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
M-- 220 100 88
--- 194 100 86
--M 130 100 87
-M- 126 100 85
TTT-MMM 63 92 93
T-TTM-- 23 100 88 ...
This looks like mostly the same order as last time.
MAFP95 87
M-- 158 100 88
--- 92 100 86
--M 83 100 87
-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
--- 75 100 90
M-- 46 100 86
MM- 44 100 85
BBT-MMM 41 100 86
TBB-MMM 35 100 88
--M 31 100 89
MMM 29 100 84
BTB-MMM 28 100 85
BBB-CCC 28 93 94
***MCCC 26 94 93
-MM 26 100 87 ...
You were right that this would do pretty well by SCWE, but your guess
for strategy was --- (which is actually a quite rare outcome under
any method).
"MCARP" 97 87
MM- 71 100 84
BBB-MMM 70 100 87
***MCCC 62 94 95 (*=M+P+B, i.e. "A=C>B")
M-M 48 100 89
MMM 32 100 88
TTB-MMM 32 100 88
BBT-MMM 30 100 87
-MM 29 100 85
BTB-MMM 28 100 87
TBB-MMM 24 100 87 ...
This was a little higher by SCWE but your MMM 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
--- 571 100 89
TT-T--- 65 100 87
-TTT--- 52 100 88
T-TT--- 40 100 88
CCC 32 94 92
C-C 30 94 94 ...
Not too special here. Like Bucklin but not as concentrated at the top
(Bucklin had 702 ---).
MJgmtER 97 87
M-- 172 100 89
--- 120 100 88
--M 101 100 86
-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
PPP 669 93 94
PPP 254 14 14
CCC 77
