CU Boulder upgrades to Approval Voting; could go even further

The recent student government elections at CU Boulder used an improved voting system called Approval Voting. Approval Voting means you can vote for as many candidates as you want, rather than being limited to the number of winners. This is a big improvement over the traditional system called Plurality Voting. Approval Voting ensures you can never be punished by voting for your favorite candidate, and solves the spoiler effect.

Approval Voting is a great way to elect in a single-winner election, e.g. for mayor, governor, senator, etc. But for multi-winner races (e.g. the CUSG Representative-at-large election, with five winners) Plurality Voting and Approval Voting can both produce lop-sided victories.

Consider, for example, the election of the Arts and Science Student Government board members. The Unite party took all five seats, despite earning only 54% of the votes. The Inspire party got almost 45% of the votes, but won zero seats. An arguably more fair outcome would have been three seats for Unite, and two seats for Inspire.

The tables were turned in the University of Colorado Engineering Council elections. Eight of the nine Representative-at-large seats went to Inspire, and only one went to Unite. But Inspire won 67% of the vote. Unite won 33% of the vote, but earned only 11% of the seats. A more fair result would have been three seats for Unite, and six seats for Inspire.

Inspire also swept the UCEC senator elections. There were four candidates (two Unite, two Inspire) running for two seats. Unite won 46% of the votes, but zero seats. Again, this was not a representative outcome. Looking at the results, it seems to me that the winners should have been Inspire's Benjamin Zatz, along with Unite's Rachel Sobke.

Arden Rose, UNITE 348 21%
Rachel Sobke, UNITE 407 25%
Jon Fearer, INSPIRE 430 26% Elected
Benjamin Zatz, INSPIRE 459 28% Elected

So what's the solution? Proportional Approval Voting!

It turns out that a Danish statistician figured out the solution to this problem back in 1890! Imagine if we elect winners one round at a time. Then after each new winner is selected, we "divide" each ballot by w, where w is "the number of winners that ballot has approved, plus one".

As an example, imagine you approved Benjamin Zatz and Jon Fearer:

• In the first round, your ballot is just divided by 1, which has no effect. Your votes count at full strength.
• Let's say Benjamin Zatz is the first winner, which he would be based on the actual election results.
• In the second round, your ballot is divided by 2 (because you voted for Zatz, who won in the previous round). Now your vote for Fearer counts as only 1/2 a vote. This means that all the people who didn't vote for Zatz (i.e. Unite voters) now have the power to elect one of their candidates.
• This process continues as seats are awarded, providing fair representation to any faction which has enough support to deserve a seat.

Proportional Approval Voting would have produced the kind of fair outcomes we just considered above. The total seats awarded apparently wouldn't have been much different. But the allocation would have allowed Inspire to have a voice in ASSG, and Unite to have a voice in UCEC.

But isn't this complicated?

Not really. Consider that Australia's senate has been elected via the much more complicated Single Transferable Vote system since 1938, far before modern computers or even electric calculators. It was all tallied by hand from paper ballots. Thus Australia has a truly representative democracy. Doesn't CUSG deserve that too?

In summation, Approval Voting is a big step forward for CUSG elections. But it can be even better in the multi-winner races. Proportional Approval Voting is worth considering.

Maine's Rep. Diane Russell's mistaken views on Instant Runoff Voting

As a founder of The Center for Election Science, I spend a lot of time doing education on electoral issues. Unfortunately, a significant amount of that time is spent fact-checking well intentioned but misinformed proponents of Instant Runoff Voting. The subject of this post will be several Twitter posts by Maine representative Diane Russell.

Some background. Today I came across a Twitter post by FairVote, urging people to support Instant Runoff Voting (IRV) for Maine gubernatorial elections, by signing this online petition. The the idea is not without merit. Maine's current governor, Paul LePage, is one of the least popular governors in the USA. A news article grimly states:

LePage’s job approval rating is significantly underwater at -16, with 39% approving and 55% disapproving. 18% of Republicans and 54% of independents disapprove of the job that LePage is doing as governor.

This isn't surprising given that Maine voters never wanted LePage in the first place. In the 2010 gubernatorial race, LePage walked away with a mere 38.33% of the vote. His win was a result of vote splitting (aka the "spoiler" effect) between his rivals. Eliot Cutler—a wealthy independent who served as Associate Director for Natural Resources, Energy and Science in the Office of Management and Budget in the Carter administration, and was the principal White House official for energy—narrowly trailed with 36.49%. Democrat Libby Mitchell came away with 19.12%. It's safe to say that if Mitchell had dropped out, her supporters would have heavily favored Cutler. And probably vice versa.

