)
-0.20715 0.91196 Cardinal: Psi (delta = 0.55)
-0.2045 0.91118 Cardinal: Psi (delta = 0.54)
-0.20185 0.91038 Cardinal: Psi (delta = 0.53)
-0.19896 0.90961 Cardinal: Psi (delta = 0.52)
-0.1958 0.90883 Cardinal: Psi (delta = 0.51)
-0.1926 0.90801 Cardinal: Psi (Sainte-Laguë)
-0.18835 0.90652 Cardinal: Psi (delta = 0.49)
-0.1851 0.90566 Cardinal: Psi (delta = 0.48)
-0.18245 0.90483 Cardinal: Psi (delta = 0.47)
-0.17955 0.90395 Cardinal: Psi (delta = 0.46)
-0.17673 0.90296 Cardinal: Psi (delta = 0.45)
-0.17339 0.90208 Cardinal: Psi (delta = 0.44)
-0.17048 0.9012 Cardinal: Psi (delta = 0.43)
-0.16753 0.90021 Cardinal: Psi (delta = 0.42)
-0.16434 0.89924 Cardinal: Psi (delta = 0.41)
-0.16148 0.89839 Cardinal: Psi (delta = 0.4)
-0.158 0.8973 Cardinal: Psi (delta = 0.39)
-0.15443 0.89628 Cardinal: Psi (delta = 0.38)
-0.15143 0.89525 Cardinal: Psi (delta = 0.37)
-0.14799 0.89411 Cardinal: Psi (delta = 0.36)
-0.14491 0.89311 Cardinal: Psi (delta = 0.35)
-0.14103 0.89199 Cardinal: Psi (delta = 0.34)
-0.13718 0.89069 Cardinal: Psi (delta = 0.33)
-0.13375 0.88955 Cardinal: Psi (delta = 0.32)
-0.12992 0.88829 Cardinal: Psi (delta = 0.31)
-0.1266 0.88713 Cardinal: Psi (delta = 0.3)
-0.12286 0.8858 Cardinal: Psi (delta = 0.29)
-0.11921 0.88453 Cardinal: Psi (delta = 0.28)
-0.1158 0.88324 Cardinal: Psi (delta = 0.27)
-0.11182 0.88186 Cardinal: Psi (delta = 0.26)
-0.10772 0.88059 Cardinal: Psi (delta = 0.25)
-0.10372 0.87912 Cardinal: Psi (delta = 0.24)
-0.09973 0.87773 Cardinal: Psi (delta = 0.23)
-0.09574 0.8762 Cardinal: Psi (delta = 0.22)
-0.09172 0.87464 Cardinal: Psi (delta = 0.21)
-0.08741 0.87307 Cardinal: Psi (delta = 0.2)
-0.08341 0.87149 Cardinal: Psi (delta = 0.19)
-0.07962 0.86977 Cardinal: Psi (delta = 0.18)
-0.07639 0.8682 Cardinal: Psi (delta = 0.17)
-0.07251 0.86642 Cardinal: Psi (delta = 0.16)
-0.06868 0.86464 Cardinal: Psi (delta = 0.15)
-0.06472 0.86272 Cardinal: Psi (delta = 0.14)
-0.061 0.86073 Cardinal: Psi (delta = 0.13)
-0.05668 0.85883 Cardinal: Psi (delta = 0.12)
-0.05252 0.85687 Cardinal: Psi (delta = 0.11)
-0.04843 0.85479 Cardinal: Psi (delta = 0.1)
-0.04357 0.85249 Cardinal: Psi (delta = 0.09)
-0.03933 0.8502 Cardinal: Psi (delta = 0.08)
-0.03476 0.84789 Cardinal: Psi (delta = 0.07)
-0.03072 0.84551 Cardinal: Psi (delta = 0.06)
-0.02629 0.84307 Cardinal: Psi (delta = 0.05)
-0.02187 0.84053 Cardinal: Psi (delta = 0.04)
-0.01799 0.83781 Cardinal: Psi (delta = 0.03)
-0.01377 0.83518 Cardinal: Psi (delta = 0.02)
-0.01045 0.83299 Cardinal: Psi (delta = 0.01)
-0.00728 0.83147 Cardinal: Psi (delta = 0)
-------------- next part --------------
0.75143 -0.02335 QPQ(div 0.005, multiround)
0.75212 -0.00981 QPQ(div 0.01, multiround)
0.75224 0.00551 QPQ(div 0.015, multiround)
0.75252 0.02036 QPQ(div 0.02, multiround)
0.75253 0.03533 QPQ(div 0.025, multiround)
0.75224 0.04993 QPQ(div 0.03, multiround)
0.75201 0.06389 QPQ(div 0.035, multiround)
0.75201 0.07747 QPQ(div 0.04, multiround)
