[EM] Why I think IRV isn't a serious alternative 2

[Kevin Venzke]

Hi,

--- En date de : Lun 1.12.08, Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> > > If we must have a
> > > single ballot, and a single winner, period, Range
> Voting is
> > > actually a trick: it is the only relatively
> objective method
> > > of assessing the expected voter satisfaction with
> an
> > > outcome, turned into an election method. It's
> ideal
> > > because it's designed that way. (The only fly
> in the
> > > ointment is the charges about strategic voting,
> but I've
> > > been arguing that this is based on a total
> misconception of
> > > what we are doing when we vote.)
> > 
> > I don't understand how you reconcile the two ideas
> here. Range is
> > "objective" and "ideal because it's
> designed that way" based on the
> > idea that voters have internal utilities and, if they
> vote them exactly,
> > under Range voting, the best candidate according to
> overall utility
> > will be elected every time.
> 
> I've responded to this in a prior post, the first part
> of it. I did not make the claim that Range Voting was
> "objective." It is a voting method and does not
> automatically choose the best candidate according to overall
> utility, neither in simulated elections with practical
> methods, not even if we assume "fully sincere
> voting."
> 
> It simply gets closer than any other single ballot method.

Can you come to this conclusion without the assumption that voters
will vote accurately?

> Of the methods that have been tested through the simulation
> process, the only method that beats Range, if I'm
> correct, is Range with a top two runoff. Not a single ballot
> method, not even considered a voting method by many
> definitions. Arrow, in particular, made
> "deterministic" one of the preconditions for his
> theorem to apply.
> 
> In the simulation process, absolute personal utilities must
> be converted to Range votes, for, with practical election
> methods, it's probably impossible to vote absolute
> utilities, even if people wanted to. The conversion process
> usually takes the preference list for candidates considered
> real options and looks only at the range of utilities among
> those candidates. While a voter *might* decide to extend the
> "coverage" of the voter's vote, this is not
> what we normally do when we are asked to make a choice. We
> restrict our consideration to the practical possibiities.
> This normalization process, to some degree, makes the same
> "mistake" as preferential methods do, it equates
> what may be a small preference with what may be, with
> another, a critical or crucial preference. Hence Range
> Voting which depends on this normalization can fail to find
> the truly optimal winner. It pleases some people with little
> preference at the cost of greater absolute preference
> satisfaction for others.

So I guess you must not just assume but *hope* that voters can vote
accurately. In that case it seems fair to criticize that voters don't
have incentive to vote accurately.

> So let me be specific, though we will get back to this.
> Range Voting isn't perfect. It does not always choose
> the best winner. When it does not, it is sometimes possible
> to detect the situation and fix it; that is why Range Voting
> with Top Two runoff gets lower regret results than Range
> alone. It detects the relatively rare situations that cause
> Range to fail to find the ideal winner.

We're talking "honest" simulated Range, yes?

> And in my opinion,
> Runoff Range is not as accurate in the simulations as it
> would be in real life; that's because real runoffs test
> *relative absolute preference strength,* free of strategic
> considerations (when write-ins are involved, this isn't
> totally true.) This effect is something which has been
> largely overlooked. Or even totally, as far as I know.
> It's original with me, but it's likely someone else
> has written about it somewhere. I don't consider it
> rocket science, just something obvious that's been
> overlooked.

If you're talking about the idea that two-candidate elections are
strategy-free, then yes, that has been noted.

> > At the same time you want to defend Range against the
> charge of
> > susceptibility to strategic voting, essentially by
> denying that the
> > Range voter is supposed to be mapping his true,
> absolute preferences
> > onto the ratings.
> 
> That's right. Range results shift, and they shift to
> increase regret, when voters vote "strategically."
> This is well know, but it's an error to consider this a
> reason to avoid Range. If, with realistic voting profiles,
> they shifted results to make Range worse than other methods,
> it would be one thing. But they do not, if the simulations
> were accurate. 

Well, if the simulations were accurate, then strategic voter behavior
wouldn't even vary for different rank ballot methods. Everyone would
apply Borda strategy according to randomized polling data. It is not
very surprising that strategic Approval can outperform a method with
this kind of behavior.

> Nobody has challenged Warren's results.

What do you mean no one has challenged Warren's results? What would you
interpret to be "challenging" the results?

> Yee diagrams are a similar approach. Nobody has contradicted
> the basic work, even though it is all published and source
> code is available, etc. Instead, we see criticism that often
> misunderstands the basic nature of the study.

I have made such diagrams myself. I have made and seen few that simulate
any strategy, except for Approval.

