[EM] One scenario, many methods, by strategies in final poll

[Jameson Quinn]

Great results.

I think it would help if you gave the SCWE of each method above the table,
and the SCWE of each line after that line. That way, we could see which
strategies were causing the problems with SCWE. Also, if you give further
scenarios, it would be great to see the results sorted by SCWE.

I would be interested to see results for MCA runoff methods with this. The
possibilities are:
MCA-Runoff-approval - runoff if tied median, two candidates with highest
portion at median advance (or highest approvals if failed majorities)
(I suspect the top result for this would be ---TTTT, with very high SCWE)

MCA-Runoff-preferred - as above, two winning candidates with highest top
ranking advance.
(I suspect that the top result would be MMMTTTT, with high SCWE)

Both of those systems will generally agree with the corresponding MCA-Asset
version. The exception is that MCA-Asset will almost always elect C if B is
eliminated (ineligible for transfers), while MCA-Runoff will tend to elect A
in that situation. That's because B will transfer votes to C even though
some of those original voters might have preferred the less-extreme A. Since
both of these results are probably Condorcet failures anyway, the only
important difference resulting would be if under MCA-Asset, C voters were
more inclined to truncate, while under MCA-Runoff, A voters would do so.
However, since the other side always has a defense, I don't think either of
those would hurt the SCWE. Still, it might be worth simulating MCA asset
(assuming that B would always choose to transfer votes to C, and C and A to
B; and that A would transfer votes to B if they could and C couldn't, that
is, that A would believe the implicit threat of B to transfer to C.)

If you're adding in these methods, you should add Majority Judgement as well
(eliminate median votes to break ties). This would probably come out the
same as MCA, but it is not quite identical, so it would be good to confirm
that.

Anyway. As to your actual results, it seems to me that the "good" methods
are the ones above 95%. Out of that set, it seems to me that it's clear that
MCA and Bucklin are the simplest methods to explain to voters. (Of course,
the MCA-runoff and -asset methods I propose are complex, not simple).

So, I'd like to see someone make a good argument against MCA being the best
practical single-winner reform, for combination of simplicity and strategy
resistance. There may be such an argument which I'm just too biased to see.
If not... well, all y'all can unite under my banner at last :).

