At 03:13 AM 12/2/2008, Kristofer Munsterhjelm wrote:
On another note, Abd says the only method that got better Bayesian Regret scores than Range, among those Warren has tested, is Range + top two runoff. To my knowledge, that's not true, as Warren says a DSV variant of Range got better scores than Range itself (according to this post: http://listas.apesol.org/pipermail/election-methods-electorama.com/2005-October/017331.html ). Again, this suggests that if you absolutely have to have a method where strategy is required to get it to work, use a computer to do the strategy since it'll be much better at it than the voters will. What you say only reinforces this point.
Actually, that post confirms the *substance* of what I've been writing. I'd missed that 2005 post or didn't remember it. Here is a quote from Warren:
In preliminary computer-sim experiments, it appeared that Sarvo-Range Voting was superior (in terms of Bayesian regret) to ordinary range voting, which in turn was as good or superior to every other voting system I had tried (about 30). Sarvo-range was better than range because it handled strategic voters better. For honest voters, sarvo-range and range behave identically thanks to the honesty button. It looked like with any nonzero fraction of strategic voters, SR was better than R.
I have long claimed that the performance of Range voting could be beaten by a hybrid system that is actually more in conformance with democratic values. I'll now claim that DSV (Sarvo-Range) can, itself, be outperformed. But to do so takes, under some contingencies, a runoff. And to nail this to the ground, a possible series of runoffs. However, even a single runoff would be rare, and by that time, the difference between an accepted result from a single runoff and a result with an indefinite series would be minute. One caution: to be fully democratic, it should be possible for a majority of voters to block the completion of an election. I.e., they make a clear choice that they would prefer further process, they are willing to tolerate more fuss, or, alternatively, they don't want the office filled at all, rather than accept a plurality winner. (I'm going to neglect exact ties.)
Now, to take home: The only way to beat Range is to use Range and tweak it. This really ought to be a no-brainer, because only a Range ballot collects the necessary information. (Note that Borda with a tweak should do almost as well, or as well, or even better, if the number of candidates exceeds the number of preference increments in Range (linear Range) and equal ranking is allowed. If equal ranking had been allowed from the beginning in Borda, and if the device of having fixed ranks at all ranks, not just the bottom, had been employed (which makes counting Borda easier and allows Borda to work without complete ranking), we might all be using Borda, it has been around a long time and has been impeded by the strategic voting and clone considerations, which disappear (as to seriousness or even entirely, depending on the definition of "strategic") by allowing equal ranking and, of course, the corollary empty ranks. Borda would have quickly been improved by adding more ranks....
Read this carefully: Range, with any combination of strategic voters, performs better than any other simple method. "Strategic voting" with Range, which means something much milder and easier to understand and practice with Range than with ranked methods, must damage Range results, but not to the extent that Range becomes worse than ranked methods. In essence, Range becomes more similar to a ranked method when voted strategically. But even with 100% strategic voters, it's better than ranked methods, and the mix of strategic and honest voters improves results over that, until it is maximized -- almost -- with 100% honest.
"Honest" and "strategic" need specific definitions here, because we may assume that not being honest is a Bad Thing. Yet the "dishonesty" in Range is nothing more than not disclosing a preference (or minimizing it). Because accurate preference strength information is not disclosed, the method cannot accurately optimize overall voter satisfaction. That's why Bayesian regret increases with "strategic voting." However, remember, ranked methods (including Approval) *force* everyone to vote strategically, and that, indeed, is part of why they result in higher regret.
How can we do better than "honest" Range Voting? Some method of testing *absolute* utilities is needed, i.e., true preference strength. If I think that all the candidates on the ballots are lousy, but, hey, I'm here, so I'll vote, and I vote with full strength, I am voting "sincerely," but my utilities would usually be normalized to full Range (and DSV would, I presume, do this for me if I don't.) To get better, we need some way to test absolute preference strength over the range of candidates, and that ain't easy. There are two ways in use. Runoff elections test preference strength, if the runoff is inconvenient. Or the primary if it is a special election. The other way is an auction, which isn't used for public elections, except that it *does* affect who makes it to the ballot and voters are influenced by campaign spending. Campaign donations are a kind of auction.
The only real proposal here for immediate consideration is that we realize that runoff elections are a very powerful reform, that they always have been. The supposed down side, the inconvenience to voters, may actually be a plus. It could be said that by not coming together before the election to agree on a candidate, a majority of voters have effectively requested a runoff. That is made fairly explicit in Approval. Don't accept enough candidates, bullet vote to try to get just your favorite elected, don't be surprised if there is majority failure and you have to vote in a runoff. This is democratic process! In direct democratic procedure, when there is majority failure in an election, the assembly has to continue to repeat the procedure. At a certain point, they'd rather complete it than continue the process, so they make compromises; effectively, they lower their approval cutoff. Those with strong preference may not change their vote, until it becomes obvious that there are three candidates left and if they don't compromise, they won't get to go home. As I recall, the Venetians sequestered the electors, who were using Approval voting for at least part of their process, until they finished. I think something similar was done for papal elections. Get it together, guys! Find the best compromise and be done with it!
Good election methods compress this, but should not totally eliminate it, insisting on completing with a single ballot. If a good method doesn't find a majority winner, *the electorate needs to consider the matter more.* It is quite likely, in fact, that the best candidate isn't on the ballot. My comment about 2000 U.S. Presidential was that the biggest problem may have been that the best candidate wasn't on the ballot. If the electorate knew its candidates, and knew itself, that close an election wouldn't happen (or the situation would not persist). This is one reason why Robert's Rules does not actually recommend "runoffs" at all, no matter what the method. It recommends, and the default is, that the election *fails*. It's null, as if it hadn't happened, the whole process is repeated, nominations and all. It's pretty close to that if the top N candidates are automatically nominated, but any two voters should be able to nominate any candidate, whether or not the candidate was on the ballot.
(There would be a way that voters could eliminate candidates, which would be an explicit vote to make them ineligible for the pending election. That could be done, actually, but I wouldn't advise it!)
Range Voting, or more advanced systems incorporating and using Range Voting, remains the best single-ballot system. Improving on this requires allowing the method to fail to complete, leading to further process.
It is unclear to me which would be better: Single-ballot Range Voting, or a non-Range method, such as Bucklin or Condorcet methods, but still requiring a majority, i.e., runoff versions of these methods. But even better is Range Voting with runoff, I'm sure of that. Simple top-two runoff is known to improve Range results.
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