> The voter *does* map his true, absolute preferences onto
> the ratings.

Really? Ok.

> Kevin, you are not being careful. There is, in
> theory, a one to one, continuous, monotonic transformation
> of absolute voter utilities (not "preferences") to
> Range votes (neglecting roundoff error, which makes the
> function a step function, still monotonic.) 

Ok. So my sincere ratings of candidates A B C can be accurately recorded
as, let's say, 1 4 and 9.

> That's why
> we can, with a reasonable definition, still call these votes
> "sincere," 

I'm not sure what you mean by "still." I guess you mean, in spite of
roundoff error.

> since they do not violate the derived
> preference profile of the voter. All that they do is to,
> possibly, equate the vote of some candidate pairs when there
> is a non-zero preference strength between them, and that is
> larger than the Range resolution. In other words, the voter
> thinks that, given all the conditions, the voter exercises
> more effective voting power elsewhere and -- presumably --
> will not regret the abstention from voting in that candidate
> pair.

But under Range this probably isn't much of an issue, if the resolution
is somewhat high.

> This is quite what we routinely do with real world
> choices under analogous conditions. We do not bid on things
> in auctions based merely on cost, when we have a limited
> amount to bid. I won't go into describing such an
> auction, but we factor in the probability of success, and we
> put our limited auction dollars into the preference pairs
> that seem more likely to be a good investment. But we never
> try to pay *more* for a candidate that we prefer *less.

Ok. But didn't you claim that the concept of "sincerity" is flawed in
Range? If it *is* possible to map real preferences to the Range ballot,
then what on earth is wrong with the concept of "sincerity" in Range?

> The transfer function, thus, is monotonic but not linear.
> With "sincere absolute preferences normalized to the
> voting Range," we'd get a limited regret-minimized
> result, and there may be some voters who decide to vote this
> way. I'd not advise it, though it's relatively
> harmless. It improves the overall outcome at small cost to
> the voter. (By definition, if the cost is large, the sincere
> preference is large.) In real world collective decision
> making on a small scale, we often do exactly this: we reveal
> our sincere preferences in absolutes, where possible, or, at
> least, in terms of preference strength across our personal
> profile.
> 
> So is Range Voting "vulnerable" to strategic
> voting? What does that mean? 

It means that given a certain understanding of what an "accurate" vote
is under Range, typically an inaccurate vote is the strategic one.

> In practice, it is used as a
> voting system criterion and a black mark against Range
> Voting. But the "harm" done is simply
> institutionalized by other voting systems, and the possible
> improvement through accurate expression of absolute
> preference strengths (within the limitations) is made
> impossible. 

"Possible improvement" must be the important thing about it all.

> Which, of course, harms the results even more.
> In order to avoid the bete noir, strategic voting, which has
> been redefined to include any failure to accurately disclose
> a sincere preference, voting systems students would avoid
> the only method which *minimizes* the effect of such, and
> allows it to operate only where it is relatively harmless.
> 
> The simulations answer the questions of "how
> much" and "how often," which cannot be
> answered through the prior approach, the use of voting
> systems criteria. Approval Voting fails the Majority
> Criterion, according to the usual interpretations (which had
> to be modified to apply to Approval Voting, and, clearly,
> the modifications were designed to *cause* Approval voting
> to fail, because the students thought, intuitively, that it
> failed. That's what I mean by subjective analysis! See
> James Armytage-Green's study and application of the
> Majority Criterion to Range Voting).
> 
> Okay, how often? It would be extraordinarily rare in real
> public elections, because it requires a significant number
> of voters to vote for both frontrunners, which is the
> opposite of standard Approval strategy and is, normally, a
> foolish vote if the voter does have a significant preference
> between them. And if the voter doesn't have a
> significant preference, well, there you go. See the second
> question!)

How long has it been since I noted that this is not correct, unless you
want to assume that Approval won't have more than two viable candidates.
If two candidates obtain majority approval, most likely one of them was
not a frontrunner, but a compromise choice.

This baffles me because I can't imagine why you like the Approval method,
if it doesn't occur to you that a non-frontrunner compromise choice
could conceivably obtain majority support.

> And how much damage from failure? Little. When the Majority
> Criterion fails, we have multiple majorities. The majority
> has Approved another candidate as well as their favorite,
> and, together with other votes, this less-preferred
> candidate has broader support. Is that bad? Many would argue
> it's good, and this again points out the subjective
> nature of the use of voting systems criteria to judge
> election methods.

I think it's probably good for frontrunners, since they have an easier
time getting that many votes.

