Friday, July 15, 2011

A Voting System without "Spoilers" -- Approval Voting

A perpetual problem with our current voting system is that it subjects third-party candidates to charges that they are "spoilers" while forcing voters to vote strategically rather than honestly. That is, if you really like candidate C, but realize that the most likely winner is either candidate A or candidate B, you may feel obligated to vote for A to prevent a win by B.

How hard is it to get around this problem? Not hard at all -- it just means considering the system that was used to vote for the first four U.S. presidents. That's Approval Voting.

Under approval voting, you can vote for as few or as many choices as you like in each election. Then, every vote for every candidate is added up, and the candidate with the most votes (approvals) wins. Easy.

More here, at the Center for Election Science.

13 comments:

broken ladder said...

We also put up some good material here:
http://www.electology.org/approval-voting

I (Clay Shentrup) live in San Francisco if any of you Humboldt County folks would care to talk voting methods.

Thanks for talking about this important issue that is so often overlooked.

Rob Richie said...

Glad you picked up on the issue of how to handle having more than two choices.

But note that the approval voting dynamic was such a problem in those early presidential elections that the Constitution was changed to eliminate it -- not a great selling point.

The problem in those elections and any meaningfully competitive approval voting elections is that an indication of support for a second choice counts directly against the chances of your first choice - -in other words, supporting your second choice may well "spoil" a potential win for your first choice. In fact, your first choice could have the support of more than 50% of voters and lose due to this kind of spoiling.

There are only three realistic ways to deal with "spoiling."

For legislative elections, the idea is some form of proportional voting (and there are a lot) that allows most voters to join with like-minded voters and elect a candidate of their choice.

For one-winner races, there are only two approaches used for governmental elections for any single winner election anywhere in the world at any level of government:

* Multiple rounds of voting / Runoffs: Winnow the field in a first round, then have a runoff ultimately between top two. California now has this with Top Two, and there are pro's and con's to this approach. (For con's, ask Debra Bowen about her defeat in the CA-36 special election, a race she may have won with ranked choice voting.)

* Forms of nstant runoff voting/Ranked choice voting: Use rankings to accomplish the goal of runoffs (www.instantrunoff.com)

For all the vigor and vitriol of backers of other single winner alternatives, they basically are vaporware-- reform illusions that act as props for defenders of the plurality voting status quo who oppose change.

Mitch Trachtenberg said...

Rob,

I haven't followed the debates between the advocates of various alternative voting scenarios.

The thing I find enormously appealing about approval voting as opposed to Instant Runoff Voting is that it places minimal demands on the voter and the voting system.

I think that's a critical criterion, and I think advocates for change in elections often underestimate the resistance to change that is present throughout the system.

I hope people put links here to sites describing the attributes of all alternative voting systems... I'd prefer any of them to the voting system Americans currently use.

Rob Richie said...

A postscript. Ireland will have an interesitng, multi-candidate election for president with ranked choice voting this October. It will get the ballot-count done by hand the day after the election.

Here's a story on St. Paul (MN) getting ready for its RCV elections. It also will use a hand-count after tallying first choices at the polls:
http://www.twincities.com/localnews/ci_18488384?nclick_check=1

broken ladder said...

The problem in those elections and any meaningfully competitive approval voting elections is that an indication of support for a second choice counts directly against the chances of your first choice

Rob Richie has been making this argument for as long as I have known of him (since 2006), but he has never shown how this is a problem. The argument he's trying to make is that this will cause voters to "bullet vote" for only their favorite candidate, causing Approval Voting to degenerate right back to the system we already have.

But as we election method researchers have pointed out to him numerous times throughout the years, many voters already vote for someone other than their favorite. For example, a Green Party member who votes for the Democrat, just like many Nader supporters voted for Gore back in 2000.

With Approval Voting, such a voter would obviously want to vote for Democrat and the Green. The basic rational strategy is to vote for your favorite "frontrunner", plus everyone you like better.

In case you think this is a "purely theoretical" argument, here are actual real world numbers from large election and exit polls using Approval Voting and IRV. It turns out (perhaps surprisingly to Rob) that "bullet voting" has been more common with IRV than with Approval Voting, exactly the opposite of what he's claiming.

Next, Rob describes this scenario as "spoiling". This is inaccurate. In election theory parlance, a "spoiler" is a candidate whose presence in the election demonstrates a failure of an election method property called Independence of Irrelevant Alternatives.

