<br><br><div class="gmail_quote">2011/3/19 Kevin Venzke <span dir="ltr"><<a href="mailto:stepjak@yahoo.fr" target="_blank">stepjak@yahoo.fr</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Hi,<br>
<br>
Jameson, I did most of what I looked into.</blockquote><div><br></div><div>Wow, thanks.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> I didn't complete the Asset<br>
methods though. I did come up with a good universal way to estimate the<br>
candidates' utilities for each other though: Have the candidates read the<br>
minds of the voters (the base quantities of each bloc), and multiply each<br>
opinion by their opinion of the candidate asking the question. (I'm<br>
assuming utilities range from 0 to 1.) So, a candidate will like the same<br>
candidates you like, if you like that candidate. This way, B will like<br>
C not because of the spectrum, but because most of his "goodwill" comes<br>
from the C voters.<br></blockquote><div><br></div><div>I think my trick is somewhat better: only have them look into the minds of voters which top-rate them specifically. My rationale is that with your method, I believe it would be impossible to have a Condorcet cycle among the candidates, since A feels about B exactly as B feels about A. With my method, a Condorcet cycle would be possible, which is good - a real-life robust Condorcet cycle would probably be some variant of three candidates, three single-issue voting blocs, and appropriate strength for each bloc. In that circumstance, I'd expect candidates to transfer to the other one who is middling where they are strong, not to the one who is strong where they are middling.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
A likely tweak would be to have every candidate assured of liking<br>
themselves the best.<br></blockquote><div><br></div><div>Mine needs no such tweak.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
I threw together a method to test something similar: The voters cast rated<br>
ballots. Voting power for each candidate is determined by top ratings<br>
(fractional if tying). "Candidates" (simulated) determine their preferences<br>
based on the voters' ratings. Then the candidates cast full sincere<br>
rankings for a round of Minmax, to find the winner. It turned out to be<br>
not that great in this particular scenario being considered:<br>
<br>
"AICMM" 86 86<br>
----MCM 79 85 85<br>
----MMC 77 85 85<br>
----CMM 69 83 86<br>
-B--MCM 32 85 85<br>
B---CMM 26 86 86<br>
-B--CMM 26 87 87 ...<br>
<br>
You can see the SCWE and utility maximizer election rates are to the<br>
right of the frequencies. This was a thousand trials, so pretty split<br>
up.<br>
<br>
Anyway, the Asset methods stumped me somewhat because I couldn't come<br>
up with a deterministic way to solve the method that doesn't seem to<br>
be contrived. For instance, it's possible that two of the three candidates<br>
are able to transfer. Who has initiative? How do they even know if they<br>
would like to have initiative? Maybe they'd rather do nothing. So, I<br>
didn't attempt to write a method that might not be faithful to the idea.<br></blockquote><div><br></div><div>All "transfers" are simultaneous and represent "copies" rather than bowing out. Since the "can I transfer to you" criterion is the same as the "will you beat me without transfers" criterion, at least in the 3-candidate case there are no issues of initiative or transfer strategy. The pre-transfer 2nd place has no motivation whatsoever to transfer to the pre-transfer 1st place, and no ability to transfer to the 3rd place. So, if transfers are happening at all, it's just that 3rd place is acting as a kingmaker (pseudo-IRV style); that's simple.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
