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

[Kevin Venzke]

Hi Jameson,

--- En date de : Ven 18.3.11, Jameson Quinn <jameson.quinn at gmail.com> a écrit :



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.


Well, I tried to sort them thematically this time. I wasn't going to discuss scores at all
at first, as there are just too many things I could say.
 
One thing that strikes me is that often the methods with strategy vulnerabilities were
better anyway, in this scenario. Sincerity doesn't necessarily translate to quality.
Would you say that that holds for dishonest strategies (C, B) or only semi-honest ones (M, T)?


Yes, I think it has to, or else you have to explain Random Ballot's terrible results with
near-perfect sincerity. Other examples would be: VFA runoff placing 3rd despite 4 of
the blocs burying most of the time. IRNR placing 15th with a BBB-CCC pattern, above
IRV, C//IRV, TTR. MAMPO and MMPO beating Approval and WV with 3 burying blocs.
The bottom placements of Coombs, DSC, and Consensus despite their top outcome
being universal sincerity.

Perhaps one way to view it is that if the method is "not very good," it's preferable for
the voters to use strategy to improve the outcome than to just vote sincerely (or feel they
can do nothing except vote sincerely) and let the outcome be bad. FPP is a good 
example.
 


 
I can understand wanting to understand the outcome of each "line" though... I'll have
to think about that.
 

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)
 
Ok, I can add these. I think there is a large Condorcet advantage to the runoff methods.
I do wonder about the clone issue though. It won't show up in this setting, but if there
were no candidate limit candidates might end up nominated in pairs.
These methods do have a problem with clones. That's why I came up with the MCA-Asset methods; I think they'd do better against clones. 


 

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.)
 
It is probably possible to do this for spectrum-based scenarios. I can't remember
what the conditions are for this to happen under that method; I wonder if you have it
handy.
By "this", I assume you mean vote transfers? If there is a median tie, then candidates can "transfer" their votes to to any other candidate who has a higher [stat of interest], where stat of interest is defined as Preferrals (see runoff-preferred) or Approvals (see runoff-approved). If A transfers to B, all ballots count B at max(A,B). If this does not resolve the election, then the winner is the member of the post-transfer tie with the highest post-transfer stat of interest.


I believe you could use "asset" for any scenario, by assuming that the candidate's preferences are the same as those of the average of the voters who rank that candidate top.
Yeah if you used sincere preferences I suppose.

I'll see if I can figure out some code for this transfer thing.










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.


I'm not sure I have understood how this method works. Can you describe it?

Say A gets (Preferred/approved/unapproved) (20/50/30) and B gets (30/30/40). Both are median approved. Eliminate 20 median votes from each and you get (20/40/30) for A - still median approved - but (30/10/40) for B - rounding down, that's median unapproved. So A wins. (Note, elimination can shift median in either direction to break the tie.)


This is not my proposal, but the idea from the book Majority Judgement.

Hmm. I'll have to think on that one.

 



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 :).


 
Well, we need to do more scenarios. I don't know if my first post, around a week ago,
made it to the list. But (assuming I'm looking at the right Excel file at the moment)
MCA placed fifteenth there, after methods like DMC and margins.
 
In a non-spectrum-based set of trials, MCA was bottom half. The best SCWE was 
actually TTR. I tend to think the quality of MCA etc. depends on the voter preferences
being distributed in a certain way. If presence or absence of a top-slot majority doesn't
inform much in the given scenario, it will boil down to Approval.
 
Plus sincere Condorcet efficiency is just one thing. We could talk about election of
utility maximizers, average utility, Condorcet losers, utility minimizers. 
With all voters strategic, I believe the first two of those metrics will just be noisier versions of SCWE. (I don't know, or honestly care much, about the latter two "worst-case" metrics, because I think they will be acceptably small under the methods I care about.)

Interesting way to look at it. If I sort by rate of electing the utility maximizer, it
looks a lot different. The top of that list is TACC, TTR, C//IRV, QR, IRNR, IRV... (do
you see a pattern?) CWP, Range, Raynaud, ICA. Actually, it seems to me that
the better methods here were those that elected B a lot, beyond (but not too far
beyond) what was needed to get the best sincere CW score. If you look back, these
methods generally had compromise or at least compression strategy from the C
voters.





 I'm also 


concerned about the possibility that some methods just won't support three candidates
in practice. That may not be relevant to MCA though.
 
My initial bets are on AWP implicit because I don't remember ever seeing it place badly,
so far.
Very interesting. Do you think AWP-implicit-minimax is an acceptable substitute for beatpath, etc? (Because AWP is tough enough to describe with just minimax). And have you tried 3-rating CWP? My feeling is that 3-rating levels is sometimes the sweet spot, like 2 and infinity, and unlike any other number.


question 1: Yes I do. The main reason to use methods like beatpath instead of
minmax is the unlikely possibility that clones will get into a strong cycle and give 
the win away to a Smith loser. I do not think that can happen when the strengths
are determined essentially on approval ballots.

On a three-slot ballot you can't even vote such cycles, with or without approval.

question 2: Yes, CWP was included and was done with 3 slots. Two-slot CWP would
actually be the same as AWP. I don't know why, but CWP has not seemed as
impressive as the AWPs.

Time to code some more.

Kevin




      
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