As the Wikipedia article on IIA says (and mathematically demonstrates), "Approval voting and range voting satisfy the independence of irrelevant alternatives criterion." Here's another look, from The Center for Election Science.

This, along with a number of other statements by Rob Richie, demonstrates that he is not a competent or objective authority on this subject. However, because he has been quite politically active, he has had a great deal of influence. Many, including myself, believe that he has done a great deal of damage to the cause of election reform. I encourage readers to spend some time researching this subject for yourselves, and making up your own minds.

broken ladder said...

Here is a list of some of the numerous advantages of Approval Voting over IRV.

To list just a few of them here:

* Approval Voting results in much better representativeness (average voter satisfaction), as objectively measured via Bayesian Regret. This is true with any mixture of strategic and honest voters.

* Approval Voting satisfies the Favorite Betrayal Criterion, meaning it can never hurt a voter to support his favorite candidate -- whereas IRV can punish a voter for doing so.

* Approval Voting is precinct summable, unlike IRV which must be centrally tabulated, resulting in chain-of-custody (fraud) concerns.

* Approval Voting is simpler/cheaper for voters and for ballot counters. This is objectively true in the sense that it experimentally results in fewer spoiled ballots than IRV, and it has lower Kolmogorov complexity than IRV.

Rob Richie said...

Clay Shentrup overlooks voting method analyses that come to different conclusions than his.

For example, here is the abstract of paper by James Green-Armytage called "Strategic Voting and Nomination". Not that he finds instant runoff voting ("Hare") to be the least vulnerable of the systems he analyzes. He finds approval voting and similar systems like range voting to be most vulnerable.

This echoes the findings of Nicolaus Tideman, who in his book Collective decisions and Voting (Ashgate 2006)ranked approval voting dead last among 25 systems in its resistance to strategic voting.

http://www.econ.ucsb.edu/~armytage/svn2010.pdf

"Abstract: Using computer simulations based on three separate data generating processes, I estimate the fraction of elections in which sincere voting will be a core equilibrium given each of eight single-winner voting rules. Additionally, I determine how often each voting rule is vulnerable to simple voting strategies such as ‗burying‘ and ‗compromising‘, and how often each voting rule gives an incentive for non-winning candidates to enter or leave races. I find that Hare [instnat runoff voting] is least vulnerable to strategic voting in general, whereas Borda, Coombs, approval, and range are most vulnerable. I find that plurality is most vulnerable to compromising and strategic exit, and that Borda is most vulnerable to strategic entry. I support my key results with analytical proofs."

broken ladder said...

Rob Richie,

Before I address the arguments made by James Green-Armytage, it's important to be clear that his research in no way supports your criticism that "support for a second choice counts directly against the chances of your first choice" with Approval Voting. That criticism has been thoroughly discredited by the sheer abundance of insincere voting under the Plurality Voting system (which, ironically, you and other IRV advocates specifically cite in your case for IRV). You argue two different sides of the same issue, depending on what's most convenient for you in a given context.

As for the very different strategic concerns of Tideman and Green-Armytage, they suffer from a few severe flaws (which we have pointed out to you many times), which your quote perfectly highlights:

* "I estimate the fraction of elections.."
* "I determine how often each voting rule is vulnerable.."

What both of these statements reveal is that:

1) Green-Armytage is arbitrarily hand-picking a set of circumstances that he subjectively deems to be important, and then

2) He is measuring only the frequency with which they happen, without regard to their severity.

Here is a rough analogy that illustrates just how disastrously wrong-headed this is. Imagine you you are comparing two types of lottery tickets with the following properties.

Lottery 1
The ticket costs 100 dollars.
You have a 50% chance of winning 150 dollars.

Lottery 2
The ticket costs 110 dollars.
You have a 1% chance of winning 10,000

If you did the comprehensive expected value calculation, it would be clear that lottery 1 has an expected value of -75 dollars, whereas lottery 2 has an expected value of -10 dollars. Clearly lottery 2 would be the more rational choice, between these two options.

But using the logic of Tideman and Green-Armytage, one could state the values as:

Lottery 1
You have a 50% chance of winning (size of prize unstated).
(Cost is completely ignored.)

Lottery 2
You have a 1% chance of winning (size of prize unstated).
(Cost is completely ignored.)

