Two-candidate runoffs: Why they fail

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One of the proposed Tulsa City Charter amendments on tonight's City Council agenda would eliminate party primaries and put all candidates on a non-partisan ballot. If no one receives 50% of the vote, the top two vote-getters in the primary would face off in the general election.

I wrote a column in March 2006 explaining the flaw in a two-candidate runoff, particularly in a non-partisan election or Louisiana-style all-party primary, using historical examples. It's too easy in such a system to wind up with a winner who is unacceptable to the majority of the voters. (That same column explains why Instant Runoff Voting is a better system.)

I've been trying to come up with a simple way to explain the problem, an explanation that doesn't involve real-world political loyalties. Here's my latest effort. I'd appreciate your suggestions for improvement:

In Council District 10, the most important concern among voters is having a city councilor who supports their favorite college football team.

Polling has shown that, of the 1000 voters in District 10:

550 are rabid OU Sooner fans
250 are diehard OSU Cowboy fans
200 wear hog hats on their heads and holler "woo, pig, sooie!"

City Council elections are non-partisan, with a primary, followed by a runoff between the top two vote getters.

Because there's such a strong base of support for the Sooners in the district, five Sooner fans filed for the seat, but only one Cowboy fan and one Razorback fan filed. (These fans are so fanatical, they've changed their names to match famous head coaches.)

Here's the primary result:

candidate
affiliation
votes
Jimmy Johnson
OSU 250
Lou Holtz
U of A
200
Bud Wilkinson OU
185
Bob Stoops OU
160
Barry Switzer OU
145
Chuck Fairbanks OU
50
Gomer Jones OU
10


If Chuck Fairbanks and Gomer Jones hadn't entered the race, any of the other three OU candidates could have had enough votes to make the runoff by beating Lou Holtz for second place. In a head-to-head runoff, an OU candidate would have no trouble winning in District 10. But because the OU vote was split five ways, there won't be an OU candidate in the runoff.

Instead, in the runoff, the 550 voters who voted for OU candidates -- the majority of those voting -- will be forced to hold their noses and pick between Jimmy Johnson and Lou Holtz.

In a party primary system, the OU voters would have chosen one candidate to represent them in a general election, and given that OU fans are a majority in the district, the OU nominee would likely have won the general. The OSU and U of A voters in the district, despite constituting a significant minority, would ultimately have no influence on the outcome.

In an instant runoff system, where all voters cast a preferential ballot ranking all the candidates, one of the OU candidates would win the election, but each voter, regardless of affiliation, would have an equal opportunity to influence the final result.

UPDATE: XonOFF asked me to elaborate on how instant runoff voting would solve this problem. I've done so in the extended entry, after the jump.

Let's imagine that instead of a two-person runoff, this city held a series of runoffs, and what you see above is the result of the first round of voting. After each round, the candidate with the lowest vote total would be eliminated and another round of voting would be held.

So Gomer Jones would be out after the first round. In Round 2, everyone who picked someone other than Gomer in Round 1 would still vote for their favorite, but Gomer's 10 first-round voters would split between the other four OU candidates -- four for Fairbanks, three for Switzer, two for Stoops, and one for Wilkinson.

These would be the results for Round 2:

candidate
affiliation
votes
Jimmy Johnson
OSU 250
Lou Holtz
U of A
200
Bud Wilkinson OU
186
Bob Stoops OU
162
Barry Switzer OU
148
Chuck Fairbanks OU
54


Still no one has a majority (501 votes), so we eliminate Chuck Fairbanks. In Round 3, let's suppose that his 54 voters split evenly between the three remaining OU candidates.

These would be the results for Round 3:

candidate
affiliation
votes
Jimmy Johnson
OSU 250
Bud Wilkinson OU
204
Lou Holtz
U of A
200
Bob Stoops OU
180
Barry Switzer OU
166


Note that with two of the OU candidates eliminated, there's been a change in the top two vote-getters, with Wilkinson replacing Holtz in second place. Switzer is bottom man on the totem pole, so he's out, and his voters split 100 for Wilkinson and 66 for Stoops.