Jameson

2011/3/18 Kevin Venzke <stepjak at yahoo.fr>

> Hi,
>
> I created a nice visual way to review what is happening in my simulation
> with regard to strategy. I ran 1000 trials under each method of the
> exact same scenario: On a 1D spectrum, candidates ABC are at
> -.30, .24, .34 on a scale from -1 to +1. There are seven voting blocs
> spread out evenly (so that the middle bloc is at 0). The blocs have the
> same "base" size, but in any given poll only a random percentage from
> 40% to 100% of the voters in a given bloc will show up. This creates the
> uncertainty.
>
> With this layout, you have three blocs on the "left" (negative side)
> with a strong preference for A over B, then C. The middle bloc has weak
> preferences of B>A>C. The right three blocs weakly prefer C over B, but
> both strongly over A. So respectively A>>B>C, B>A>C, C>B>>A you could
> say.
>
> For simplicity I am just grabbing the votes from the final poll. So you
> can't directly tell how stable the votes were. I'll describe the
> strategies using a seven-letter string, one for each bloc. A "-" means
> sincere. C means compromise. M compression. T truncation. B burial.
> P pushover (voting worst top). I also used * for simultaneous compression
> and pushover, but it was rare.
>
> I should note that the results from this scenario may not be
> representative of all scenarios. I thought the results of this one were
> a bit interesting, is all, and it takes time to review the differences
> between scenarios.
>
> First let's do Random Ballot. There were only five possibilities:
> ------- 962
> ----C-- 14
> -----C- 13
> ------C 10
> ----CC- 1
>
> So you can see that overwhelmingly the final state involved all voters
> being sincere.
>
> The "Consensus or Else" method performs Random Ballot unless the first
> preference winner has 60% of the vote, in which case he simply wins:
> ------- 497
> ----CCC 494
> ----C-- 5
> ------C 2
> -----C- 2
>
> So, half of the time everyone was sincere, and half the time the C voters
> compromised to give B a chance at the 60%. It was uncertain to me whether
> this method would work at all, since in theory I suppose the voters are
> supposed to know that if they can think of a compromise choice, they
> should vote for it. But in practice, in the sim, the blocs can't "talk"
> to each other or anything.
>
> FPP:
> ---C--- 500
> ----CCC 499
> CCC---- 1
>
> Only three possibilities. Surprisingly it is about even whether the B
> voters or C voters used favorite betrayal. In one single case the A voters
> did it.
>
> My disqualification plurality (VDP/VFA):
> ----CCC 65
> BBBBCCC 16
> BBB-CCC 15
> TBT-CCC 11
> B--BCCC 11
> BBBTCCC 11
> --B-CCC 11
> TBTBCCC 11
> ...
>
> The C voters compromise all the time. It is only a touch more sincere-
> Condorcet-efficient than FPP.
>
> Top-two runoff:
> ----CCC 439
> -----CC 191
> ----C-C 187
> ----CC- 177
> ---PCCC 5
> ---C--- 1
>
> Still a lot of compromise.
>
> In contrast, the VFA ballot runoff:
> BBBBCC- 109
> BBBBC-C 100
> BBBB-CC 79
> BBB-CC- 14
> BBBB--- 10
> BBBB-C- 10
> ...
>
> In other words the A voters reliably voted "against" B, B voters usually
> voted against A, and C voters frequently gave their "for" vote to B,
> voting (sincerely) "against" A.
>
> Results? TTR elected B 93.4% of the time and VFAR only 88.3%: TTR's
> sincere Condorcet efficiency was 93.5% to VFAR's 98.7%.
>
> Now IRV. The full list is quite long due to the A voters being unable
> to determine how best to use their second preference.
> ----CCC 88
> ----CC- 44