0.75093 0.09101 QPQ(div 0.045, multiround)
0.74925 0.10413 QPQ(div 0.05, multiround)
0.74818 0.11598 QPQ(div 0.055, multiround)
0.747 0.12825 QPQ(div 0.06, multiround)
0.74588 0.13992 QPQ(div 0.065, multiround)
0.74446 0.15141 QPQ(div 0.07, multiround)
0.74295 0.16249 QPQ(div 0.075, multiround)
0.74078 0.17349 QPQ(div 0.08, multiround)
0.73903 0.18525 QPQ(div 0.085, multiround)
0.737 0.1953 QPQ(div 0.09, multiround)
0.73456 0.20538 QPQ(div 0.095, multiround)
0.73245 0.21562 QPQ(div 0.1, multiround)
0.73019 0.22499 QPQ(div 0.105, multiround)
0.72799 0.23417 QPQ(div 0.11, multiround)
0.72564 0.2438 QPQ(div 0.115, multiround)
0.72288 0.25249 QPQ(div 0.12, multiround)
0.72001 0.26176 QPQ(div 0.125, multiround)
0.71687 0.27006 QPQ(div 0.13, multiround)
0.71431 0.27848 QPQ(div 0.135, multiround)
0.71153 0.28607 QPQ(div 0.14, multiround)
0.70843 0.29389 QPQ(div 0.145, multiround)
0.70572 0.30136 QPQ(div 0.15, multiround)
0.70264 0.30918 QPQ(div 0.155, multiround)
0.69945 0.31643 QPQ(div 0.16, multiround)
0.69674 0.32337 QPQ(div 0.165, multiround)
0.69342 0.33272 QPQ(div 0.17, multiround)
0.69 0.33961 QPQ(div 0.175, multiround)
0.68713 0.34598 QPQ(div 0.18, multiround)
0.68374 0.35262 QPQ(div 0.185, multiround)
0.6804 0.35929 QPQ(div 0.19, multiround)
0.67694 0.3659 QPQ(div 0.195, multiround)
0.67359 0.3726 QPQ(div 0.2, multiround)
0.67004 0.37897 QPQ(div 0.205, multiround)
0.66707 0.38503 QPQ(div 0.21, multiround)
0.66334 0.39123 QPQ(div 0.215, multiround)
0.66053 0.39689 QPQ(div 0.22, multiround)
0.65769 0.40313 QPQ(div 0.225, multiround)
0.65462 0.40852 QPQ(div 0.23, multiround)
0.65119 0.41388 QPQ(div 0.235, multiround)
0.64749 0.41919 QPQ(div 0.24, multiround)
0.64417 0.42457 QPQ(div 0.245, multiround)
0.64054 0.43096 QPQ(div 0.25, multiround)
0.63703 0.43708 QPQ(div 0.255, multiround)
0.63385 0.44175 QPQ(div 0.26, multiround)
0.63122 0.44629 QPQ(div 0.265, multiround)
0.62781 0.4513 QPQ(div 0.27, multiround)
0.62484 0.45596 QPQ(div 0.275, multiround)
0.62176 0.46076 QPQ(div 0.28, multiround)
0.61895 0.46512 QPQ(div 0.285, multiround)
0.61508 0.47008 QPQ(div 0.29, multiround)
0.61195 0.47444 QPQ(div 0.295, multiround)
0.60897 0.47874 QPQ(div 0.3, multiround)
0.60591 0.48316 QPQ(div 0.305, multiround)
0.60318 0.48702 QPQ(div 0.31, multiround)
0.60006 0.4911 QPQ(div 0.315, multiround)
0.59763 0.49484 QPQ(div 0.32, multiround)
0.5953 0.49873 QPQ(div 0.325, multiround)
0.59251 0.50254 QPQ(div 0.33, multiround)
0.58858 0.5092 QPQ(div 0.335, multiround)
0.58583 0.51266 QPQ(div 0.34, multiround)
0.58359 0.51631 QPQ(div 0.345, multiround)
0.58092 0.51997 QPQ(div 0.35, multiround)
0.57848 0.52348 QPQ(div 0.355, multiround)
0.57599 0.52708 QPQ(div 0.36, multiround)
0.57273 0.53066 QPQ(div 0.365, multiround)
0.5703 0.53418 QPQ(div 0.37, multiround)
0.56831 0.53749 QPQ(div 0.375, multiround)
0.5666 0.54103 QPQ(div 0.38, multiround)
0.56428 0.54429 QPQ(div 0.385, multiround)
