Thursday, April 10, 2008

Review - Gaming the Vote

Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It) (GtV) by William Poundstone is a maddening book, full of interesting stories about voting, but flawed as a book. (Before you ask, William is a cousin of comedian Paula Poundstone.)

One of the fascinating results in mathematical economics is the proof by Kenneth Arrow of what is called the impossibility theorem, which demonstrates that, given a set of desirable criteria, no voting scheme can be devised that is totally fair. Obviously, this applies to voting in which there are three or more candidates; normal pick-one voting works fine for two-candidate races. One of the most common demonstrations is to show that transitivity is violated: A may be preferred to B, B to C, and C to A, which strikes most of us as wrong.

GtV begins with a lengthy recap of the 1991 Louisiana governor race in which former governor Edwin Edwards manipulated the incumbent governor out of the runoff, where Edwards defeated former Klansman David Duke. The book contains other stories of cases where the "wrong" candidate was elected, even for president - the 1912 campaign, in which Teddy Roosevelt split off the Republican vote from Taft, giving the White House to Woodrow Wilson, is the best known.

Poundstone has written a lot more books than I have, so I'm going to assume he has his reasons for jumping around in his topic. For me, though, I found it tedious. After the long prologue about Louisiana (which is a fascinating story, with outsized personalities, and Poundstone didn't really capture it), GtV launches into the theory behind the problem. The story jumps from person to tiny bits of math and back to person, in what I can only feel is a sop to the popular reader. You come out with the flavor of the Arrow impossibility theorem without any deep understanding; the impression is simply that normal plurality voting (voting for your favorite) is flawed beyond redemption.

If you want a flavor for this book, let me quote from the table of contents. Here is a list of topics in order from one of the chapters: ""syphilis; slavery; mother murder; Lyndon Johnson; farm animals; television; Rush Limbaugh; Arthur Finkelstein; the $12 Man; Jesus," and on and on. This list, by the way, gets us from page 95 to page 97. It is an impressive feat to weave these disparate topics into three pages, but it takes away from the coherence of Poundstone's arguments.

And there is an underlying argument here. After taking us through the often-entertaining stories of the origins of Borda Count, Condorcet voting, instant-runoff voting, and so forth, Poundstone shows us why these are all inferior to range voting.

Range voting is the kind used on Amazon to rate books, where there is a fixed scale (0 to 5, but it can be as much as 0 to 100 in Poundstone's examples) and a voter can pick any number for any of the candidates. For example, if Hillary were to stay in the current presidential race (and there's no guarantee that we can get her out), a voter who didn't want to perpetuate the Bush legacy could (on a 0 to 10 system) give Obama 10 points, Hillary 9, and McCain 0 or 1. In theory, this system minimizes the chance that voters will vote strategically instead of due to their real preferences.

DtV presents some, but not conclusive, evidence that range voting is superior to all other voting schemes. That may be true, but it remains to be seen how we explain the results of a sample presidential vote (on a range voting advocacy site, http://rangevoting.org), in which the winner among all U.S. presidents is...Chester A. Arthur. The result comes from, as of this writing, 2428 ballots. Perhaps some of those people are fooling around, but you have to wonder about results in which the list of presidents over 80 (on a 0-100 scale) are W.H. Harrison, Polk, Taylor, Grant, Garfield, Arthur, B. Harrison, McKinley, and Eisenhower. (If you're curious, those ranked under 30 are Cleveland, Wilson, F. Roosevelt, Truman, and L. Johnson.)

Specific examples aside, there really isn't enough here to convince anyone that range voting minimizes the probability of Arrow's theorem creating undesirable results. The conclusion seems to be that it's worth a try, but that politics will get in the way. After all, political candidates and consultants have adjusted to the existing system, and it will be difficult to effect change. (In a curious omission, Poundstone tells us that Cleveland, Cincinnati, and New York all adopted single transferable voting in the early part of the 20th century, but doesn't explain how politicians were convinced that these systems were preferable.)

So I have to give a thumbs-sideways review here. I was already reasonably familiar with the formal literature on voting schemes, being a reformed math guy, and GtV is a pleasant, gentle introduction. As a book, however, it was repetitious (we understood the problems with Condorcet voting the first time), disorganized (there are references to things that weren't previously mentioned), and, at times, simplistic. So, read it if you're interested in voting schemes, but understand that you'll have more reading to do if you want to appreciate the fullness of this topic.

