[EM] Results, for Jameson; ER-DAC; ER-IRV

Sat Mar 19 15:06:56 PDT 2011

Hi,

Jameson, I did most of what I looked into. I didn't complete the Asset
methods though. I did come up with a good universal way to estimate the
candidates' utilities for each other though: Have the candidates read the
minds of the voters (the base quantities of each bloc), and multiply each
opinion by their opinion of the candidate asking the question. (I'm
assuming utilities range from 0 to 1.) So, a candidate will like the same
candidates you like, if you like that candidate. This way, B will like
C not because of the spectrum, but because most of his "goodwill" comes
from the C voters.

A likely tweak would be to have every candidate assured of liking
themselves the best.

I threw together a method to test something similar: The voters cast rated
ballots. Voting power for each candidate is determined by top ratings
(fractional if tying). "Candidates" (simulated) determine their preferences
based on the voters' ratings. Then the candidates cast full sincere
rankings for a round of Minmax, to find the winner. It turned out to be
not that great in this particular scenario being considered:

"AICMM"		86	86
----MCM	79	85	85
----MMC	77	85	85
----CMM	69	83	86
-B--MCM	32	85	85
B---CMM	26	86	86
-B--CMM	26	87	87 ...

You can see the SCWE and utility maximizer election rates are to the
right of the frequencies. This was a thousand trials, so pretty split
up.

Anyway, the Asset methods stumped me somewhat because I couldn't come
up with a deterministic way to solve the method that doesn't seem to
be contrived. For instance, it's possible that two of the three candidates
are able to transfer. Who has initiative? How do they even know if they
would like to have initiative? Maybe they'd rather do nothing. So, I
didn't attempt to write a method that might not be faithful to the idea.

Here are some methods to compare.

MCA		97	87
TTTTM--	220	100	88
TTTT---	194	100	86
TTTT--M	130	100	87
TTTT-M-	126	100	85
TTT-MMM	63	92	93
T-TTM--	23	100	88 ...

This looks like mostly the same order as last time.

MAFP		95	87
TTTTM--	158	100	88
TTTT---	92	100	86
TTTT--M	83	100	87
TTTT-M-	80	100	88
TTT-MMM	49	94	95
-TTTM--	22	100	86 ...

Really this could be called "MATR" because it breaks all mid-slot ties
on top ratings.

"MCARA"		96	87
BBB-MMM	99	100	86
TTTT---	75	100	90
TTTTM--	46	100	86
TTTTMM-	44	100	85
BBT-MMM	41	100	86
TBB-MMM	35	100	88
TTTT--M	31	100	89
TTTTMMM	29	100	84
BTB-MMM	28	100	85
BBB-CCC	28	93	94
***MCCC	26	94	93
TTTT-MM	26	100	87 ...

You were right that this would do pretty well by SCWE, but your guess
for strategy was ---TTTT (which is actually a quite rare outcome under
any method).

"MCARP"		97	87
TTTTMM-	71	100	84
BBB-MMM	70	100	87
***MCCC	62	94	95 (*=M+P+B, i.e. "A=C>B")
TTTTM-M	48	100	89
TTTTMMM	32	100	88
TTB-MMM	32	100	88
BBT-MMM	30	100	87
TTTT-MM	29	100	85
BTB-MMM	28	100	87
TBB-MMM	24	100	87 ...

This was a little higher by SCWE but your MMMTTTT guess never occurred
once in any (recorded) result for any method!

By the way, it seemed to me that there was only one difference between
MCARA and MCARP. That is, MCARP's tie finalists are only picked by TRs,
while MCARA could be based on TRs or approval. Let me know if that sounds
wrong.

Next, Majority Judgment, with ER and non ER. This was tricky to think
through. However, it seems to me that this method gives the same result
as MCA unless there is a tie on the middle slot. In that case you must
find how many votes must be removed to make each eligible candidate a 
majority favorite or majority disapproved. I don't think it matters where
you take the votes from as long as it's on the correct side of the 
boundary. (It's possible to find that more votes must be removed than are
even there, but I doubt these values ever determine the result.)

I can certainly share the method code I used here. Strict then ER:

MJgmtSt		96	86
TTTT---	571	100	89
TT-T---	65	100	87
-TTT---	52	100	88
T-TT---	40	100	88
TTTTCCC	32	94	92
TTTTC-C	30	94	94 ...

Not too special here. Like Bucklin but not as concentrated at the top
(Bucklin had 702 TTTT---).

MJgmtER		97	87
TTTTM--	172	100	89
TTTT---	120	100	88
TTTT--M	101	100	86
TTTT-M-	99	100	88
TTT-MMM	38	93	94
TT-TM--	22	100	88
TT-T--M	17	100	87 ...

So, very similar to MCA but not as certain for some reason.

-----

I tried, out of curiosity, FPP where the *second* candidate wins:

WrFPP		73	72
CCCCPPP	669	93	94
PPPPPPP	254	14	14
PPPPCCC	77	90	80

Interesting that most of the time a decent candidate wins.

-----

DAC update: I have DAC with ER and no ER.

DACstr		96	86
TTTT---	569	100	87
-TTT---	61	100	85
TT-T---	52	100	88
T-TT---	45	100	86
TTTTCCC	36	94	93 ...

DACer		97	87
TTTTM--	172	100	88
TTTT-M-	129	100	87
TTTT---	116	100	88
TTTT--M	101	100	87
TTT-MMM	29	94	93 ...

Interestingly the ER version doesn't seem to have as much compression as
I expected. A bit comparable to MCA actually.

-----

Next, I thought I should try the ER versions of IRV. IRV earlier gave
these results:

IRV (93 and 93 stats)
88	----CCC
44	----CC-
39	-----CC
36	----C-C
34	--T-CCC ...

ER-IRV(fractional) gives:
IRVerF		93	93
----MMM	37	93	94
----MCM	26	93	94
----MMC	19	92	93
----CMC	18	92	95
----CCM	17	94	95
----CMM	17	93	93
-T--MMM	16	94	94
T---MMM	15	92	94 ...

ER-IRV(whole) gives:
IRVerW		93	93
----MMM	182	94	94
T---MMM	65	93	92
--T-MMM	57	94	94
-T--MMM	50	93	94
----MMC	33	93	94
----CMM	27	93	93
----MCM	22	94	94
----MCC	19	93	94 ...

So, ER didn't make IRV any better but it did reduce the amount of
compromise. Chris had an idea, I believe, that ER-IRV(whole) was
susceptible to a straightforward push-over strategy, but I'm not sure
I see that here unless some Ms or Cs are playing that role. Since the
C voters are very frequently using that strategy (in many methods) I'm
doubtful...

Also, you can note here that the IRV methods did better wrt utility
maximizers than the other methods in this post. You can see (by scanning
for high values) that this is expected when C is losing his win odds
due to the voting patterns, and B is winning when sincere Condorcet says
it should be C.

Kevin