Two-candidate runoffs: Why they fail

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:

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:

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:

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:

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

These would be the results for Round 6:

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.