I think your analysis of my scenario is generally right on. (I changed the last candidate with 6 voters from X to RR at the last minute, which changed the EMAV winner from CL to CR)<div><br></div><div>But I think you're missing my main point, which is that there are more strategies available under EMAV than under MAV. In particular, as I set it up, the L and R factions (factions 1 and 4) have no reason to strategically exaggerate at all under MAV, but certainly do under EMAV. That was my main point. Would you prefer a simpler scenario to demonstrate this?</div>
<div><br></div><div>Also, you are right that the near balance between all 4 main candidates is unrealistic, but the scenario works the same if you shift voters between the L and CL groups and/or between R and CR (I believe that for MAV, these shifts can be any size and either direction. Clearly you could impact the EMAV results by doing large enough shifts like this.) So in real life it could easily be that, say, CL and R dominate in first-choice support.</div>
<div><br></div><div>Jameson<br><br><div class="gmail_quote">2013/7/4 Abd ul-Rahman Lomax <span dir="ltr"><<a href="mailto:abd@lomaxdesign.com" target="_blank">abd@lomaxdesign.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div class="im">At 11:38 AM 7/4/2013, Jameson Quinn wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
OK. I think we can work this out. Before I make more arguments, I'm going to try to explain the disagreements as I see them, and ask you more about what you're saying.<br>
<br>
A. MAV vs. ER-Bucklin (ERB, though we should probably find a better name at some point). That is, completion using above-median, or completion using median-or-above.<br>
<br>
I don't see a huge difference here. I think MAV is slightly better because of the chicken dilemma, but it's possible that that regular voters would see ERB as simpler by a big enough margin to make it worth supporting instead. I'm probably not a good judge of that because my mathy brain tends to see them as exactly symmetrical.<br>
<br>
I think you're beginning to understand my point about symmetry. Your view is that ERB is better because of apparent simplicity (empirical question about voters; we could find agreement here with more evidence) and also because of some Deep Principle of counting all the votes which I don't understand (because in my view MAV and ERB are exactly as likely to "count a given vote" or not, that is, to make a given gap in ratings between two candidates significant or not). I'm not sure that explaining your Principle further would help me understand it, because it's probably not going to fit with my logic. I would, however, like to understand more about whether you see the simplicity or the Principle as more important here.<br>
<br>
B. MAV vs. EMAV<br>
<br>
On this question, our principal disagreement is around the strategic impact of the voting system, both for general exaggeration and for specific chicken dilemma scenarios. Here's my logic:<br>
<br>
...Start Jameson's logic...<br>
<br>
1. In different systems, different strategies are effective. I'll give one "5 candidate linear" (5CL) scenario and one chicken dilemma (CD) scenario to illustrate my point.<br>
<br>
Honest utilities<br>
5CL:<br>
23: L100, CL75, CR25, R00, RR00<br>
25: L50, CL100, CR50, R00, RR00<br>
24: L00, CL50, CR100, R50, RR25<br>
22: L00, CL25, CR75, R100, RR50<br>
06: L00, CL00, CR25, R50, RR100<br>
<br>
(To make this comparison clearer, I'm going to use 4+1 ratings for both systems, though it would actually work the same if under EMAV, "25" represented a coinflip between the closest available ratings, 50 and 0)<br>
</blockquote>
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EMAV uses 25% as a non-approved rating. Bucklin-ER could be voted with the coin flip, it does not have that below-expectation rating.<br>
<br>
What I prefer to see is utilities that are normalized not only to the extremes, but also to the election expectation as midrange. This, in theory, could mean that the value of a point in the negative scale was different from that in the positive scale (i.e, below and above midrange.) Sophisticated voters would handle this by compressing the ratings at the extremes<br>
<br>
It's quite true that this is not strictly summable. We could do a separate study to see how this translation affects utility. I'll note, however, that this is the test used in Approval Voting.<br>
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What I'm going to claim here, without having gone over the example, and presumably we will examine this, is that if the above are truly honest utilities -- we can treat them as absolute, not distorted by "strategy" -- and if 50 is the minimum acceptable rating, i.e,. the election expectation, the voter will not be disappointed by the election of a candidate rated 50, at least not by itself, then a reasonable voting strategy will be simple: vote the honest utilities as the ratings.<br>
<br>
Now, as I start to go over this, I notice that all the voters have a candidate at each utility value. That's highly distorted from expectation. A voter, for example, who only knows their favorite may have a max *sincere* utility of 100, and zero for every other candidate. I don't know if this will impact the analysis. Ah, I see now that Jameson called this 5CL, "5 Candidate Linear." I read the votes this way:<br>
<br>
23: L100, CL75, CR25, R00, RR00 voters at L<br>
25: L50, CL100, CR50, R00, RR00 voters at CL, balanced between L and CR<br>
24: L00, CL50, CR100, R50, RR25 voters at CR, balanced between CL and CR<br>
22: L00, CL25, CR75, R100, RR50 voters at R<br>
06: L00, CL00, CR25, R50, RR100 voters at RR<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
CL is the honest winner under both MAV and EMAV, with a median of 50.<br>
</blockquote>
<br></div>
However, the utility numbers show a clearer picture:<br>
<br>
SU for all the candidates from stated ratings taken as utilities, as percentage of maximum;<br>
L : 35.50%<br>
CL: 59.75%<br>
CR: 60.25%<br>
R : 37.00%<br>
RR: 23.00%<br>
<br>
CL is not the SU winner, it is CR, but only by 0.5%. An election this close would be unpredictable. It has, as well four candidates balanced by first preference, it's rare to have three. It's clearly been set up to do this.<br>
<br>
How does this election proceed if the utilities are votes and with normal Bucklin amalgamation, majority is 50%+ :<br>
<br>
4 3 2<br>
L 23 23 48<br>
CL 25 48 72 majority<br>
CR 24 46 71 majority<br>