> -----CC 39
> ----C-C 36
> --T-CCC 34
> -T--CCC 23
> --T-C-C 22
> --T-CC- 22
> T---CCC 19
> T---CC- 17
> ...
>
> If we go lower the A voters had some burial as well. It is nice to see
> that sincerity beat truncation and truncation beat burial though. The
> C voters were typically voting for B instead of C, while the B voters
> presumably saw no reason to ever compromise.
>
> QR's compromise disappointed me:
> ----CC- 69
> ----C-C 69
> -----CC 64
> ----CCC 56
> ---BCCC 30
> T---CC- 22
> --T-C-C 19
> ...
>
> The A voters were quite confused as in IRV, though you can't quite see it
> from the top of the list here.
>
> If we try Condorcet//IRV:
> TTT-C-C 26
> TTT-CC- 25
> TTT--CC 25
> TTB-CC- 21
> BTT-CCC 19
> TTB--CC 18
> BTT-CC- 18
> TBT-CC- 18
> TBT-CCC 18
> ...
>
> I'd have to say I don't think this is too promising. The A voters are
> never sincere and the C voters are compromising a lot.
>
> Here's the IRNR method:
> BBB-CCC 165
> BBT-CCC 41
> TBB-CCC 41
> BTB-CCC 38
> ---T--- 30
> TBB-CMM 21
> BTB-CMM 16
> ...
>
> There are a few of these BBB-CCC methods. A pretty ugly situation,
> although electing B most of the time gave IRNR decent Condorcet
> efficiency.
>
> Let's look at the King of the Hill (KH) method:
> ---T--- 324
> ---TCCC 26
> ----CCC 16
> -T--CC- 15
> ----CC- 15
> ...
>
> Almost a third of the trials ended with no strategy except bullet voting
> by the B voters. If we continue down the list, though, the compromise
> by various C blocs continues.
>
> If we stick Condorcet on the front of KH (C//KH):
> ---T--- 161
> TTT-CC- 25
> TTB-CCC 20
> BTT-CCC 19
> TTT-CCC 19
> TTT--CC 17
> TTT-C-C 16
> ...
>
> I kind of think it looks worse.
>
> DSC is a bit interesting... I am including DSC with no ER allowed (top),
> and DSC where it is allowed (second). So the only difference between
> these methods is whether tying at the top (compression) is possible.
> While the methods look a little different, few in the end are actually
> using any compression. Puzzling.
> ------- 392
> ---BCCC 17
> ----CCC 16
> BBB-CCC 12
> --B-CCC 11
> --TBCCC 10
> ... (DSC no ER)
>
> ------- 509
> ----CCC 38
> ---M--- 30
> ---BCCC 26
> B---CCC 13
> --BC--- 12
> --B-CCC 12
> BBB-CCC 12
> ... (DSC ER)
>
> The ER version looks better to me (and also has better (though still
> quite bad) sincere CW efficiency... something which incidentally you can't
> depend on in this scenario), but why should it be?
>
> Next let's do DAC and transition into the Bucklinesque methods:
> TTTT--- 584
> TT-T--- 60
> -TTT--- 53
> T-TT--- 47
> TTTTCCC 29
> TTT-CCC 22
> T--T--- 22
> ...
>
> So, truncation heavy (A and B blocs) with touches of compromise.
>
> As I write this I realize that I allowed equal-ranking but didn't allow
> tied at the top preferences to be counted as FPs. It's likely that
> DAC is actually a compression-heavy method, if I fixed this.
>
> Bucklin itself (no ER):
> TTTT--- 702
> -TTT--- 40
> T-TT--- 35
> TT-T--- 31
> TTT-CCC 31
> TTTTCCC 30
>
> Similar but less varied. DAC's sincere CW efficiency was a touch better.
>
> Now QLTD, Woodall's Bucklin variant:
> TTTT--- 518
> TTT-CCC 65
> TTTTCCC 56
> T-TT--- 53
> -TTT--- 50
> TT-T--- 41
> ...
> The compromise makes it look worse than Bucklin, and also the "SCWE"
> (shorter than "sincere CW efficiency") was worse.
>
> Now MCA or ER-Bucklin(whole):
> TTTTM-- 214
> TTTT--- 209
> TTTT--M 144
> TTTT-M- 119
> TTT-MMM 55
> TT-TM-- 16
> ...
>
> Generally much bullet-voting from A and B voters and some compression
> from C (especially if the B voters vote B>A).
>
