Aspen Update

Never mind. The vote will be between keeping IRV or going back to the 2007 system. One simple, binary choice. I guess deciding between three things is just too hard.

Irony: Aspen To Use Approval Voting... Once

In 2009, Aspen, Colorado voters chose to begin using instant runoff voting in some elections. They were, apparently, less than satisfied with it, and are now working out their options for replacing it. Aspen Daily News describes how the choice will be made:

Aspen voters will be asked if they support the winner-take-all system that was used through 1999, and one that requires a majority for council members and the mayor, which was used through 2007.

Both options will have their own “yes” or “no” question on the ballot. Whatever receives the most support will become the new voting method...

Does this sound familiar to you at all? It should, because this is approval voting! Each option can be approved or disapproved of independently, and the most-approved option is the winner.

There is one hitch though:

If neither method gets a majority, IRV will remain.

For this to be a proper approval voting election, the un-stated third option in favor of the status-quo ought to also be on the ballot. After all, it is possible that both replacement options will get more than 50% support but that an even greater percentage would approve of keeping IRV. (I didn't say likely, I said possible.) Or, conversely, that both alternatives could get less than 50% but that even fewer voters would want to keep IRV. Leaving one of the options unstated leaves open these possibilities. Imagine if this near-approval format were used when two challengers faced an incumbent office-holder; you wouldn't want the incumbent off-ballot and to make these sorts of assumptions about how the voters truly judge them!

Thankfully, Ward Hauenstein, a member of the city's election commission, has suggested precisely this; although his reasoning was due to the possibility of voter confusion. Either way, it's not clear if the people in charge of the ballot will take him up on the idea.

So, Aspen will be using approval voting (or at least something close to it) this one time; but they will be using it to decide which less-effective-than-approval voting method to use for future votes. Come on Aspen, you're so close!

Instant Runoffs Elects (a) Third-Party Candidate

It's a red-letter day for supporters of instant runoff voting; after a three-cycle drought, the instant runoff system used for the Australian House of Representatives has elected a member of a third party. As there are 150 seats elected in the house each cycle, this means that one sixth of one percent of all elections were won by a third party member over the last four cycles.

Previous elections had seen a number of independent candidates win seats, but all of these had won their seats primarily because of previous membership in one of the two major parties, before falling out to run on their own (think Joe Lieberman in the US Senate, for comparison.)

Although The Coalition is officially two separate parties--the Liberal party and the National party--the two have an agreement whereby they do not challenge each others incumbents, have been united (as government or opposition) in the legislature for 60 years, and have formally combined as a single party in some Australian states. Virtually all Australian news sources refer to "the two party vote" as being between Labor and the Lib/Nat coalition.

Meanwhile, the Australian Senate uses single transferable vote, which is a system of proportional representation, on which IRV was based (but in such a way that it loses all proportionality.) There, the greens hold 5 of the 76 seats, while the Country Liberal and Family First parties hold 1 each (and 1 independent); for about 9% third-party representation, versus the 0.16% now available in the House.

So congratulations to Adam Bandt and to all the people out there tell us that IRV would be a huge boon to third parties; today you are a little less wrong.

Book Review: Numbers Rule

After being directed to it by The New Yorker Book Review (and getting involved in the debate about the review and the response to it) I borrowed a copy of Numbers Rule, by George G. Szpiro, from my local library.

Numbers shares a similar concept to Gaming the Vote, of presenting the somewhat dry topic of voting theory via the colorful true stories of the great thinkers who have wrestled with the subject over the centuries. And I do mean centuries; we start with Plato, who is harshly criticized for his didactic and entirely unscientific approach to the issue. Quickly, the realization that it's hard to decide among three or more choices is brought out, as Pliny the Younger presides over a choice between the innocence, banishment, or execution of an Athenian slave.

Next, we are introduced to Ramon Llull and Nikolaus Cuanus, who, Szpiro tells us, developed the Borda count and the Condorcet method, over 350 years before the stars of the following chapters, Borda and Condorcet, were born. While the rediscovery and repetition for these two pairs of chapters is interesting and historically relevant, unfortunately it doesn't add anything to the readers knowledge about elections. To further the irrelevance, each chapter ends with entirely irrelevant (but still interesting) additional historical information on the main characters.

In the following chapter on Laplace—a contemporary of both Borda and Condorcet—the clever idea to "guarantee" majority-choices is introduced: If a vote doesn't result in a majority decision, vote again. Laplace's original thought was that voters would, eventually, settle on a compromise. Instead, his legacy is France's consistent use of top-two runoff, and the mathematically-unsound claims of instant runoff proponents. I think Laplace, as a mathematician of the highest caliber, would be displeased.

And then we go through much of the same material one last time—only with accusations of pedophillia—thanks to Charles Dodgson; better known as Lewis Carroll. Again, interesting, but the repetition is not especially helpful for learning the issue at hand.

It's here that the book takes a two-chapter and mostly-unconnected side trek to discuss the difficulties of apportioning seats in a legislature to its constituent districts. Even the impending re-apportionment that will soon occur on the heels of the 2010 census couldn't bring me to really care about the issue. A one-seat difference, out of 435, every 30 or 40 years, just seems insignificant to me. (Or maybe it's just that my new home state will certainly continue to have just one representative.)