10 comments:

BROKEN LADDER said...

Specific examples aside, there really isn't enough here to convince anyone that range voting minimizes the probability of Arrow's theorem creating undesirable results.

Really? What about the fact that Arrow's theorem doesn't apply to Range Voting?
http://rangevoting.org/ArrowThm.html

As for the kinds of undesirable results that Range Voting is not immune from, their net effect is measured via Bayesian regret. Per this objective metric of voting method performance, Range Voting for exceeds the other "non-exotic" voting methods (there are some very complex voting methods that perform better, but would be infeasible to implement in real political elections).

(In a curious omission, Poundstone tells us that Cleveland, Cincinnati, and New York all adopted single transferable voting in the early part of the 20th century, but doesn't explain how politicians were convinced that these systems were preferable.)

He didn't really have the time in this book to segue into proportional representation. All though you can read more about it, starting here.

Thanks for reviewing a book on this critical topic.

BROKEN LADDER said...

:s/for/far
:s/All though/Although

Androcass said...

Broken:

I actually knew that Arrow doesn't apply to range voting, but the brain didn't get fully through the fingers in this post.

My point was, and I did understand the Bayesian regret portion (but I had some prior knowledge), that the text did not do enough to convince the reader that Warren Smith's work was sufficient. I actually believe in range voting, and would love to see some jurisdiction give it a try, mostly to ensure that it is practical across a voting population.

As for Mr. Poundstone's not having space to allude to the politics behind the adoption of STV, my feeling was that there was space for a lot of other things. That just seemed so glaring, when practicality is the greatest challenge to adoption. Thanks for the link, and thanks for the comment.

Greg said...

RangeVoting is a highly untested voting system, not currently used in any public election anywhere. So it's very hard to say how it might work in practice.

Though we can speculate how it might work in theory, as scholar Nicolaus Tideman did in his latest book on Social Choice theory. In it, he rated Range Voting amongst the most unsupportable of all voting methods, because it is so vulnerable to strategic voting.

In contrast to Tideman's work, Smith's work on voting has not been submitted to any academic conferences or journals whatsoever, so it hasn't received the kind of academic peer review needed to verify its worth.

I feel it would be highly irresponsible to subject the public to such an untested and dubious voting system as Range Voting.

Furthermore, the supposed problems with IRV are vanishingly rare in practice. Notice how the "real life" examples that critics raise to show off its problems, like the LA Governor's race, are not actual IRV elections. The exampels are virtually always plurality or two-round runoff elections, from which critics extrapolate in a dubious manner.

If we look to locations where IRV is in place, there is no detectable concern over its theoretical defects, including non-monotonicity and failure to elect the compromise candidate. These are non-issues.

Sure, IRV is not suitable for electing legislatures, where some form of proportional representation is ideal, but neither is any single-winner (i.e. winner-take-all) system. For legislatures, there is a pretty widespread consensus amongst academics and reformers that the Single Transferable Vote (STV) is ideal. Because IRV is just the STV applied to elect a single individual, it serves as a very good stepping stone to proportional representation via multi-winner STV.

BROKEN LADDER said...

Greg is continuing the tradition of gross deception by IRV advocates, using the standard talking points. (It's like the creationists who claim Darwin had a conversion at his death bed.)

RangeVoting is a highly untested voting system, not currently used in any public election anywhere. So it's very hard to say how it might work in practice.

False. Range Voting was used for hundreds of years in ancient Sparta, and Venice. It's simplest form, Approval Voting, has been used for years by several technical professional societies, whose membership numbers in the tens of thousands, far exceeding the populations of many cities.

More telling though are the extensive Bayesian regret calculations by Princeton math Ph.D. Warren D. Smith, which quantify the representativeness of various voting methods in objective "economic" terms, showing Range Voting to handily surpass the alternatives -- especially with a large number of strategic voters who attempt to game the system. These figures are in many ways superior to any kind of real world experiments, because they allow us to read the voters' minds and have 100% ballot data access, which is a far cry from most real world situations.

Finally Greg's criticism here is very hypocritical, since he supports IRV, a method which was far more "untested" when it was first adopted, decades ago, than Range Voting is now. Range Voting actually benefits from extensive computer modeling of elections, as well as several experiments.