These would be the results for Round 4:

candidate
affiliation
votes
Bud Wilkinson OU
304
Jimmy Johnson
OSU 250
Bob Stoops OU
246
Lou Holtz
U of A
200

Holtz was one of the top two vote getters after round one, and would have made the finals in a traditional two-man runoff, but now he's in last place, and he's off the island. His Razorback loyalists mostly prefer U of A alum Johnson (150 votes), but the remaining Holtz voters love Bob Stoops, for some reason.


These would be the results for Round 5:

candidate
affiliation
votes
Jimmy Johnson
OSU 400
Bud Wilkinson OU
304
Bob Stoops OU
296


Still no majority. Stoops is eliminated, and all of his votes go to Wilkinson.

These would be the results for Round 6:

candidate
affiliation
votes
Bud Wilkinson OU
600
Jimmy Johnson
OSU 400


Wilkinson has a majority and is declared elected after the sixth round, and the OU majority in the district will be represented by an OU candidate.

(In a real series of runoffs, some voters might change their votes between rounds, and many voters will get bored and not go to the polls.)

This method eliminates the problem of spoiler candidates and any concern about a large number of candidates splitting a majority of the electorate and allowing a candidate representing a minority point of view to be elected. You can vote in each round for your favorite of those still on the ballot, without having to calculate whether your vote might help elect someone you don't like.

But it's cumbersome and expensive to have half a dozen runoff elections. This is where instant runoff voting comes in. By ranking the candidates in order of preference, you're providing the same information as if you voted in all six of these runoff elections: If your favorite candidate were eliminated, whom would you support instead? If your second pick were out, whom would you support? And so on, until all candidates are ranked.

In counting instant runoff ballots, they're tallied by first preferences for Round 1. If no one has a majority, you eliminate the candidate with the lowest total. You don't need to hold another election to find out who that candidate's voters would pick among the remaining candidates, because they've already indicated that on their ballots, which rank all the candidates in order of preference. So the ballots from the eliminated candidate's pile are distributed to the second choice marked on each. And so on until one candidate has a majority of ballots.

Effectively, there would be six runoff elections, but they'd all be accomplished with one election day and one ballot from each voter.

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6 Comments

XonOFF said:

I've become a fan of your instant runoff elections.

They do provide the best representation, at least as it relates to the people's choice.

When you get some time (ha,ha), it would seem beneficial if you expanded your example above to show what would happen in an instant runoff scenario. While it's easy to see how the majority fail to be installed with the two-candidate runoff, it's less clear, here, how an instant runoff would solve that.

Anything which helps people see what it would do for them, and why they should be demanding it.

Paul Tay said:

Hey, where da Santa at? :-P

Don Author Profile Page said:

Just to play devil's advocate...with party primaries, don't you run a greater risk of there only running in the general election extremists with rabid support of their base but little appeal from the center...resulting in the lack of a good centrist with wide appeal who could unite the imaginary community.

What does a large percentage of non-loyal cross-over voters, such as people from out of state who don't get this whole college loyalty thing, do to your hypothetical?

XonOFF said:

Thanks for the expansion.

Now, I have to ask...
How is it you seek instant runoff, but don't support non-partisan elections?

In your example, you have four OU candidates, yet in a partisan election, only one of those would have formal party support. The other three would essentially be running as independents.

Having a little trouble turning loose of the party?


XonOFF said:

With regard to my prior comment above, I've come to recall you actually favor what you've termed "mult-partisan" elections, where a candidate may write in multiple designations, similar to Mr. Eagleton's idea, but even more expanded. At least, if I'm remembering correctly.

I think at the time I termed it "NASCAR Candiates" with the mental image of those driver's suites pasted with logos of all their sponsers.

Can't say the idea thrilled me. But, I've really yet to come to a conclusion about that. More time/study required. Need to read more about the pros/cons of such.

IAC, the Instant Runoff remains a good idea and should be implemented.

David V said:

A more direct example would be the special election for Tulsa Mayor, back in the 90s'.

Roger Randle resigned to take a position at a college.
Several Republican politicians ran and one relatively unknown democrat. The "winner-take-all", non-partisan election resulted in Susan Savage becoming mayor with a minority of the votes.

About this Entry

This page contains a single entry by Michael Bates published on October 18, 2007 12:22 PM.

City Charter amendments on tonight's agenda was the previous entry in this blog.

A curious change in terminology is the next entry in this blog.

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