Here are some methods to compare.<br>
<br>
MCA 97 87<br>
TTTTM-- 220 100 88<br>
TTTT--- 194 100 86<br>
TTTT--M 130 100 87<br>
TTTT-M- 126 100 85<br>
TTT-MMM 63 92 93<br>
T-TTM-- 23 100 88 ...<br>
<br>
This looks like mostly the same order as last time.<br>
<br>
MAFP 95 87<br>
TTTTM-- 158 100 88<br>
TTTT--- 92 100 86<br>
TTTT--M 83 100 87<br>
TTTT-M- 80 100 88<br>
TTT-MMM 49 94 95<br>
-TTTM-- 22 100 86 ...<br>
<br>
Really this could be called "MATR" because it breaks all mid-slot ties<br>
on top ratings.<br>
<br>
"MCARA" 96 87<br>
BBB-MMM 99 100 86<br>
TTTT--- 75 100 90<br>
TTTTM-- 46 100 86<br>
TTTTMM- 44 100 85<br>
BBT-MMM 41 100 86<br>
TBB-MMM 35 100 88<br>
TTTT--M 31 100 89<br>
TTTTMMM 29 100 84<br>
BTB-MMM 28 100 85<br>
BBB-CCC 28 93 94<br>
***MCCC 26 94 93<br>
TTTT-MM 26 100 87 ...<br>
<br>
You were right that this would do pretty well by SCWE, but your guess<br>
for strategy was ---TTTT (which is actually a quite rare outcome under<br>
any method).<br>
<br>
"MCARP" 97 87<br>
TTTTMM- 71 100 84<br>
BBB-MMM 70 100 87<br>
***MCCC 62 94 95 (*=M+P+B, i.e. "A=C>B")<br>
TTTTM-M 48 100 89<br>
TTTTMMM 32 100 88<br>
TTB-MMM 32 100 88<br>
BBT-MMM 30 100 87<br>
TTTT-MM 29 100 85<br>
BTB-MMM 28 100 87<br>
TBB-MMM 24 100 87 ...<br>
<br>
This was a little higher by SCWE but your MMMTTTT guess never occurred<br>
once in any (recorded) result for any method!<br></blockquote><div><br></div><div>After some thought, I understand why my guesses were wrong. I was thinking that truncation was a strategy for near-clones, emphasis on near, whereas actually it's a strategy for competitive near-clones, emphasis on competitive. So even though A and B are farther apart than B and C, the voters are treating A and B as the "competitive near clones" because C is an also-ran with the methods I care about.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
By the way, it seemed to me that there was only one difference between<br>
MCARA and MCARP. That is, MCARP's tie finalists are only picked by TRs,<br>
while MCARA could be based on TRs or approval. Let me know if that sounds<br>
wrong.<br></blockquote><div><br></div><div>If I understand you correctly (not totally sure) then I agree. </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
Next, Majority Judgment, with ER and non ER. This was tricky to think<br>
through. However, it seems to me that this method gives the same result<br>
as MCA unless there is a tie on the middle slot. In that case you must<br>
find how many votes must be removed to make each eligible candidate a<br>
majority favorite or majority disapproved. I don't think it matters where<br>
you take the votes from as long as it's on the correct side of the<br>
boundary. (It's possible to find that more votes must be removed than are<br>
even there, but I doubt these values ever determine the result.)<br></blockquote><div><br></div><div>Agreed. </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
I can certainly share the method code I used here. Strict then ER:<br>
<br>
MJgmtSt 96 86<br>
TTTT--- 571 100 89<br>
TT-T--- 65 100 87<br>
-TTT--- 52 100 88<br>
T-TT--- 40 100 88<br>
TTTTCCC 32 94 92<br>
TTTTC-C 30 94 94 ...<br>
<br>
Not too special here. Like Bucklin but not as concentrated at the top<br>
(Bucklin had 702 TTTT---).</blockquote><div><br></div><div>This system is advocated by nobody. MJ is by definition ER. </div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
MJgmtER 97 87<br>
TTTTM-- 172 100 89<br>
TTTT--- 120 100 88<br>
TTTT--M 101 100 86<br>
TTTT-M- 99 100 88<br>
TTT-MMM 38 93 94<br>
TT-TM-- 22 100 88<br>
TT-T--M 17 100 87 ...<br>
<br>