Given that assessment, you might actually believe that lottery 1 was 50 times as valuable as lottery 2. But of course, you would be very very wrong.

This is why The Center for Election Science focuses on Bayesian Regret, which measures voting systems holistically, simultaneously weighing the objective frequency-times-severity of all properties and criteria (even ones that have never been invented).

Another analogy is that it is like measuring the average race time for a variety of Formula 1 cars, rather than comparing a few arbitrary criteria such as mass, drag, and horsepower, given arbitrary weight in an artificial formula.

As I said, this has been explained at great length to Rob Richie as well as Tideman and Green-Armytage themselves. They haven't countered these points. They've just sort of ignored them. In fact, back in October of 2009, on another comment area, a Seattle mathematician named Louis Stern said:

And I have met and talked with Nicolaus Tideman. He is not in favor of IRV in any way. Tideman currently favors a combination of Score Voting and a robust Condorcet method, so using his results to imply support for IRV is disingenuous.

This is what you get with FairVote. Highly incompetent people who are also very disingenuous.

Rob Richie said...

FairVote has posted a detailed analysis of approval voting and its track record (along with the record of voting methods that also are highly vulnerable to strategic voting) here:
http://www.approvalvoting.blogspot.com

I'd urge anyone tempted to consider approval voting for meaningfully contested elections to read this analysis closely.

broken ladder said...

Rob and I have been going back and forth like this for many years now. It's a very complex issue, but I think it can be fairly well distilled down to a few key points.

The basic strategy with essentially any voting method is "frontrunner exaggeration". In other words, say you prefer Green over Progressive over Democrat over Republican. You live in an area where the winner has historically been either a Democrat or Republican for as long as you can remember, and indeed the pre-election polls show those two major party candidates leading the pack.

With the ordinary pick-just-one Plurality Voting system (aka First Past the Post), the strategy is pretty obvious. You want to cast a vote for the Democrat, so as not to "waste" your vote on a candidate who probably won't win anyway. (Richie and lots of other IRV proponents have repeatedly cited this very problem as evidence of the need for a better voting system.)

With Approval Voting, you still would want to cast that same strategic vote for the Democrat. But the crucial difference is that you don't have to stop there! You can safely show your sincere support for everyone you like better than the Democrat as well. So in this case you'd want to approve the Democrat, the Progressive, and the Green. Approval Voting satisfies the "Favorite Betrayal Criterion", meaning it can never hurt you to cast a vote for your sincere favorite candidate.

This point alone refutes Rob Richie's common argument that Approval Voting users will "bullet vote" only vote for their favorite candidate, causing Approval Voting to degenerate right back into ordinary Plurality Voting. In fact, real world data from large elections and exit polls shows that this problem is actually worse for IRV than for Approval Voting. The fact that Richie and other FairVote associates have continued to make this argument in spite of the overwhelming evidence to the contrary illustrates to me that FairVote is not an objective and accurate source of information on this subject. It is also telling that the vast majority of mathematicians and political scientists who have studied this matter disagree with Richie's claims, e.g. NYU political science professor Steve Brams.

As for IRV, it would behave quite poorly in this situation. Your best bet would be to rank the Democrat in first place, to prevent the Green or Progressive from becoming a "spoiler". This runs counter to the claims of IRV proponents, as well as to many people's intuition. But straightforward statistical analysis verifies it. And having spoken with political party offices in Australia (where they have used IRV in the House of Representatives since 1918), I have heard that many voters intuitively do this without even understanding the underlying mathematics. They feel that this exaggeration somehow ensures that their favorite "viable" candidate has the best shot of beating their less favored viable candidate. It is mere coincidence that they happen to be right.

broken ladder said...

Within the first couple of paragraphs at Rob Richie's blog post, he repeats the same argument I mentioned in my previous post:

Among other methods that should not be used in meaningfully contested elections are range voting, score voting, the Borda Count and Bucklin voting. They all share approval voting’s practical flaw of not allowing voters to support a second choice without potentially causing the defeat of their first choice.

For anyone who read my previous post, it should be clear that Richie is portraying a feature of Approval Voting as a flaw. Thus the extensive argumentation that descends from this core point, at his cited link, is equally invalid.

Election Software said...

Approval voting is a good system, it paves the way for a fair election.

Cedric said...

Great!