[EM] Comments on the declaration and on a few voting systems

[MIKE OSSIPOFF]

I’m back for a while, at least to make a few comments. Maybe just a little longer too.
 
The declaration, posted recently, is encouraging. It’s good to hear that some big names are underwriting a declaration regarding the need for a better voting system. 
 
A few comments about the declaration:
 
I liked the open-ended nature of it. Recommending some of the best methods, such as Condorcet, Approval, Range-Voting, and that appealing median cardinal ratings method, the declaration emphasized that those might not be all of the best methods. 
 
Before commenting on the methods themselves, I’d like to suggest that emphasizing the need for a better voting system should be only half of the declaration’s purpose: It should also advise voters on how to use Plurality. Voters can benefit greatly from some Plurality strategy advice, long before we can get a better voting system.
 
As you know, and this is the problem, many voters in Plurality elections vote strategically, but without adequate information to inform their strategic voting. Plurality, like Approval, is a method in which strategy is justified, if there’s sufficient information for it. 
 
So, tell people that there’s nothing wrong strategic Plurality voting, if there were enough information for it. The information would consist of knowledge of other voters’ preferences. Specifically, we’d need information about each pair of candidates’ probability of being the 2 frontrunners,  _based on voters actual preferences_.  Maybe the easiest ways to estimate those pair-frontrunner probabilities would be to estimate the individual candidates’ or parties’ probabilities of being a frontrunner, based on past elections (but not on elections where people vote strategically without sufficient information) and multiplying those probabilities together for each pair of candidates.
 
But of course we don’t have any information about actual  preferences. That’s because, when voters strategize in Plurality, the resulting vote totals tell us nothing about the voters’ actual preferences.
 
So tell people that, for that reason, our Plurality elections are zero-information elections.
 
Plurality’s strategy in a zero-information election is simple: Vote for your favorite. That’s what voters need to do, if we’re ever to have the information needed to inform strategic voting in Plurality.
 
And, if that day ever comes, when, from sincere voting, voter-preference information is available, then there could be website Pluralilty-strategy calculators, to advise people on whom they should vote for, given their (or someone’s) estimate of the frontrunner probabilities, and given the individual’s estimates of the merit-differences among the candidates. It’s easier to estimate merit differences than it is to estimate absolute merit, even though the number of candidate-pairs is many times the number of candidates.
 
Of course, we should all be doing polling about preferences among the candidates. And we should be encouraging organizations to do so too. We should be in the public plaza, with a card-table, polling people about which voting systems they’d vote yes on the adoption of, and sign the initiative petition for. Of course we’d limit the poll to a few of the best and most briefly described methods. I’d include Approval, PC, and MPPO. Maybe RV, but maybe only if they didn’t like the others.  
 
(RV might have the best acceptance-chance, because it’s familiar. But some people will rate sincerely, and some people will rate strategically. If they all rated strategically, that would be fine—it would be Approval. If they all rated sincerely, that would be fine too. But when some do one, and some do the other, that will really mess the results up. As a progressive, I don’t want other progressives giving away the election to more strategic voters. But, in perspective, that isn’t a problem, compared to Plurality’s strategy problem.  So I consider RV one of the best public proposals.)
 
As you know, the polls we hear about in the media invariably ask people “If the election were held today, whom would you vote for? Of course, that reveals nothing about preferences, and such polls are quite useless for informing strategic Plurality voting. So maybe our plaza-polls should also include a vote on presidential candidates or parties. Plurality would do, since the main purpose would be to get the necessary information to inform Plurality-strategy. But Approval and rankings would be good to include too, to demonstrate how those methods work, how they’re voted, how they allow more sincere voting—How none of them makes you vote someone else over your favorite. 
 
There’s a media myth that people are voting for their favorites.  ….Even as the media refer to the Democrat and Republican as “the two choices”, thereby encouraging people to vote for one of “the two choices” instead of for their favorite. Point out those mutually-contradictory media statements or implications.
 
Regarding the determination of voters’ preferences, let me say a few brief words about IRV.
 
Though I, of course, don’t consider IRV to be adequate as a voting system, I now admit that it’s better than Plurality, because it reveals some preferences that Plurality doesn’t reveal. For instance, IRV, unlike Plurality, would show us how many people prefer the Greens’ candidate to the Republican. That’s no small accomplishment. For that reason, I wouldn’t campaign against IRV proposals. Regardless of how good or bad a voting system IRV is, it would, at least, for the first time, reveal some voter preferences. 
 