Though we can speculate how it might work in theory, as scholar Nicolaus Tideman did in his latest book on Social Choice theory. In it, he rated Range Voting amongst the most unsupportable of all voting methods, because it is so vulnerable to strategic voting.

Tideman's strategy resistance measure was seriously flawed, because it stated an arbitrary set of strategy-related criteria, and incorrectly treated all of them as equally important. The idea was that for each criterion, a voting method could either pass or fail it. Well, imagine student X gets two "failing" D's and 4 A's, while student Y gets one "failing" F and 5 "passing" C's. Is student Y really a "better" student than X because Y passed more classes? Most people would prefer to have X on their Quiz Bowl team, or as a tutor. GPA takes a student's total strength in all classes into account, rather than just looking at a student's pass/fail ratio.

Likewise, Warren Smith's Bayesian regret simulations looked at how well various voting methods perform, depending on the preponderance of strategic voters (and several other factors, like voter ignorance, number of candidates, etc.). Using Tideman's own data, Smith's simulations yield substantially different results. -- Range Voting dominates, whereas IRV is almost as bad as our present plurality system (especially if there are a lot of strategic voters).

Also I'm not sure why Greg would draw attention to Tideman, as he also calls IRV "unsupportable" (assuming it is feasible to calculate a matrix of majorities, which is actually simpler than tallying an IRV election).

Here's another huge flaw with Tideman's perspective, that is a bit more abstract. Tideman is looking at strategy resistance in terms of the difference strategy makes to the voting method, rather than looking at the actual performance that is achieved. Consider a somewhat awkward, though poignant analogy. Say that we measure an engine's "resistance to flooring it" in terms of the effect that extra gas has on its likelihood of breaking down in the course of an hour. Here's a little chart.

______Pedal 50% to the metal :: Pedal 100% to the metal
Engine X: --- 1% likely :: 10% likely
Engine Y: --- 13% likely :: 14% likely

By increasing the gas from 50% to 100% "to the metal", engine X has become 9% more likely to break down in the course of an hour, whereas engine Y has become only 1% more likely to break down. If we look at this in Tideman's framework, that means engine Y is "more resistant" to the degrading effects of fast driving. But that's horrendously misleading, since engine Y is still more likely to break down.

Tideman's flaw here seems both obvious and severe. Yet this is the kind of stuff people like Greg Dennis will use to do a hit job on Range Voting.

In contrast to Tideman's work, Smith's work on voting has not been submitted to any academic conferences or journals whatsoever, so it hasn't received the kind of academic peer review needed to verify its worth.

Science is not restricted to some professional orthodoxy. The peer review process simply a filter for those who don't wish to waste their time with every scientific discovery or insight that is announced, but would rather focus on things that have at least made it through the rounds of professional and academic criticism. I have a background in computer engineering, not science, but I feel more than qualified to critique Tideman's analysis, as there are some very basic flaws to it, that even a layman can understand. You're also free to review it yourself and point out flaws. If you don't feel like you have the scientific/mathematical expertise to do that, and instead you must rely on review by a body of experts on the subject, then why do you feel qualified to criticize Range Voting and promote IRV in the first place?

I feel it would be highly irresponsible to subject the public to such an untested and dubious voting system as Range Voting.

This is another highly ironic statement coming from you:

1. Range Voting has been far more tested than IRV had been when it was first implemented -- and by complex computer simulations that hadn't been done until 2000.

2. You yourself support IRV, so you must be glad that it was initially adopted, in spite of having been much less tested at the time than Range Voting has been at present.

3. In case you haven't noticed, we are already using plurality voting in most of the world, and there is no conceivable way that Range Voting could be worse than plurality (though there are some ways that IRV could be, e.g. increased ballot spoilage, and conduciveness to central tabulation and fraud).

Furthermore, the supposed problems with IRV are vanishingly rare in practice. Notice how the "real life" examples that critics raise to show off its problems, like the LA Governor's race, are not actual IRV elections. The exampels are virtually always plurality or two-round runoff elections, from which critics extrapolate in a dubious manner.

Because full IRV ballot data is rare, voting experts like Warren Smith have had to extrapolate the probable behavior of IRV based on what occurred in real elections like the runoff elections held in many countries. Smith has cited ample evidence that his extrapolations were reasonable, and calling them "dubious" is not a substitute for actual evidence that they were inaccurate.