R 22 22 52 majority<br>
RR 6 6 28<br>
<br>
Three majorities!<br>
<br>
Under EMAV, if there is a multiple majority at a round, the sum of ratings prevails, shown above, so CR would win with a very small margin, not CL as he stated.<br>
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Under ordinary Bucklin-ER, CL would win by a whisker. B-ER does not handle the lower ratings.<br>
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Under MAV, the election looks at the previous round, and CL wins there -- but also only by a small margin.<br>
<br>
These methods are dithering with their introduced errors and a very small difference in utility.<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Under both systems, the CR voters could win by dropping CL's rating to 25, and the CL voters could defend against this by dropping CR to 25. Under both, the RR voters could elect CR by rating them at 75 or above. But EMAV presents a number of further possible strategies: for instance, the R and L voters could both help their preferred frontrunner by rating CR and CL at 100 and 0 or vice versa, whereas with MAV these strategies would have no impact.<br>
</blockquote>
<br></div>
Indeed. What is utterly unrealistic here is the idea that the utilities would be voted as such. This is an election with *four first preference frontunners.* If a voter has a significant preference strength for their favorite, and 25% is significant, they will not immediately approve the second preference. They *may* approve this preference at a lower round, or even in the disapproved rank. Remember the basic strategy for Range, max rate the preferred frontrunner, min rate the worst, and then make the rest of the ratings as makes sense in relation to those? Some voters may do just this, others may back off from it a notch.<br>
<br>
Let's see what this election looks like with more realistic votes. I'm going to assume that there is some history here, and that range poll data is available, because the plurality data will drive the voters nuts. The voters will know that the likely winners are CL and CR, and they will vote accordingly.<br>
<br>
23: L100, CL75, CR00, R00, RR00 -- maintain preference for L, but min rate CR, the other frontrunner from CR<br>
25: L50, CL100, CR00, R00, RR00 -- min rate CR<br>
24: L00, CL00, CR100, R50, RR25 -- min rate CL<br>
22: L00, CL00, CR75, R100, RR50 -- maintain preference for R, min rate CL<br>
06: L00, CL00, CR75, R75, RR100 -- maintain preference for RR, uprate CR and R<br>
<br>
Notice: I have the voters here maintain a first preference indication, which has a cost (1/4 vote in the frontrunner race). I'd like to see rating interpolation, remember? That would allow a half-rating to be used for that, reducing the cost to 1/8 vote.<br>
<br>
The resulting strategic sums, percentage of max rating:<br>
<br>
L 35.50<br>
CL 42.25<br>
CR 45.00<br>
R 38.50<br>
RR 23.00<br>
<br>
Bucklin amalgamation:<br>
<br>
L 23 23<br>
CL 25 48<br>
CR 24 52 majority<br>
R 22 28<br>
RR 6 6<br>
<br>
CR wins again by B-ER, EMAV (which doesn't use the rating sum for this), and by MAV, because it's a single majority.<br>
<br>
Notice that the sincere utility sums above were balanced for CL and CR, with a slight edge for CR. It was well above election expectation for both.<br>
<br>
What sometimes happens in studying examples is that one faction is portrayed as using a strategy, while the other sits there stupid. But "strategy" here is simply sensible voting, and all factions are likely to use it to roughly the same extent. Notice that it doesn't make a big difference. The CR supporters simply accelerated their support, while keeping their first preference clear. They could have provided more support by going for 100% for CR, and the CL supporters could have done the same; both groups could pay the cost: failure to distinguish their favorite (i.e, L for CL and R or RR for CR).<br>
<br>
52% of voters are at CR or to the right, 48% at CL or to the left. It is not a surprise that CR has an edge.<br>
<br>
Various strategic patterns could flip this election between CR and CL, because strategy introduces error in utility representation, but the question is *how much* error?<br>
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This example, by the way, shows a superiority of EMAV over B-ER and MAV.<br>
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Jameson, I'm guessing, thinks that the possible strategic voting is an inherent negative. With five candidtaes, the five-rank system is a bit primitive. Vote interpolation would improve the resolution, allowing maintaining preference order while casting a more powerful vote. Voting systems theorists who think strategic voting is "bad" seem to want to prevent voters from using their power. That's favoring a theory over the empowerment of voters.<br>
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(Vote interpolation: the votes above were in five ranks, with a value, from first to last, of 4 to 0. Vote interpolation is a method of handling overvoting without discarding or seriously misrepresenting the intended vote, and it then has a use (just as counting all the votes has a use with plurality: it creates approval voting.) With vote interpolation, the highest and lowest rating marked for a candidate are averaged. So if one has a favorite and votes 4 (or 100 in the charts above), *and 3*, the vote is counted at a value of 3.5. Thus the cost of maintaining a designation of favorite is reduces to one-eighth of a vote, without the ballot becoming more complicated. It would actually be easy to use, one could mark straight ratings, then "nudge" them one way or the other.<br>
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This election is weird because if we look at first preference, we have *four* frontrunners. It's really that there are two major wings, and they each field two candidates, plus there is a small extreme right party with enough power to spoil an election if they choose -- or if the method doesn't allow them flexibility. This election is presented as partisan. In the setup, the right is split into *three* parties. That weakens them; the method barely saves their bacon. But notice, if they screw up, CL wins, and that is not actually a huge loss for them.<br>
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Jameson went on to cover a chicken dilemma scenario, but I'm bailing for the night, at least on this issue. I've queued it.<br>
<br>
</blockquote></div><br></div>