Of course, Approval, Range Voting, Condorcet, MMPO, and MDD (with various completion methods) should be proposed to the public by us, because they are the best methods that we know of.
 
(More about those methods below)
 
About the median cardinal ratings method, I suggest that it needs a better, more descriptive, name. How about “Median Cardinal” (MC), or “Cardinal Median” (CM)?  It was my first impression that that point-count would do a lot toward encouraging sincere ratings, minimizing the effect of extreme strategic ratings, though it could  backfire if enough people vote extreme strategic ratings.
 
But does anyone know what is the strategy, in Median Cardinal? I don’t have rigorous proof, but it seems to me that its strategy would be very similar to that of Range Voting and Approval. I should save the details for another posting. I’d say that, for simplicity and familiarity, RV is better, especially if, as I suspect, both methods have nearly the same strategy. I suggest that, therefore, MC shouldn’t be included among the  recommended or suggested best methods until someone tells us what its strategy is, or until we’ve at least discussed its strategy.
 
“MC” is an abbreviation for “Majority Criterion”, and so maybe the median method should be called Cardinal Median, and abbreviated CM.
 
A word about Condorcet methods:
 
When the declaration recommends Condorcet methods, I suggest that it should be more specific about what kinds of Condorcet methods it recommends. Specifically, it’s widely agreed now that the Condorcet methods that compare pairwise defeats in terms of pairwise opposition are the ones that bring the greatest strategy improvement. They’re the ones that are being proposed, and used by organizations, more and more.
 
“Condorcet” is often taken as synonymous with “pairwise-count”. While it’s true that Condorcet suggested a pairwise-count, with the purpose of electing a candidate who has no pairwise defeats, he also suggested a way to solve the situations when there is no such candidate. He probably suggested more than one, but there is one that is often called “Condorcet’s method”: When there is no “Condorcet winner”, then the election goes to the candidate whose greatest pairwise defeat is the least. Of course, if more people rank X over Y than vice-versa, then X pairwise-beats Y, and that’s a pairwise defeat for Y.
 
But pairwise-count methods, in general, don’t optimally avoid the lesser-of-2-evils dilemma. In fact, whether Condorcet’s comparison of pairwise defeats avoids that problem depends on how pairwise defeats are measured.
 
In the late ‘80s or early ‘90s, I began pointing out that, if pairwise-defeats are measured by pairwise-opposition, that would tremendously improve the strategic situation, and would greatly reduce strategic need.
 
If X pairwise-defeats Y, then Y’s pairwise-opposition consists of the number of people who ranked X over Y.
 
In the earlier discussions, I referred to pairwise-opposition as “winning-votes”, because they’re the votes in favor of the candidate who wins that pairwise comparison. Maybe “pairwise opposition” would be a better term, but, having used “winning-votes” so much, often abbreviating it “wv”, I should stay with that term, for the sake of consistency.
 
I often say “wv” to refer to the winning-votes Condorcet method, in all of its versions (discussed immediately below).
 
Here’s the simplest wv method:
 
Plain Condorcet (PC):
 
If a candidate has no pairwise-defeat, s/he wins.
 
Otherwise, the winner is the candidate whose greatest pairwise defeat is the least.
 
[end of PC specification]
 
Actually, of course, we could almost leave out the first line of that specification, since a nonexistent pairwise defeat could count as the least pairwise defeat. Maybe a little rewording could do that in a solidly-literal way. That gives us one brief line for PC’s specification.
 
Don’t let the IRVist tell you that that’s more complicated than the specification of IRV.
 
I’ll say right now that PC brings the most important anti-LO2E strategic benefits, among the benefits offered by any wv method, including the fancier, much more elaborately and wordily-defined ones.  Yes, the fancier ones meet ICC, and maybe a few other more demanding criteria, but we need something briefly-defined enough to be publicly-proposable, but with significant avoidance of the LO2E problem. Among the Condorcet versions, that’s PC. PC, unlike the other Condorcet versions, is simple enough and brief enough for a public proposal.
 
I recommend PC, as the simplest and briefest and most publicly proposable of the Condorcet versions. 
 
But I also used to mention the use of PC with its choice limited to the Smith set. Then, Markus Schulze proposed a more elaborately-defined wv version/implementation called “Beatpath”. Others of us then suggested “Schwartz Sequential Dropping” (SSD), an equivalent way of getting Beatpath’s result. Also, someone noticed Ranked-Pairs in a journal article, another deluxe Condorcet version with results nearly the same as Beatpath and SSD, and with nearly the same criterion compliances. Some find it aesthetic to always choose from the Schwartz-set, as do those methods. But isn’t it just as aesthetically appealing to elect the least pairwise-defeated candidate, the one with the least pairwise opposition from any one candidate? …as do PC and MMPO? (PC only looks at pairwise opposition _in pairwise defeats_ while MMPO looks at them all).
 