When we return to elections proper, we are following Kenneth Arrow, to learn about the impossibility of perfection. Numbers gives a more in-depth explanation of why Arrow only considered ranked-order ballots, but armed with that understanding, I am now more confident both that Arrow's work can't be applied, for good or bad, to approval voting and score voting, and that the election simulations I often refer to can still be valid. A strange parallel is drawn between Arrow's work on voting, Hisenberg's work on physics, and Godel's work on logic; the point of which seems to be "Give up; nothing in the world works!" Again; interesting, but even more so than the chapters on districting, it seems out of place.

The book closes with one final chapter on districting—with an extra side of impossibility, for good measure—followed by a short and un-directed prance through the modern issues. This is the first, and only time, that any sort of proportional representation is mentioned, or that approval voting is brought up. (And the misleading description of approval voting that led off the New Yorker review? Not present at all.) Instant runoff voting is not mentioned by name, but single transferable vote is, and that it can be used for single-winner elections is discussed. But Szpiro avoids discussing them in any depth, and keeps far away from taking any sides. Having now spent a year and a half myself participating in the argument, perhaps this is a wise move on his part; but if the intent of the book is to educate, it's a missed opportunity to avoid what's happening in the world today.

If you love historical trivia (and I admit, I do) Numbers Rule is great. But if you're looking to get a handle on the issue of elections, Gaming the Vote is not only better focussed, but is more engaging to read. While Gaming sucked me in and inspired me to get involved and make this blog what it is today, I had to pull myself back into Numbers each time; happy that I would get a few more interesting tidbits, but knowing that I wasn't going to learn anything about voting that I didn't already know.

Topsy-Turvy Instant Runoff

Instant runoff voting (IRV) is known to display a number of perverse problems when there are more than two strong candidates. As a thought experiment, and mental exercise, Professor Warren Smith--mathematician and founder of the Center for Range Voting--try to determine the simplest IRV election that can showcase the greatest number of these issues.

9 voters: A > B > C
12 voters: B > C > A
8 voters: C > A > B

The example has only three candidates, and needs just 29 voters, but still illustrates:

• Reversal Paradox: if all the ballots have their order reversed, the "winner" stays the same, so the "best" choice is also the worst choice. (It's A in both cases.)
• Less-is-More: one of two forms of non-monotonicity, where by lowering the rankings for a losing candidate on certain ballots, they become the winning candidate. (Change two B-first voters to C-first, and B wins instead of A.)
• More-is-Less: the other form of non-monotonicity, where raising the winning candidate's rank on certain ballots makes them lose. (Raise A from bottom to top on 5 of the B-first ballots, and C wins instead of A.)
• Participation Paradox: where, if certain voters had just stayed home instead of voting, the result of the election would have been better for them. (Remove 5 B-first voters (who rank A last!) and C wins instead of A.)
• Anti-Participation Paradox: where, if more of a certain group of voters had shown up and voted, the results of the election would have been worse for them. (Add 2 C-first voters (who rank B last!) and B wins instead of A.)
• Precinct Paradox: the ballots can be divided into precincts, and the winner in each precinct is the same, but is not the same as the winner of the overall election. (Break into 3 precincts such that A-first/B-first/C-first in each is 3/4/4, 3/4/4, 3/4/0; B wins in each precinct, but A wins the aggregate.)
• Tactical Opportunity: some voters could prevent their least-favorite choice from winning by ranking a different candidate above their honest favorite. (If at least 2 B-first voters instead rank C above B, then A doesn't win; either B or C wins.)

I want to emphasize the last point, tactical opportunity; because this is the number-one problem that I see IRV-proponents falsely claiming that IRV doesn't have. It is simply not true that IRV removes the incentive to vote for the "lesser of two evils". There are less-contrived examples that can show this too, but it's worth pointing out every time it comes up.

How would approval voting handle this election? That, of course, depends on exactly how many voters in each faction approve of their second choice, but the Nash equilibrium is a win for B. I believe this is also true for IRV, but it involves the majority of voters ranking their second-favorite above their true favorite. Meanwhile, under approval it never helps you to lower your vote for your true favorite. I'll explore equilibria more in a future post.

Further Thoughts: Minneapolis RCV Report

I was contacted via email by a concerned reader about my last post, discussing Minneapolis' use of ranked choice voting (RCV, AKA instant runoff voting (IRV)). This reader had attempted to contact the report's lead author, Dr. David Schultz, with the hope of clarifying a few points, such as:

• The paper notes a factor of four increase in ballot spoilage rates, but the prose refuses to acknowledge the possibility that any of this increase was due to the use of RCV. What else would Schultz attribute the increase to?
• How is such a large number of votes being tossed out not disenfranchisement? How would Schultz identify disenfranchisement?
• How does Schultz reconcile the 7.5% ballot-error rate with a claim that there did not seem to be any voter confusion?

Unfortunately, Dr. Schultz chose not to answer any of these salient points at all, and was rather short--I would say insultingly dismissive, if the message forwarded to me is any indication--with the few questions he did answer. (One question, about why Schultz's report made constant comparisons to first-past-the-post while Minneapolis had previously used top-two-runoff, was answered with "SO? Your point?")

So perhaps I was too generous to the good doctor. It seems he desperately wants to "prove" that RCV/IRV works, and despite reporting the numbers truthfully (which, he should be praised for), it seems he will continue to support pro-IRV rhetoric, even when his own numbers strongly suggest against it; and that he isn't interested in discussing it.