> Quite simply, to make sound decisions from preference
> profiles, we need to know preference strength. Preferential
> ballots can, sometimes, approximate this (Borda does that,
> and works better if there is a broad spectrum of candidates
> on the ballot, thus creating, in the real preference pairs,
> an approximation of preference strength), and usually the
> majority preference will also be the ratings winner. But a
> Range ballot directly expresses this.

Well, that is subject to your interpretation of what the Range ballot
signifies. It certainly *could* be used for that.

> And, of course, we'd compare these results with
> simulation predictions and eventually we might build up
> enough data to confirm or improve the models. The problem
> with this approach for the short term is that the
> simulations can study thousands of elections and thus see
> the behavior of a voting system under many different
> conditions, whereas the actual experimental approach, with a
> lot of effort, only shows one instance. Useful, still, but
> probably best used to improve the models used in
> simulations.

I strongly agree with improving the models used in simulations.

> > If the idea of a sincere set of ratings irrespective
> of context is "a
> > total misconception of what we are doing when we
> vote," then what useful
> > theory is Range based on? What makes it
> "objective" and "ideal" if not
> > what I stated above?
> 
> It does not depend on relatively subjective considerations
> like which voting systems criteria are more important than
> the others. It defines an optimal winner in a manner that,
> once understood, most people would agree is reasonable, and
> that matches how we make decisions, when we are sane and
> collectively functional, in real life. The approach defines
> the "ideal winner" in a way that works when we
> know absolute utilities, and there is no reason to expect
> that it would stop working simply because the utility
> profile can't be directly determined. (It works when we
> can see it and test it, why would it stop working when we
> can't?)

Because real people will be involved

> There is no usable definition of "a sincere set of
> ratings irrespective of context," because there is no
> way for voters to even determine such in a manner that they
> could vote them. 

Ok, I will concede again that there is no way for voters to determine 
their sincere set of ratings in a votable way.

> The ratings that we can determine, in
> practice, are not absolute, independent ratings.

Yes, I thought this was the sincere/strategic vs. accurate concept.

> We can approach, this, though, in certain respects, through
> runoff elections, and we can approach it through binary
> choices in sequence.

I don't really mind if it's theoretically possible.

> > I also wonder, what, theoretically, does it look like
> when Range fails
> > and gives a poor result. Is such a thing allowed?
> 
> Well, what's a "poor result"? My claim is
> that the only way to objectively study this is to see how
> the method performs when absolute utilities are known.

Well, if we know the absolute utilities, then we can definitely call
certain votes inaccurate.

> That's what the simulations do, the "know" the
> absolute utilities by assuming them, in some hopefully
> reasonable way. (Don't think it's reasonable? The
> simulators are configurable. Use a better simulation of
> underlying utilities! Until then, Warren's work is the
> best we've got!)

I have no problem with the representation of utilities.

> Now, following Warren's work, Range would very rarely
> give a truly "poor result." It would take some
> very bizarre preference profiles. You can construct them
> .... but for them to occur in real life would be practically
> impossible. What it can do, and the simulations show it, is
> to miss the true ideal winner according to the normalization
> of absolute utilities, and, as well, due to the non-linear
> expression of utilities (but still monotonic) by voters
> seeking to maximize the effect of their vote. However, when
> it does this, it would not then flip to a much worse
> candidate, unless, again, the conditions were truly bizarre.
> It would simply choose, in almost every simulation (quite
> likely all or nearly all), the next best winner, and the
> best would be in second place.

Actually a lot of methods fail in this way: The best candidate actually
places second.

> In real life, though, the majority will surprise us. The
> runoff will have different turnout than the original
> election, and some voters will change their votes, and both
> of these effects will favor the *fully sincere, absolute*
> Range winner over the majority preference, because, in this
> situation the majority preference must be weak. So only if
> the normalization or strategic voting have sufficiently
> distorted the Range results, I'd predict, would the
> apparent Range winner fail to win the runoff. You hold the
> runoff, indeed, because of this possibility, the possibility
> of distortion.
> 
> Are you starting to see this, Kevin? I'm not writing
> just for you, as I assume you know, and much of this,
> I'd think, you already understand. Or did you? Or do
> you?

Which part are you asking about, the runoff part? I'm well aware of
the fact that you prefer a runoff, and I don't disagree with the idea 
that the result of the runoff could be different.

Actually the fact that you are not writing just for me, makes it hard for
me to find the answers to my questions, or even determine whether you
are specifically trying to answer them, at any point in time.

Kevin Venzke