The point that I emphasize here is that PC has the most important strategic  benefits of the more elaborate wv methods mentioned in the previous paragraph, and, unlike them, PC is sufficiently simply and briefly defined for a public proposal.
 
We’ve already discussed Approval and RV enough to know that many of us, including me, highly recommend those two methods. They may well be the best proposals, due to their natural obviousness, and their simplicity. Approval is easier to implement, and, in my opinion, more beautifully elegant and simple. But RV is more familiar to people. Of course, when proposing Approval, it’s important to point out that it  _is_ RV. It’s the 0-1 RV method. And it’s the method that lets you vote one set of candidates over another, saying “I vote this set over that set”. Maybe Approval should be called “Set Voting”, or the 0-1 Points System.
 
Just one more comment about Condorcet. I was impressed by the beautifully simple and briefly-worded specification of Ranked-Pairs. Just maybe, it might qualify as simple and briefly-defined enough for a public  proposal, putting it in competition with PC, MMPO, and MDD (with its various completions), as the best rank-methods for a public proposal.
 
Enhancement of PC: (these could also enhance MMPO too):
 
I suggest that there are other rank methods that are at least a little better than unenhanced PC. They include enhancements to PC, though, of course an enhancement is also a complication, and some of the PC enhancements are too complicated for a first public proposal.
 
Here’s a PC enhancement:  PCA (PC with Autodrop):
 
If there is a circular tie consisting entirely of majority defeats, then, from each ranking, drop, from that ranking, every candidate who is in that circular tie, and has, ranked over him in that ranking, another member of that circular tie.
 
The advantage? In ordinary PC, let’s say there are somewhat more than 3 candidates: Livingstone, Obama, and Palin, and someone worse than Palin, someone we can mostly ignore, because they won’t win.
 
(Even though British members of Parliament can’t really be candidates in U.S. presidential elections—except when conducted at EM)
 
Say the Palin voters attempt offensive order-reversal (the only significant cause of strategy problem for the best rank-counts).
 
They do offensive order-reversal against Obama, by insincerely ranking Livingstone over Obama.
 
And say that the Obama voters don’t use PC’s defensive strategy of defensive truncation. They sincerely rank Palin over the worse candidate.
 
(I’ve pointed out that, in PC, offensive order-reversal can only succeed if its victims are trying  to help the perpetrators)
 
What is the requirement, in terms of 1st choice support, for Palin to win?
 
Palin needs to have the most votes. More than Obama and more than Livingstone.
 
That’s for PC. What about PCA?  In PCA, for Palin to win, the requirement is for Obama to have the fewest votes, among those three candidates (Livingstone,  Obama and Paliin).
 
I suggest that that is an improvement, even if a small one. Both methods require Palin to be bigger than Obama, in 1st choice votes. PC additionally requires Palin to be bigger than the candidate whom her voters rank over Obama. They can easily choose a candidate probably less popular than Palin, to rank over Obama. PCA requires, additionally, that Obama be smaller than Livinstore. It’s easier to find someone smaller than their own candidate than to find someone bigger than the Condorcet Candidate.
 
 (I’m going to stop calling that candidate the CW, and start calling him/her the Condorcet Candidate, because CW properly means someone who actually pairwise beats everyone. Since “CC” already stands for “Condorcet Criterion”, I’ll abbreviate “Condorcet Candidate” as “CCt)
 
As I said, it’s probably only a small improvement. PC already doesn’t have a strategy problem. The burden of information is on the offensive order-reversers.  They need much information for their strategy. If they have that information, so will their intended  victims, who will know against whom they need to use defensive truncation.  And, if they do, that will thwart and majorly penalize the offensive order-reversal. As I said, offensive order-reversal can only work if its victims are trying to help their victimizers.
 
So I don’t really suggest PCA as a replacement for the extremely simple PC, as a first public proposal. Enhancements like that can be proposed later.
 
PCA could be accompanied by a ballot indication that the voter wants to protect some candidates from the autodropping, or wants to only do autodropping  below a certain point in their ranking. –with autodropping as the default for all candidates in one’s ranking.
 
