[EM] How to convert a set of CR ballots to a set of Approval ballots

[Forest Simmons]

Kevin, thanks for doing the simulations.

The offending example below led me to the improvement in my previous
message.  I simplified the faction sizes from 56, 92, 100 to

9  C D B A
10 C A B D
13 B D A C

which gives the same results.

Forest

On Fri, 1 Aug 2003, [iso-8859-1] Kevin Venzke wrote:

> I implemented the new method (picking the least viable rank and merging it with
> the less viable neighbor) and did some trials.
>
> First, I should say that the Condorcet cycle-breaker I have implemented is:
> "Successively drop the weakest defeats (as measured by WV) until a Smith set
> member is undefeated."  I'm not sure what the proper name for this is, but I'll
> call it "SD."
>
> To my great surprise (should I have been?), I could not generate any three-candidate,
> three-rank scenarios where MPCR did not elect the CW when one existed:
>
> With 3 factions (random sizes) and 3 candidates and ranks:
> matches        10474         100%  (this is total trials)
> sdindec        36            .34  (SD was indecisive)
> (I should've checked that Borda and MPCR were decisive, but I didn't.)
> mpcr<>cw       0             0   (was a CW, MPCR didn't pick him)
> mpcr=cw        9935          94.85  (was a CW, MPCR picked him)
> unanimous      220           2.1 (MPCR, Black, SD agreed)
> mpcr=borda     0             0   (MPCR and Black agreed against SD)
> mpcr=sd        112           1.06 (MPCR and SD agreed against Black)
> borda=sd       171           1.63 (Black and SD agreed against MPCR)
> no matches     0             0  (Black, SD, MPCR all disagreed)
>
> I got the same results with 5 and 8 factions.
>
> With 4 candidates and ranks (5 factions), some "errors" appeared:
> matches        4594
> sdindec        5             .1
> mpcr<>cw       7             .15  (.175%, excluding no-CW cases)
> mpcr=cw        3971          86.43
> unanimous      203           4.41
> mpcr=borda     23            .5
> mpcr=sd        192           4.17
> borda=sd       165           3.59
> no matches     28            .6
>
> Five factions and 7 candidates:
> matches        3563
> sdindec        67            1.88
> mpcr<>cw       27            .75    (1.08%)
> mpcr=cw        2469          69.29
> unanimous      250           7.01
> mpcr=borda     66            1.85
> mpcr=sd        306           8.58
> borda=sd       254           7.12
> no matches     124           3.48
>
> 15 candidates:
> matches        431
> sdindec        20            4.64
> mpcr<>cw       6             1.39   (2.79%)
> mpcr=cw        209           48.49
> unanimous      33            7.65
> mpcr=borda     9             2.08
> mpcr=sd        41            9.51
> borda=sd       57            13.22
> no matches     56            12.99
>
>
> I went through and picked out some appalling results from the 4-rank batch.
> Here's one which would have been OK if the "merge the pair minimizing the sum
> of viability" rule had been used.
>
> This is pretty nasty because it elects the Condorcet and Borda Loser, and
> ignores a majority favorite:
>
>  56 22% CDBA
>  92 37% CABD
>  100 40% BDAC
>  248
>
> Borda order is B>C>D>A
> RP order is C>B>D>A
>
> :[viability order] [new grouping as result]  etc...
> :BCDA C,D,BA  CA,B,D  B,DA,C
> :CBAD C,DBA  CA,BD  BDA,C
> :ACBD   (MPCR's result)
>
> Using the earlier rule, the MPCR part goes:
> :BCDA CD,B,A  CA,B,D  B,DA,C
> :BCAD CD,BA  CA,BD  B,DAC
> :CBAD
>
> But in general it doesn't seem to me that one variant is clearly better than
> the other.  (I did 9-candidate trials on both methods and found that the new
> version was twice as likely to miss a CW, but it might've been a fluke.)
>
> I hope no errors crept into this message.
>
> Kevin Venzke
> stepjak at yahoo.fr
>
>
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