Tuesday, May 03, 2011

 

Britons should vote NO on AV

On Thursday, Britons will vote on the voting system to be used in future parliamentary elections. This blog does not endorse candidates or parties, but it does endorse methods of voting and vote counting. The current British method, plurality, is elegantly simple: each voter selects one candidate, and the candidate with the most votes wins the election. It is not perfect, but the substitute method up for a vote, alternative vote (or instant runoff voting), is far too flawed for British voters to approve.

Alternative vote (AV) is a type of preferential voting in which voters are asked to rank the candidates from first to last. The basic idea is that if no candidate is the first choice of 50% + 1 voters, then the candidate who received the fewest first place votes is eliminated. This candidate's voters then have their votes reallocated to the candidate they ranked second. This reallocation process continues until one candidate achieves 50% + 1 votes (more on this later). A majority is achieved (or so we think)!

AV supposedly gives voters more freedom of expression to vote for the candidates they want. I will allow AV supporters to develop this argument further.

What I want to do first is give you three reasons why AV is an unacceptable system to me.

1. No-Show Paradox. The number 1 rule I hold for any voting system is that when you vote for a candidate you should be helping her/him. Conversely, when you stay home and do not cast a ballot, you should hurt the candidate you want to win. In plurality voting, these simple (and very logical) rules hold true. In AV, these rules do NOT hold.

Consider, the follow 21 voter and three candidate example borrowed from Warren Smith's Range Voting website (a great site for a more in-depth look at the problem described below).


In this example, the Liberal Democrat candidate has the most votes (8), but it does not hold a majority. The Conservative candidate has the second most first places votes (7). The Labour candidate has the fewest first place votes (6), and its voters have their votes reallocated to their second choice.

With the votes reallocated from those who ranked Labour first, the Conservative candidate has a majority with 13 votes and wins. All seems well... but is it?

What happens if 3 of the voters who ranked the Liberal Democrat first got sick on Election Day and could not make it to the polls? The modified electorate from above would look like this


Now, the Conservative candidate has the most first place votes (7), while the Labour candidate has the second most first place votes (6). The Liberal Democrat is eliminated, and its voters have their votes reallocated to their second choice.

All of a sudden, it is the Labour candidate (with 11 votes) who wins the election. Nothing may seem wrong with that at first glance, but a further examination reveals something is quite wrong here. Three voters who preferred the Labour candidate to the Conservative were only able to get the Labour candidate elected by NOT VOTING! Put another way, the three voters who were sick would have gotten their least favorite candidate elected by voting!

The mere thought of such an event occurring is a deal breaker for me. Another scary statistic is that when the AV and plurality winner differ, the chance of a no-show paradox occurring is about 50%!

2. Non-monotonicity. Related to the no-show paradox are violations of monotonicity. Ranking a candidate (e.g. Liberal Democrat) higher should help, not hurt, her/his chances of winning, while ranking them lower should hurt, not help, their chances of winning. Seems pretty obvious, and we know in plurality voting that voting for a candidate helps them, while not voting for them hurts them. Yet, AV fails this simple test.

Consider, this one example, again from Warren Smith's Range Voting website, with 3 candidates and 17 candidates demonstrating how IRV show this terrible characteristic.


Here, the Labour candidate has the most votes (8), but just misses a majority. The Conservative advances to the second round with 5 votes, and the Liberal Democrat is eliminated with 4 votes. With the votes from those who placed the Liberal Democrat first redistributed, the Conservative comes from behind and wins 9 votes to 8 over the Labour candidate. Seems good that a majority was formed... right?

But look at what happens when two of the voters who ranked the Labour candidate first and Liberal Democrat second decided at the last moment that they preferred the Liberal Democrat to the Labour candidate...


Now, the Conservative is eliminated with only 5 first place votes, while the Liberal Democrat and Labour candidate advance with 6 votes. With the Conservatives votes re-distributed, the Labour candidate has won the election over the Liberal Democrat 11 to 6.

Did you just see what happened? 2 voters who had initially preferred the Labour candidate to the Liberal Democrat were able to secure the election of a Labour candidate by ranking the Liberal Democrat over the Labour candidate!

And yes, it is possible (see Smith's website) to ensure the defeat of a candidate by ranking so-said candidate higher (as opposed to ranking a candidate lower to ensure victory as the above example illustrates). In combination, these two monotonic problems occur no less than in 5% of the time in 3 candidate elections. The percentage is even higher for elections with more candidates.

3. AV violates one-man/one-vote. Certain electoral systems (e.g. cumulative voting) allow voters to vote for more than one candidate, but they give each voter the right (even if they choose not to execute it) to theoretically cast and have the same amount of votes counted as one another. The current British system is one-man/one-vote. AV, on the other hand, gives certain voters more votes than others.

Take a gander at any of the examples above. You'll note that the voters who have their first choice eliminated in the first round have their second-choice votes counted in a second round. In other words, they have 2 votes counted. The voters whose top choices make it into the final 2 only have 1 vote counted. If there were more candidates in this election, there is the obvious possibility of some people having infinite votes counted, while others still having only 1.

Now, for those whose first choice is the winner, I have little sympathy. But re-examine our first example,


As shown above, the Conservative wins, while the Liberal Democrat (who would win a plurality election) advances to the second round and loses. The voters who ranked the Liberal Democrat first only have 1 vote counted. This characteristic of AV is even more ridiculous when you realize that the Liberal Democrat voters in this election would have preferred any candidates besides the Conservative. In fact, they could have formed a majority with first-place Labour voters to allow the Labour candidate (Liberal Democrat voters second choice) to win the seat.

An unfair outcome has clearly occurred.

Finally, I want to make two points with regards to the idea that AV allows a majority to be formed.