IRV (which also goes by the misnomer "Ranked Choice Voting", despite the fact that there are numerous other ranked voting methods besides IRV) would have avoided this mess. Democrat Libby Mitchell would have been eliminated, and her 19.12% would have almost surely sent Cutler to victory—much like a traditional runoff, but without the second round election.

Now it appears that Maine may be in for a repeat in the 2014 gubernatorial race. From the previously cited article:

PPP’s latest poll finds LePage ahead by 4 to 7 points in every potential three-way contest while losing every head-to-head contest by 8 to 21 points. If LePage and independent Eliot Cutler were the only two candidates, Cutler would lead LePage 49% to 41%. But in every three-way scenario, Cutler’s strength as an independent candidate gives LePage the lead over their possible Democratic opponents.

Given these facts, Diane's Russell's support for IRV seems outwardly sensible. But a closer look at the details reveals some concerning misconceptions. The petition's description says:

Maine politicians should be elected with a majority vote. Please join me in supporting Rep. Diane Russell’s bill to elect the Governor and Legislature with Ranked Choice Voting (AKA Instant Runoff Voting). Her bill encourages voter choice while avoiding “spoiler” candidates.

This statement claims that IRV prevents the spoiler effect, and that it ensures politicians are elected with a majority. As anyone who's spend an afternoon studying election methods on Wikipedia can tell you, both of these claims are completely false. Here's a simple four-candidate electoral scenario which demonstrates this.

% of voters - their ranking
 35% W > Y > Z > X
 17% X > Y > Z > W
 32% Y > Z > X > W
 16% Z > X > Y > W

Instant Runoff Voting selects candidate X as the winner, beating W in the final round, 65% to 35%. But note that:

1. A huge 67% majority of voters prefer Y to X (the 1st and 3rd rows). And Y received nearly twice as many first-place votes as X, 32% vs. 17%.
2. An even larger 83% super-majority of voters prefer Z to X (and Z gets just slightly fewer first-place votes than X).
3. Y is preferred to Z by an 84% super-majority.
4. Y is preferred to W by a 65% super-majority.

Y is the indisputable "majority winner", but IRV elects X. So the very first sentence of the petition description was misleading, to say the least.

Further, W is a spoiler. If W would drop out of the race, then Y would win instead, even with no change in voter preferences. So the final sentence in the petition description was also false.

This situation is similar to what occurred in the 2009 IRV mayoral race in Burlington, VT. The Progressive won, but a large majority of the voters preferred the Democrat to the Progressive, and to all other challengers. And the Republican served as a spoiler—if he had dropped out, with all voters preferences unchanged, then the Democrat would have won. (Note that Burlington voters repealed IRV by a significant majority after that, their second, IRV election.)

In the ensuing discussion on Twitter, Russell responded to a comment from Maine blogger Gerald Weinard:

Ranked Voting worked well in Portland and has a lot of support. Majority leaders super important.

Here we see Russell once again making the false implication that IRV ensures majority winners. It's concerning enough for an elected official not to understand a substantial reform that she's vocally pursuing. But more so because Russell has worked with the IRV advocacy organization FairVote, which has been involved in electoral reform since 1993, and presumably should understand IRV by now.

This rhetoric continued over the course of several more posts. In response to a criticism about IRV's being less than intuitive, Russell replied:

I've been ranking ice cream choices since I was a kid. Also pretty intuitive.

This comment demonstrates a lack of appreciation for the deeper issue of whether voters understand the tabulation process. A usability study in the San Francisco area (SF has used IRV since 2004) produced a couple of relevant conclusions:

• Some participants remarked that because they didn’t understand how the votes were counted that they didn’t trust the system.
• Many participants theorized that ranked choice operates on a weighted or point system. A few participants suggested that it was for breaking ties, but they could not describe how the second place votes were tallied. It was not uncommon for participants to talk themselves into corners as they tried to describe how the counting was done. Most ended with “I don’t know.”
• Very few people accurately described how ranked choice votes are counted, even in zip codes with high education and socio-economic levels; people in poorer neighborhoods had even more difficulty describing how their ranked choices were counted.
• It’s unclear that reading the instructions for ranked choice voting would help people vote as they intend, because the instructions are only about how to mark the ballot, not about how the votes are counted or what the consequences of ranking are.

I work as a software engineer in San Francisco. And my informal polling of numerous co-workers has been consistent with these observations. Here's a brief instant message conversation I had with one particularly smart software engineer who claimed to be a voter. I don't think anyone can read that and seriously claim that IRV is intuitive.

I replied to Russell, linking her to the above demonstration that IRV does not guarantee a majority winner, and is susceptible to the spoiler problem:

I linked you to mathematical proof that IRV doesn't guarantee majority winners. Response?

