[EM] another reason to avoid strategic motivations

[Abd ul-Rahman Lomax]

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.