Of course, the default could be to do nothing, to just leave the candidate in the ranking. And the voter could  be given the option to indicate that autodrop apply only to specified candidates, or to candidates below a particular point in the voter’s ranking. I’ve already proposed that here, calling it “ATLO” (Automatic Truncation Line Option)
 
But it now seems to me that, if we’re going to have such options, applying autodropping to all candidates qualifying for it should  be the default, because the result is a little better than unenhanced PC. If we’re going to complicate the method with options, they should be options, described two paragraphs before this paragraph, to protect some candidates from autodropping.
 
Very likely, it would be necessary to give the voter a box to mark, to turn off autodroppng for that voter, if it is perceived that a voter should have the right to not have his/her ballot changed in any way.
 
Of course, a good alternative to autodrop would be to say: “If there is an all-majority-defeats cycle, then hold another election (after some specified duration, as soon as possible after the first election).  In that 2nd election, the victims of the offensive order-reversal would have easy opportunity to do defensive truncation, to thwart and penalize any offensive order-reversal that has been noticed  to have occurred (It would be blatantly noticeable).
 
In EM polls, I suggest that Condorcet versions should always offer the option for voters to modify their rankings by defensive truncation, after the results are announced, and the pairwise defeats posted. 
 
That covers my possible suggestions for PC enhancements for public elections.
 
Two other pairwise-count rank methods for public election method proposals:
 
MDDA:
 
Probably in 2005, I proposed MDD. I don’t remember what completion I proposed, for when MDD would disqualify all the candidates. The best one would be to actually disqualify them all, and hold a new election, as soon as  possible. Note that would be vanishingly rare for that to happen. Victims of offensive order-reversal could respond to it by defensive truncation in the next election, by PC or PCA or MMPO.
 
Nor do I remember how I said to choose  among the undisqualified candidates, if any. I’d now say that PC, PCA, or MMPO would be a good way. Of course, PC, PCA, or MMPO could be the completion method, too, if all candidates are majority-beaten, if it’s desired to avoid a 2nd election.
 
It was then suggested that MDD be completed by approval: The winner is the candidate ranked on the  most ballots.
 
I thought that sounded pretty good, because, in wv, the reversers’ strategy hurts the intended victim in the circular tie solution, but doesn’t hurt the reversers’ candidate, because they aren’t ranking their insincerely-upranked candidate over their favorite. But, in MDDA, they’re giving an Approval vote to their less-liked, insincerely-upranked candidate.  For that reason, I claimed that MDDA was the best. The best solution to offensive order-reversal.
 
Now I believe that I was mistaken. Regarding the above discussed election with Livingstone, Obama and Palin, and someone worse than Palin (from the point of view of Obama and Livingstone voters):
 
If the Obama voters don’t do defensive truncation, but, instead, sincerely rank Palin over Livingstone, what is the requirement for Palin to win?
 
Only that Livingstone be the smallest of the  3 candidates. That’s a much easier requirement than that of PC or unenhanced PCA.
 
Chris: As you know, I’ve been looking for completion methods for MDD. I’ve mentioned a few possibilities above. You suggested Bucklin(whole). But I point out that, if the Condorcet candidate doesn’t have a 1st choice majority (S/he couldn’t have a majority defeat if s/he did), then all 3 candidates in a 3-candidate majority cycle will have a majority in Bucklin’s 2nd count. In other words, Bucklin will be like Approval. That means that the requirement for the reversers to succeed will be the easily met requirement that the less-liked candidate they rank over the CCt merely have fewest 1st choice votes.
                                                                                                                                                                    -
MMPO:
 
When someone, probably Forest, proposed MMPO, I said that it was very significantly better than PC, so much so that I called it a member of a new generation of rank-methods.
 
But, now, I don’t know why I said that. Looking at the requirements for offensive order-reversal to succeed, with and without defensive truncation; and looking at truncation-resistance, I can’t find where MMPO is any better than PC. Just as good, but not better. Of course, if, as seems to be the case, MMPO is  just as good as PC, then MMPO’s more briefly-worded specification would make it a better public proposal. Do others agree?
 
Or was I right before, and is MMPO very significantly better than PC? Tell me, if you know.
 
MMPO is certainly one of the best, along with PC, PCA, and MDD.  Maybe the best, due to being more briefly-worded than PC.
 
As I said, maybe Ranked-Pairs should be included among the competitors for best public proposal, due to its brief wording.
 
This concludes my discussion about the declaration and the best public proposals.
 
  		 	   		  
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20111013/96bdff44/attachment.htm>