Her reply was simply:

Answer: http://www.pressherald.com/opinion/brennan-ranked-choice-voting-both-winners_2011-11-12.html

That's a link to an article in the Portland Press Herald, which touts the virtues of IRV and repeats the same inaccurate talking points:

Brennan, the candidate who proved to have the broadest appeal, ended up the winner. He will go into office next month with a majority of voters at his back.

I pointed out to Russell that her article was actually not an answer to my criticism:

That article doesn't refute the mathematical fact that IRV *does not* guarantee "majority winners".

Her well reasoned rebuttal?

Again, you have no vested interest in Maine. Why do you care? Oh wait... this is all you do. FOR YEARS.

It's hard to know what to say to that kind of response. It's an extreme example of both ad hominem and red herring fallacies, diverting attention from her mistaken claims by personally attacking me. Nevertheless, I feel compelled to address this.

The Center for Election Science is a non-partisan 501(c)3 non-profit, devoted to the objective scientific study of electoral systems, and the advocacy of systems that we believe will improve human welfare. We are something like the FactCheck.org of electoral reform. To that end, we strive to make the public better informed about election methods. That includes the occasional response to people who make the sort of false and misleading claims discussed herein.

Rather than attacking myself or my colleagues at the CES, I would ask Representative Russell to consider reading up on the subject of voting methods, and trying to be more careful with her statements. Election science will be critical to solving issues like the Maine gubernatorial elections, so it's important that we get the facts right.

Clay Shentrup

Co-founder, The Center for Election Science

The economic consequences of an economically irrational decision-making system

Amidst the hype surrounding the "fiscal cliff", some calm voices have emerged to challenge the fear mongering. One of them is Stephanie Kelton, an assistant professor of macroeconomics, finance, and money and banking at UMKC. Kelton has pointed out that the cliff is in large part a manufactured crisis. She suggests we start to address it by (among other things) repealing the Budget Control Act of 2011, whose key provisions established the cliff in the first place. She further suggests that the government should spend, and generally avoid tax increases, in order to increase the GDP (the oft-ignored denominator in debt-to-GDP ratio)—basically the opposite of what a lot of the mainstream pundits are advising.

I now want to take a step back and look at this issue from a very different perspective. The gravest danger in any calamity like this is not that we fail to fix it, but that we fail to detect underlying causes (i.e. calamity generators). Join me for a bit of abstract thinking...

Let's assume that Kelton is correct, and society is generally convinced that we need to implement the policies she's advocating. How do we do that? Well, primarily by electing people to public office who we believe will implement those policies. But imagine we're faced with an election for some highly influential position, and the preferences look like this:

33% Keltonite 1 > Keltonite 2 > Boehnerite
32% Keltonite 2 > Keltonite 1 > Boehnerite
35% Boehnerite > others

In this election, a massive 65% majority of the voters wants Keltonite policies. But if we use the ordinary vote-for-one "Plurality Voting" system, the Boeherite candidate wins with 35% of the votes. The lives of hundreds of millions of people are then significantly worse because of an obvious defect of the voting system.

But this is preventable! There are numerous other ways to vote. And voting systems can be objectively measured for "economic efficiency" using a metric called "Bayesian regret", which effectively measures average voter satisfaction. Here are some sample Bayesian regret figures from William Poundstone's book Gaming the Vote (2008).

Observe that a change from Plurality Voting to Range Voting (aka Score Voting) or Approval Voting virtually doubles the improvement gotten by the invention of democracy in the first place (the performance of Plurality Voting minus the performance of random non-democratic selection).

And these systems are very simple. Approval Voting just uses an ordinary ballot, but lets voters vote for as many candidates as they wish. The candidate with the most votes still wins. Score Voting is like Yelp reviews—you rate the candidates and the one with the most points wins. Not as simple, but more expressive.

So the question is, why aren't these economists who want to save the world talking about voting reform? If they're interested, I recommend they check out The Center for Election Science.

Candidate strategies with Instant Runoff Voting

In a recent email to her supporters, San Francisco District 5 supervisor candidate Hope Johnson outlines a strategy for the upcoming Instant Runoff Voting election.

Johnson and Resignato are launching The People's Ticket to give voters a better choice than the big-money downtown and progressive machine candidates who are constantly at odds with each other.  They are asking D5 constituents to vote for them in either the first and second or first and third positions, in any order, on November 6’s ranked choice ballot.

A friend asks, "Does this make sense, from a strategic voting perspective?" The answer is, it's complicated. Say you have these hypothetical preferences:

35% X > Johnson > Resignato
32% Johnson > X > Resignato
33% Resignato > X > Johnson

Johnson has only 32% of the first-place rankings, so she's the first eliminated, which causes 32% of the votes to be transferred to X in the next round. X then trounces Resignato 67% to 33%.