So, very similar to MCA but not as certain for some reason.<br>
<br></blockquote><div><br></div><div>Pretty much as expected. </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
-----<br>
<br>
I tried, out of curiosity, FPP where the *second* candidate wins:<br></blockquote><div><br></div><div>Wouldn't that be SPP? :) </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
WrFPP 73 72<br>
CCCCPPP 669 93 94<br>
PPPPPPP 254 14 14<br>
PPPPCCC 77 90 80<br>
<br>
Interesting that most of the time a decent candidate wins.<br>
<br>
-----<br>
<br>
DAC update: I have DAC with ER and no ER.<br>
<br>
DACstr 96 86<br>
TTTT--- 569 100 87<br>
-TTT--- 61 100 85<br>
TT-T--- 52 100 88<br>
T-TT--- 45 100 86<br>
TTTTCCC 36 94 93 ...<br>
<br>
DACer 97 87<br>
TTTTM-- 172 100 88<br>
TTTT-M- 129 100 87<br>
TTTT--- 116 100 88<br>
TTTT--M 101 100 87<br>
TTT-MMM 29 94 93 ...<br>
<br>
Interestingly the ER version doesn't seem to have as much compression as<br>
I expected. A bit comparable to MCA actually.<br>
<br>
-----<br>
<br>
Next, I thought I should try the ER versions of IRV. IRV earlier gave<br>
these results:<br>
<br>
IRV (93 and 93 stats)<br>
88 ----CCC<br>
44 ----CC-<br>
39 -----CC<br>
36 ----C-C<br>
34 --T-CCC ...<br>
<br>
ER-IRV(fractional) gives:<br>
IRVerF 93 93<br>
----MMM 37 93 94<br>
----MCM 26 93 94<br>
----MMC 19 92 93<br>
----CMC 18 92 95<br>
----CCM 17 94 95<br>
----CMM 17 93 93<br>
-T--MMM 16 94 94<br>
T---MMM 15 92 94 ...<br>
<br>
ER-IRV(whole) gives:<br>
IRVerW 93 93<br>
----MMM 182 94 94<br>
T---MMM 65 93 92<br>
--T-MMM 57 94 94<br>
-T--MMM 50 93 94<br>
----MMC 33 93 94<br>
----CMM 27 93 93<br>
----MCM 22 94 94<br>
----MCC 19 93 94 ...<br>
<br>
So, ER didn't make IRV any better but it did reduce the amount of<br>
compromise. Chris had an idea, I believe, that ER-IRV(whole) was<br>
susceptible to a straightforward push-over strategy, but I'm not sure<br>
I see that here unless some Ms or Cs are playing that role. Since the<br>
C voters are very frequently using that strategy (in many methods) I'm<br>
doubtful...<br>
<br>
Also, you can note here that the IRV methods did better wrt utility<br>
maximizers than the other methods in this post. You can see (by scanning<br>
for high values) that this is expected when C is losing his win odds<br>
due to the voting patterns, and B is winning when sincere Condorcet says<br>
it should be C.<br></blockquote><div><br></div><div>In other words, what's happening is that voters are pre-emptively compromising for "insurance" against an unreliable system, and that ends up electing a centrist, utility-maximizing candidate even when it turns out that the compromisers' sincere favorite could have been the CW. Given that real-life elections are never one-dimensional, but in fact always include a "quality" dimension on which all voters tend to agree, I think that in real life this "superior" utility would actually be inferior.</div>
<div><br></div><div>(By "quality", I mean that I'd always prefer an intelligent, equanimous, empathetic, and charismatic candidate to one who was otherwise the same but was stupid, vindictive, selfish, and unappealing. That is true regardless of my ideology. Someone with an ideology which favored government paralysis might ideologically prefer non-charismatic or even stupid candidates, but I suspect even such a person would have a hard time actually voting for them.)</div>
<div><br></div><div>Jameson</div><div><br></div><div>ps. I criticize Obama for being too equanimous, but that's a matter of his convictions — I think he'd actually rather be evenhanded than right — and not his temprament, which I still applaud.</div>
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