0.56161 0.54752 QPQ(div 0.39, multiround)
0.55909 0.55061 QPQ(div 0.395, multiround)
0.55689 0.55404 QPQ(div 0.4, multiround)
0.55381 0.55747 QPQ(div 0.405, multiround)
0.55109 0.56066 QPQ(div 0.41, multiround)
0.54836 0.56372 QPQ(div 0.415, multiround)
0.54595 0.56713 QPQ(div 0.42, multiround)
0.54356 0.57009 QPQ(div 0.425, multiround)
0.54071 0.57413 QPQ(div 0.43, multiround)
0.53789 0.57716 QPQ(div 0.435, multiround)
0.53567 0.57998 QPQ(div 0.44, multiround)
0.53267 0.58371 QPQ(div 0.445, multiround)
0.5305 0.58634 QPQ(div 0.45, multiround)
0.5277 0.58936 QPQ(div 0.455, multiround)
0.52496 0.59213 QPQ(div 0.46, multiround)
0.52272 0.59509 QPQ(div 0.465, multiround)
0.5201 0.59789 QPQ(div 0.47, multiround)
0.51795 0.60071 QPQ(div 0.475, multiround)
0.5157 0.60356 QPQ(div 0.48, multiround)
0.51244 0.60656 QPQ(div 0.485, multiround)
0.50954 0.60927 QPQ(div 0.49, multiround)
0.50659 0.61165 QPQ(div 0.495, multiround)
0.50256 0.6162 QPQ(div Sainte-L, multiround)
0.49818 0.62163 QPQ(div 0.505, multiround)
0.49562 0.62417 QPQ(div 0.51, multiround)
0.4922 0.62695 QPQ(div 0.515, multiround)
0.48962 0.62963 QPQ(div 0.52, multiround)
0.48653 0.63238 QPQ(div 0.525, multiround)
0.48447 0.63511 QPQ(div 0.53, multiround)
0.48193 0.63774 QPQ(div 0.535, multiround)
0.47973 0.64031 QPQ(div 0.54, multiround)
0.47718 0.64279 QPQ(div 0.545, multiround)
0.47465 0.64577 QPQ(div 0.55, multiround)
0.47252 0.64803 QPQ(div 0.555, multiround)
0.47 0.65097 QPQ(div 0.56, multiround)
0.46792 0.65345 QPQ(div 0.565, multiround)
0.46562 0.65586 QPQ(div 0.57, multiround)
0.46317 0.659 QPQ(div 0.575, multiround)
0.4611 0.66157 QPQ(div 0.58, multiround)
0.45888 0.66426 QPQ(div 0.585, multiround)
0.45669 0.66671 QPQ(div 0.59, multiround)
0.4547 0.66916 QPQ(div 0.595, multiround)
0.4519 0.6719 QPQ(div 0.6, multiround)
0.44811 0.67597 QPQ(div 0.605, multiround)
0.4453 0.6784 QPQ(div 0.61, multiround)
0.44221 0.68094 QPQ(div 0.615, multiround)
0.43971 0.68334 QPQ(div 0.62, multiround)
0.43685 0.68581 QPQ(div 0.625, multiround)
0.43362 0.68881 QPQ(div 0.63, multiround)
0.43064 0.6913 QPQ(div 0.635, multiround)
0.42742 0.69381 QPQ(div 0.64, multiround)
0.42417 0.69631 QPQ(div 0.645, multiround)
0.42091 0.69881 QPQ(div 0.65, multiround)
0.41777 0.70111 QPQ(div 0.655, multiround)
0.41472 0.70335 QPQ(div 0.66, multiround)
0.41191 0.70561 QPQ(div 0.665, multiround)
0.40691 0.71057 QPQ(div 0.67, multiround)
0.40416 0.71269 QPQ(div 0.675, multiround)
0.40118 0.71482 QPQ(div 0.68, multiround)
0.39778 0.71711 QPQ(div 0.685, multiround)
0.39427 0.71951 QPQ(div 0.69, multiround)
0.39112 0.72176 QPQ(div 0.695, multiround)
0.3876 0.72404 QPQ(div 0.7, multiround)
0.38447 0.72611 QPQ(div 0.705, multiround)
0.38186 0.72805 QPQ(div 0.71, multiround)
0.37888 0.73049 QPQ(div 0.715, multiround)
0.3761 0.7325 QPQ(div 0.72, multiround)
0.37273 0.73447 QPQ(div 0.725, multiround)
0.36961 0.73659 QPQ(div 0.73, multiround)
0.36699 0.73856 QPQ(div 0.735, multiround)