But say Johnson and Resignato successfully convince their supporters to adopt the strategy. Then it would look like this:

35% X > Johnson > Resignato
32% Johnson > Resignato > X
33% Resignato > Johnson > X

Johnson is still eliminated first (indeed, this strategy cannot possibly affect the election prior to the elimination of the first of the two colluders). But now Resignato trounces X 65% to 35%. So the strategy worked.

But things aren't so simple! The strategy helped one of the candidates, but it also caused 32% of voters to get their 3rd choice instead of their 2nd. So from their point of view, it was the opposite of strategic. While the Johnson supporters certainly want the Resignato supporters to help Johnson, they don't want to help Resignato, particularly within the privacy of the voting booth. And vice versa. This is the classic prisoners' dilemma.

History has disproved the notion that voters care more about loyalty to their favorite candidates than about getting what's best for themselves. Consider that exit polls in the 2000 U.S. presidential election showed that 90% of Nader-favoring voters claimed to have voted for someone other than Nader. Obviously a Nader supporter who preferred Gore to Bush was maximizing his expected value by voting for Gore instead of Nader. Likewise, we expect that Johnson and Resignato would have a hard time convincing people to vote against their own best interests.

There's also some interesting game theory related to which partner you should pick, if engaging in this strategy. Notice that if X were to team up with Johnson in the last example, that would lift X one ranking up (above Resignato) on 32% of the ballots. The same deal with Resignato would create a one-rank lift on 33% of ballots, but above Johnson. Which strategy makes sense? In this case, it doesn't matter, because X loses head-to-head against any rival. But in general, the strategy is to team up with someone whom you think will be ranked higher than your greatest rival, by a lot of voters. But you also want to pick someone whom you believe will be eliminated before you, otherwise you don't benefit from the strategy.

I'll leave the more complicated analysis to my math Ph.D. associates at The Center for Election Science.

Rob Richie misleads on Approval Voting at Dartmouth

In a recent spate of Twitter posts, FairVote executive director Rob Richie has criticized Approval Voting, citing specific elections at Dartmouth University.

On Dartmouth, see low winning %'s in its 2 uses.. Winner [of the 2012 Student Assembly election] had <33% & may have won due to tactical voting.

Richie commits a mathematical fallacy here which is a little hard to see. To expose it, consider the following hypothetical voter preferences, unrelated to the Dartmouth election. The letters represent candidates, ordered by preference. The bolded blue letters represent the candidates who are above the approval threshold for voters of that faction.

% of voters	their ranking
31%	W > Y > Z > X
4%	W > Y > Z > X
17%	X > Y > Z > W
32%	Y > Z > X > W
16%	Z > X > Y > W

Just to be sure we're clear here, the first row tells us that 34% of the voters favor W, followed by Y in second, Z in third, and X in fourth. They would approve W in an Approval Voting election. The next row represents the 4% of voters with those same ordered preferences, but who would also approve Y.

With Rob Richie's favored system of Instant Runoff Voting, we would eliminate Z, then Y, at which point X would defeat W, 65% to 35%.

With Approval Voting, Y wins with 36% approval. The full results are:

Y 36%, W 35%, X 33%, Z 16%

Richie likes IRV because he believes it guarantees a decisive "majority winner". He would predictably argue that IRV elected X with a "65 majority victory". But this is merely an illusion. Notice that Y is favored to X by a huge 67% majority of the voters (31% + 4% + 32%). And Y is the first choice of 32% of the voters, compared to only 17% for X. The flaw in Richie's argument is that IRV's "65% majority" is based on head-to-head rankings, and after eliminating a sufficient number of candidates.

Approval Voting has produced a definitively superior outcome in this example. Yet we can be sure that Richie would criticize it for electing a candidate with "only 36%". Despite copious evidence that Approval Voting produces more representative election outcomes than IRV, Rob Richie's IRV dogma continues, unabated.

When I explained to Richie that he was making some serious logical/mathematical errors, he simply replied:

Hmm. I'd say your math breaks down because of not understanding psychology. Thus, failing to grasp Dartmouth

No further evidence was supplied as to how psychology could prove Richie's point or even refute mine. For those who know Richie like I do, this is not surprising.

UPDATE: Richie responds on Twitter:

Richie: Clay ignores what voters do & strategies develop. IRV shows NO evidence of tactical insincerity. Approval does
Clay: I *just cited* candidates urging their supports to vote tactically. Wake up.
Richie: Anything other than asking each other's backers to rank them 1st & 2nd is nonsense and FAR more likely to hurt than help

So the tactical voting doesn't count if it's "more likely to hurt than help"? On top of that, he said "other than asking each other's backers to rank them 1st and 2nd". What does he mean "other than"? That is tactical voting.