> My Bucklin variant (VBV) with and without equal rankings:
> ---T--- 460
> TTT---- 208
> T-T---- 36
> -TT---- 36
> TT----- 28
> -T----- 21
> ...   (no equal rankings)
> ---T--- 546
> BTT-CCC 25
> TTB-CMM 22
> TTB-CCC 22
> TBT-CCC 22
> BTT-CMM 17
> ---TMMM 16
> ...   (equal rankings allowed)
>
> It is interesting how allowing equal rankings creates not just compression
> but also burial and outright compromise. Despite this, the SCWE of the
> ER version was better, at 92.7% vs 80.8%! (The strict version was less
> capable of electing B.)
>
> Conditional Approval (CdlA):
> ------- 162
> ---B--- 80
> TTT-CMM 70
> TTT-MMC 51
> TBT-CCC 48
> TTB-CCC 44
> BTT-CCC 40
> TTT-MCM 39
> ...
>
> I like that fairly large chunk of sincerity or near-sincerity. On that
> second line you can see the B voters are trying to give C some more
> votes, to force A voters to give up their B preferences. I wonder if
> technically that is an example of "pushover."
>
> Chris' SMDTR:
> ---TM-- 110
> ---T--M 67
> ----MMM 63
> ---T-M- 61
> -T--MMM 43
> -TT-MMM 42
> ...
>
> Fair amount of compression. Middling SCWE.
>
> Chris' IBIFA (original definition):
> TTT-MMM 592
> ---TTTT 39
> TTB-MMM 36
> BTT-MMM 34
> TBT-MMM 31
> ----M-- 25
> TTT---- 19
> ...
>
> Looks like not that many lower preference slots are getting used. SCWE
> was slightly worse than SMDTR.
>
> Antiplurality:
> ------- 276
> --B---- 235
> -B----- 231
> B------ 217
> ---B--- 32
> ...
>
> Not a lot of different scenarios. B wins virtually all the time, which
> gives mediocre SCWE despite all the sincerity.
>
> MAP (Majority Favorite//Antiplurality):
> ------- 220
> B------ 204
> --B---- 179
> -B----- 175
> ---B--- 45
> -----CC 11
> ...
> Rather similar sincerity, and SCWE jumps from 87.1% to 97.4%.
>
> Coombs:
> ------- 540
> BBBC--- 238
> ---B--- 154
> BBBC-C- 14
> BBBC--C 13
> ...
>
> Coombs has a lot more burial, and SCWE of only 74.1%, being relatively
> unable to elect B.
>
> Borda (full strict rankings):
> BBB-CCC 662
> -B--C-- 78
> --B-C-- 63
> B---C-- 52
> B-B-C-- 21
> BBBBCCC 19
> -BB-C-- 17
> ...
>
> Basically at least 2/3rds of the time you have the A side burying and
> the C side compromising. The Condorcet efficiency was pretty poor, at
> 76.6%.
>
> I checked that Baldwin and Black are similar but a bit milder.
>
> Now for Approval and Range:
> TTTTMMM 862
> TTTMTTT 48
> TTTTMMC 28
> TTTTMCM 27
> TTTTCMM 23
> TMMTMMM 5
> TTTTCMC 4
> TTTTMCC 2
> TTTTCCM 1
> (Approval, whole list)
> TTTTMMM 812
> TTTTMMC 45
> TTTTMCM 44
> TTTTCMM 43
> TTTBMMM 11
> TTTTMCC 9
> ... (Range)
>
> There are some illogical strategies in there. But under both the most
> common scenario by far was that the race was won by B (more likely) or
> A, with C having no odds at all. That's pretty consistent with my past
> impressions. SCWE was 89.7% Approval, 92.4% Range.
>
> Now for some pure pairwise methods. Minmax with Winning Votes:
> --B-MMM 213
> B---MMM 197
> -B--MMM 174
> ----MMM 126
> BBBM--- 82
> ---B--- 68
> ---BT-- 15
> ...
>
> A lot of compression from C voters, and some burial here and there.
>
> If we try, say, Margins, we get:
> BBB-CCC 603
> ---B--- 79
> BBBC--- 44
> TBB-CCC 26
> BBT-CCC 24
> BTB-CCC 19
> TBBC--- 15
> ...
>
> It looks worse to me, but the SCWE is still 81% to WV's 87%.
>
> I'll whip through a few of these:
> MMPO:
> BBB-MMM 341
> B-B-MMM 44
> BBBM--- 43
> BBB-CMM 42
> ...  ^--- so, like WV but with more burial!
> WV with no ER allowed:
> BBB-CCC 360
> BBBC--- 175
> ---B--- 61
> ...  ^--- marginsesque
> margins with no ER allowed
> BBB-CCC 356