0.36408 0.74032 QPQ(div 0.74, multiround)
0.36101 0.74211 QPQ(div 0.745, multiround)
0.35767 0.7445 QPQ(div 0.75, multiround)
0.35195 0.74864 QPQ(div 0.755, multiround)
0.34912 0.75021 QPQ(div 0.76, multiround)
0.34607 0.75188 QPQ(div 0.765, multiround)
0.34276 0.75368 QPQ(div 0.77, multiround)
0.34031 0.75523 QPQ(div 0.775, multiround)
0.33702 0.75705 QPQ(div 0.78, multiround)
0.33395 0.75859 QPQ(div 0.785, multiround)
0.3313 0.7602 QPQ(div 0.79, multiround)
0.3285 0.76158 QPQ(div 0.795, multiround)
0.32455 0.76396 QPQ(div 0.8, multiround)
0.32218 0.76545 QPQ(div 0.805, multiround)
0.31936 0.76688 QPQ(div 0.81, multiround)
0.31648 0.76829 QPQ(div 0.815, multiround)
0.31387 0.7698 QPQ(div 0.82, multiround)
0.31091 0.77126 QPQ(div 0.825, multiround)
0.30843 0.77249 QPQ(div 0.83, multiround)
0.30531 0.77447 QPQ(div 0.835, multiround)
0.30253 0.77573 QPQ(div 0.84, multiround)
0.30036 0.7769 QPQ(div 0.845, multiround)
0.29781 0.77813 QPQ(div 0.85, multiround)
0.29514 0.77931 QPQ(div 0.855, multiround)
0.29205 0.78098 QPQ(div 0.86, multiround)
0.28985 0.78205 QPQ(div 0.865, multiround)
0.28719 0.78321 QPQ(div 0.87, multiround)
0.28469 0.78441 QPQ(div 0.875, multiround)
0.28221 0.78551 QPQ(div 0.88, multiround)
0.27989 0.78654 QPQ(div 0.885, multiround)
0.27705 0.78778 QPQ(div 0.89, multiround)
0.2746 0.78876 QPQ(div 0.895, multiround)
0.27208 0.78989 QPQ(div 0.9, multiround)
0.27005 0.79089 QPQ(div 0.905, multiround)
0.26767 0.79197 QPQ(div 0.91, multiround)
0.26525 0.79292 QPQ(div 0.915, multiround)
0.26284 0.79398 QPQ(div 0.92, multiround)
0.26063 0.79494 QPQ(div 0.925, multiround)
0.25853 0.79588 QPQ(div 0.93, multiround)
0.25637 0.79685 QPQ(div 0.935, multiround)
0.25384 0.79789 QPQ(div 0.94, multiround)
0.25146 0.79886 QPQ(div 0.945, multiround)
0.24947 0.79975 QPQ(div 0.95, multiround)
0.24732 0.80056 QPQ(div 0.955, multiround)
0.24556 0.80143 QPQ(div 0.96, multiround)
0.24354 0.80219 QPQ(div 0.965, multiround)
0.24119 0.8031 QPQ(div 0.97, multiround)
0.23946 0.80382 QPQ(div 0.975, multiround)
0.23735 0.80459 QPQ(div 0.98, multiround)
0.23549 0.80531 QPQ(div 0.985, multiround)
0.23367 0.80602 QPQ(div 0.99, multiround)
0.232 0.80671 QPQ(div 0.995, multiround)
0.2278 0.80926 QPQ(div D'Hondt, multiround)
-------------- next part --------------
-1.08219 0.98757 Maj[Schulze(wv)]
-1.03167 0.99008 Maj[Cardinal-20(norm)]
-0.96976 0.99052 Maj[ER-Borda]
-0.77986 0.99494 ?Linear Range STV
-0.71905 0.93486 Maj[Ext-Minmax(margins)]
-0.35933 0.93565 PSC-CLE
-0.29291 0.89928 Cardinal: LPV0+
-0.10956 0.90776 DHwL(Schulze(wv))
0.17557 0.82993 STV-ME (Schulze)
0.25191 0.80054 Meek STV
0.26192 0.79069 STV
0.26474 0.79642 Warren STV
0.28495 0.65722 Maj[ER-Plurality]
0.33388 0.67222 C-Elim[ER-Plurality]
0.38075 0.68178 Schulze STV
0.39678 0.68592 Maj[Eliminate-[ER-Plurality]/fd]
0.87565 0.02416 Cardinal: Birational
0.23069 0.32589 Random ballots
More information about the Election-Methods
mailing list