1. You might be lead to believe that AV guarantees that the Condorcet winner (the candidate who would win one-on-one match-ups against each other candidate), if it exists, wins the election. The truth is that it does not.

Look directly above to the prior example, and you'll quickly realize that if there were one-on-one match-ups, the Labour candidate would win every single one. 14 voters prefer the Labour candidate to the Conservative, and 13 voters prefer the Labour candidate to the Liberal Democrat. Yet, in AV, the Labour candidate is the first one eliminated. AV does not even do something that many would argue it should.

2. Recognize that the candidate who eventually wins the majority does not necessarily have the vote of 50% + 1 of the voters who cast a ballot. When a ballot is filled with many candidates, many people might not rank all of the candidates (e.g. for lack of time).

I can speak from real experience. In the 2010 Dartmouth Student Assembly Vice-Presidential election, which utilized AV, Brandon Aiono won by 7 votes over Will Hix (1,075 to 1,068). It turns out, however, that 2,246 ballots were cast in this race. That means that Aiono actually only won with a little less than 47.9% of the people who voted in this race.

If AV actually encourages more third-party voting (which is debatable) as some AV supporters suggest, then it really is possible than many Britons will not rank every candidate. If they do not rank every candidate, then we could get a winner who does not have support from 50% + 1 of the voters.

This last example is typical of AV's failure to deliver. AV gives voters a false sense of security that they are in greater control of the electoral process. In reality, they are in less control and cannot truly be sure what their vote truly means.

Comments:
"The mere thought of such an event occurring is a deal breaker for me.... An unfair outcome has clearly occurred. "

I believe that it's been mathematically demonstrated that no voting system is perfect. Here you seem to be using that fact to advocate for retaining a particular (flawed) system, which seems illogical to me.
I mean, in your scenario A under first-past-the-post, the Lib Dem is elected despite losing 15-8 in a runoff against either of the other two candidates. How is that not a deal-breaker to you? How is that not an unfair outcome?

I put it to you that in deciding which voting system you prefer, you must allow that none of them produce perfect outcomes. You must decide what kind of unfairness you prefer.
My rationale for preferring AV (or, really, almost anything other than first-past-the-post) is that FPTP kills 3rd party viability in almost every case, promoting entrenched interests (and I suspect political apathy, as voters repeatedly hold their nose and vote for the lesser of two evils).
Whereas AV- there's a possibilty for weird results, but it's not clear to me that those have a real-world negative effect. Can the system be gamed ahead of time somehow by an advocate of a particular candidate? Does it have other detrimental side effects on the political process?

"The current British system is one-man/one-vote. AV, on the other hand, gives certain voters more votes than others.
Take a gander at any of the examples above. You'll note that the voters who have their first choice eliminated in the first round have their second-choice votes counted in a second round. In other words, they have 2 votes counted. The voters whose top choices make it into the final 2 only have 1 vote counted."

Politely, bullcrap. Each voter gets one vote per round. When their candidate is eliminated this will be for an alterate choice. When their candidate is not eliminated it is for that candidate again. No one is ever prevented from voting in every round.
Saying that this violates one man/one vote is a rhetorical trick suggesting that this disenfranchises some or privileges others.
 
Well, so I guess it depends on whether you think the purpose of voting is to adhere to certain norms and principles (the "no-show" rule, "one man, one vote", etc), or to accurately represent the preferences of the populace. Because you seem to make a pretty compelling case that what we usually think of as signals for the "fairness" of an election are actually pretty poor indicators that the election has accurately represented the preferences of the voting public.
 
You really need to study up on the British system further before posting such an article. I believe your first statement "The current British method, plurality, is elegantly simple: each voter selects one candidate, and the candidate with the most votes wins the election." is critically flawed and the article goes downhill from there.

If the system was as "elegantly simple" as you state then it would not be possible that 36% of votes for the Conservative party resulted in them winning 47% of parliamentary seats and 23% of the votes for the Liberal Democrats resulting in only 9% of seats. Your argument does not take into account the 'seats' system and is therefore flawed from the onset.

The examples you state show major balance shifts that are only really viable on the small scale where one voter represents a large percentage; however, larger numbers of voters should iron out such statistical discrepancies in the system.

Moreover, the fact remains that voters do NOT have to vote for any candidate that they do not wish to be in power. In that instance, an undesired candidate would not receive a single vote from someone who definitively did not wish them to be in power under any circumstance.

AV may not be the best system out there but it sure if fairer than the first-past-the-post system used currently. You should remember that the government should be representative of the MAJORITY of the public and not just MOST of the public. As such, this is not a simple race to have one winner but rather a set of heats to find the best candidates and then choose the candidate that represents the majority view.
 
A simple modification in the way the votes are tallied completely solves all the problems cited here with AV.

Instead of eliminating the candidate who received the fewest first-place votes, eliminate the candidate who received the most last-place votes. In each example cited in the article, this better method of allocating the votes would result in the election of the candidate most likely to be the consensus choice of the district's voters.
 
As Kamron has pointed out, the assertion that Alternative Voting (IRV) violates one-person/one-vote is utterly bogus. I would highlight that this part of your argument applies equally well to Approval Voting.

I think you did a great thing moving Dartmouth student elections from IRV to Approval, as I think Approval is a much better voting system. But this argument is not consistent with your support for Approval Voting.
 
Leon et al.,

I think my words written were quite consistent re: Approval and one-man/one-vote. With my definition of one man / one vote, i'm invoking a common phrase to define a new problem. I have no issue with the idea of more than one vote per person (hence the cumulative vote reference). I even have no problem with the idea that certain voters will choose 5 candidates, while others might only vote for 1. My issue with IRV (or AV) is that voters have no say with how many of their ranks are used. I think the post lays out the problem with IRV well with concern to this problem.

Feel free to email me with other concerns.
 
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