I invite readers to judge for yourselves, looking at some examples.

If we look to locations where IRV is in place, there is no detectable concern over its theoretical defects, including non-monotonicity and failure to elect the compromise candidate. These are non-issues.

Baloney.
Australia 2007
Ireland 1990

There are plenty of examples that prove this is not, as you deceptively claim, a "non-issue". Moreover, in a statistical/mathematical sense, it is extremely likely that these types of pathologies happen with great regularity, but that this is hidden because of incomplete access to full ballot data in some digestible format.

And again, in simulated elections where this is not a problem (because we actually have both access to the ballots, and access to the voters' real preferences,and can detect strategic voting, which can only be inferred if we're looking at real ballot data), IRV's performance is terrible.

Sure, IRV is not suitable for electing legislatures, where some form of proportional representation is ideal, but neither is any single-winner (i.e. winner-take-all) system.

But Range Voting at least has the potential to rapidly eliminate the two-party duopoly in single-winner elections. IRV has been used for decades in countries such as Australia and Ireland, and has proved that it cannot do that. It maintains duopoly.

For legislatures, there is a pretty widespread consensus amongst academics and reformers that the Single Transferable Vote (STV) is ideal.

No, not "ideal" necessarily, but just better than existing single-winner methods. But this ignores that

1. Good single-winner methods (such as Range Voting) may be better than proportional representation systems. There's no irrefutable evidence that P.R. is better.

2. There is a proportional version of Range Voting called Reweighted Range Voting that is better and simpler than proportional STV.

Because IRV is just the STV applied to elect a single individual, it serves as a very good stepping stone to proportional representation via multi-winner STV.

There are numerous flaws with this statement:

1. IRV has only been a stepping stone to STV in a few rare instances, in which impediments to the advent of proportional representation were not as huge as they are in the U.S. So if we want proportional representation in our Congress, for instance, we have to start by breaking up the two-party duopoly which will otherwise keep us entrenched in laws antithetical to the adoption of P.R.

2. IRV does not escape duopoly, though Range Voting almost certainly does (e.g. we already know of some single-winner methods, like genuine runoffs, which do tend to support 3 or more viable parties, and RV has properties which strongly suggest it would do the same, and probably to an even greater extent).

3. Even if you could transition to STV, you'd still be stuck with the very poor IRV system in your single-winner elections, like mayor, governor, senator, etc.

Greg's entire set of talking points are based on misinformation, logical fallacies, and deceiving rhetoric.

Clay Shentrup
San Francisco, CA
206.801.0484
clay@electopia.org

Androcass said...

A brief comment: I personally appreciate the discussion here, it is a real education (and, without beating the horse, a little more of what I might have wanted from Poundstone's book, though, in retrospect, I may be guilty of having expected too much from a popular treatment - the book is pretty good).

I don't have any more to say, yet, about the relative strengths of the voting systems. I'd still love to see more boots-on-the-ground testing. Acknowledging that we do have some experience already, we also have thousands of elections in this country every year, and, theory aside, we could get some idea of how various systems work for real by doing some reasonably-controlled tests. I don't think anyone would contend that moving away from plurality voting wouldn't be an improvement.

BROKEN LADDER said...

Androcass,

IRV and Range/Approval Voting have had decades and centuries (respectively) of "boots-on-the-ground testing". And the computer simulations are arguably a far better type of test. There is massive overwhelming evidence already in favor of Range Voting and against IRV. It's not like there's a need for more tests because we don't have enough experience. The verdict is in, at least in the Range vs. IRV debate. Things are more complicated if you compare Range to a method like Condorcet voting, but still the evidence weighs in favor of Range by a good margin.

As for the IRV movement, they are a cult, peddling inaccurate data, logical fallacies, and outright lies, just as we've seen here from Greg Dennis, their latest antagonist.

Alf Mikula said...

Here's a great site you can use to learn more about Range Voting by using it in your own polls:

Vote!

BROKEN LADDER said...

alf,

Your range voting system is absolutely superb. You even included the abstention/quorum system, and used intuitive slider knobs. Great work.

Alf Mikula said...

Hey, thanks BL! It needs a few features...an option to close out results until the poll is closed, for example, but I think it's a good start.

Clicky Web Analytics