> ---B--- 69
> BBBC--- 51
> ...  ^--- same
> minmax with no ER or truncation allowed
> BBB-CCC 376
> BBBC--- 172
> ---B--- 84
> ...  ^--- same
>
> Interestingly MMPO was the best of these with SCWE of 90.4%. But Raynaud
> was even better at 93.8%:
> ----MMM 150
> ----M-- 119
> ----MM- 119
> ----M-M 107
> --B-MMM 92
> ...
>
> Where are all the buriers under Raynaud? I thought this method would
> be similar to MMPO.
>
> Forest's TACC:
> TTT-CCM 42
> TTT-CCC 39
> TTT-MMC 38
> TTT-CMM 34
> TTT-MCM 33
> TTT-MMM 32
> TTT-CMC 31
> ...
>
> So, a lot of truncation, and some compromise, but it remains true as I
> reported before that TACC has very few burial attempts.
>
> DMC:
> ------- 298
> BBB-CCC 148
> ---B--- 112
> BBBC--- 52
> --T---- 49
> -T----- 42
>
> I like the top chunk, not so much the second one. SCWE was a bit lame,
> lower than WV and Antiplurality but higher than margins.
>
> Cardinal-Weighted Pairwise:
> ----MM- 241
> ----M-M 233
> ----M-- 168
> ---T--- 121
> -----MM 60
> ...
>
> Approval-Weighted Pairwise (implicit approval):
> ------- 377
> ---B--- 91
> -T----- 75
> --T---- 72
> T------ 66
> ...
>
> Approval-Weighted Pairwise (explicit approval):
> ------- 243
> B------ 61
> T------ 57
> -B----- 57
> --T---- 56
> ...
>
> Quite impressive sincerity with these, and at the same time these were
> the two top methods wrt SCWE (98.8% explicit, 99.3% implicit).
>
> Condorcet//Approval (implicit):
> ------- 138
> ---T--- 68
> TBT-CCC 66
> TTT-CMM 65
> TTT-CCC 63
> ...
>
> and the explicit version:
> ------- 173
> ---B--- 116
> --T---- 70
> T------ 69
> -T----- 63
> ...
>
> I do think the explicit version is junk (even here the burial rate was
> double), but here the SCWE was fourth place for explicit... I will have
> to hypothesize that there was just no great opportunity for burial here.
>
> ICA:
> TTT-MMM 343
> TTT-MCM 76
> TTT-CMM 61
> TTT-MMC 57
> ---T--- 31
>
> Rather disappointing. It's interesting and puzzling to me that modifying
> a method (C//A implicit) so that it satisfies FBC would create, say,
> compression incentive where there had not been compromise incentive,
> and furthermore truncation incentive that hadn't been there and doesn't
> even seem related.
>
> MDDA:
> TTTT--- 225
> TTT-MMM 108
> T-TT--- 42
> TTT-M-- 37
> TT-T--- 34
> ...
>
> A lot of truncation, some compression.
>
> MAMPO:
> BBB-MMM 258
> BBB-CMM 49
> BBBM--- 46
> BBB-MCM 37
> BBB-MMC 36
> ...
>
> Wow, look at all that burial, for a method that is supposed to be a
> fairly small alteration to Approval!
>
> I've probably said this before, but MDDA and MAMPO were both designed
> to satisfy three of Mike Ossipoff's criteria (FBC, SDSC, and SFC). They
> both have heavy approval components. But it seems they aren't
> interchangeable.
>
> ---
>
> To conclude this long mail I'll just give you the SCWE ranking I've
> been referring to.
>
> 99+%: AWP implicit
> 98+%: AWP explicit, VFA runoff, C//A explicit
> 97+%: MCA, MAP
> 95+%: DAC, Bucklin, CdlA
> 93+%: QLTD, KH, CWP, C//KH, Raynaud, IRNR, TACC, MDDA, TTR, C//IRV,
> QR, SMDTR, C//A implicit, IRV
> 89+%: ICA, VBV (ER), Range, IBIFA, MAMPO, MMPO, Approval
> 85+%: WV, Antiplurality, DMC
> 74+%: margins, VBV (strict), margins (no ER), Borda, WV (no ER), minmax
> (full rankings only), Coombs
> 50's%: DSC (ER), DSC, VDP/VFA, FPP
> 40%: "Consensus or Else"
> 20%: Random Ballot
>
> If you want more stats or a certain scenario, let me know.
>
> Thanks.
>
> Kevin Venzke
>
>
>
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20110318/ece34ed3/attachment-0004.htm>