Saturday, November 4, 2006

One Person, One Vote, Many Voting Systems

In an election, winners and losers are sometimes determined as much by the voting system as the voters. For example, the United States’ Electoral College allows a candidate to win the U.S. presidency without winning the popular vote, as happened in 1824, 1876, 1888, and 2000.

In San Francisco, we have a special voting system, Ranked Choice Voting, for certain local elections. Instead of voting for a single candidate, voters rank their choices.

Given a population of voter preferences, Ranked Choice Voting not only can lead to different results from traditional voting but it can also have different results among the various Ranked Choice Voting implementations.

The implementation of Ranked Choice Voting that San Francisco uses, Instant Runoff Voting (IRV), works like this:

  • You rank multiple candidates for an office, indicating your first choice, second choice, and so on.
  • If no candidate attains a majority of first-choice votes, the candidate with the fewest first-choice votes is eliminated.
  • Those who voted for the eliminated candidate have their second-choice votes added to the remaining candidates’ totals.
  • If that reallocation does not create a majority for one candidate, the process continues until a majority is reached.

The process is called Instant Runoff Voting because it resembles a series of run-offs. Whereas traditional run-offs happen over time, IRV gets all the necessary information up front, allowing all elimination stages to occur immediately.

Wikipedia’s entry on the subject gives an interesting example of how the same voter preferences can have different results depending on the voting system. (I’ve added some definitions, in brackets, to the Wikipedia text.)

Imagine an election in which there are three candidates: Andrew, Brian and Catherine. There are 100 voters and they vote as follows...

#39 voters12 voters7 voters42 voters

In a plurality election [where the winner is the candidate with the most first-choice votes], Catherine would be elected.

In a [standard] runoff election, the voters would choose in a second round between Catherine and Andrew.

In [a San Francisco-like Ranked Choice Voting] election Andrew will be elected.

Under Condorcet’s method [each ballot’s rankings are converted into pairwise preferences, such as A beats B but C beats A, which are then tallied across all ballots] or the Borda count [each candidate gets points in proportion to his/her rank on a ballot, such as first-choicers get 5 points and fifth-choicers gets 1 point] Brian would win.

Don’t worry about processing the details. Let’s cut to the implications (also quoted from the Wikipedia article):

[Instant Runoff Voting] may be less likely to elect centrist candidates than some other preferential systems, such as Condorcet’s method and the Borda count. For this reason it can be considered a less consensual system than these alternatives. Some IRV supporters consider this a strength, because an off-center candidate, with the enthusiastic support of many voters, may be preferable to a consensus candidate and that this candidate still must be accepted by a majority of voters.

IRV produces different results to Condorcet and the Borda count because it does not consider the lower preferences of all voters, only of those whose higher choices have been eliminated, and because of its system of sequential exclusions. IRV’s process of excluding candidates one at a time can lead to the elimination, early in the count, of a candidate who, if they had remained in the count longer, would have received enough transfers to be elected.

You get the idea: same voter preferences, different results.

And for a final twist, does the scenario with Brian, Andrew, and Catherine work in the real world? It assumes that the voter preferences and the voting systems are independent—or, put another way, that different voting systems would elicit the same preferences.

But in a real-world election, candidates know which voting system will be used, and they target their campaign spending to shape the preferences of specific segments of voters. Depending on the voting system, it could make sense to target different voters, thus leading to potentially different preferences.

The takeaway: A lot of potential complexity lurks behind “one person, one vote.”

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