Ranked-choice voting with limited rankings

Summer 2004

A potential worry with San Francisco's implementation of ranked-choice voting is that the voting equipment in SF can only handle 3 rankings. If there are many more strong candidates than that, there will be a lot of exhausted ballots (those that don't rank any of the final-round candidates and can't be counted, thus diminishing the 'majority' mandate that we want the winner to have). The poll for District 5, with 22 candidates, has typically shown a quite wide spread, and a lot of exhausted ballots - still fewer than (or at least comparable to) the drop in turnout seen in past San Francisco two-round runoffs, but it makes one wonder what can be done to improve this.

For example, the best way may be to allow for more rankings on the ballot. But often people don't even use all the rankings they have available, so it may work better to just persuade voters to rank more candidates (or require this, as the Australians do, perhaps in reaction to this problem).

To address these questions, I ran several DemoChoice RCV elections using the ballots from the 2003 Cambridge, MA city council election - another wide-open election with about 20 candidates (see the original results).

The voters in this election did not know that I would be limiting them to three choices, so they did not vote strategically to account for this fact (by voting for a very strong third choice, for example). Voters who know of a three-choice limit would, so the actual results would have fewer ballots run out of valid choices, but it's valuable to understand what would happen without this effect.

For the RCV elections I imposed a few constraints:

"min": Only ballots with at least n candidates ranked were used. This helps show the effect of persuading people to rank more candidates.

"max": Only the first n rankings on a ballot were considered. This shows the effect of giving people the opportunity to rank more candidates.

"both": Both of these (both constraints, and both effects).

Here are the percentages of exhausted ballots for the various conditions:

5 9.9%31.6%20.6%
6 8.0%29.2%16.1%
7 6.8%27.9%13.1%
8 6.5%27.2%11.8%
9 5.9%26.8%10.9%
10 5.8%26.6%12.3%

Some observations you can make:

Another dimension of this is worth a look. Most of the exhausted ballots discussed above were making a useful contribution until right up until the end. In that sense it isn't fair to compare final-round exhausted ballot numbers with the drop in turnout seen in two-round runoffs.

Here are the numbers of remaining (non-exhausted) votes, plotted against the number of remaining candidates, for the 2003 Cambridge City Council ballots run as an RCV election with either unlimited rankings, limited to no more than 3, or exactly 3 rankings. This last scenario is the best we could expect with 3-rank voting equipment, but it may be unrealistic to expect such cooperation from voters.

remaining candidates unlimited rankings max 3 rankings exactly 3 rankings

So even if there are a lot of ballots that don't make a contribution in the final round, those ballots do have an important effect in determining who gets to be in the final round. The number of votes contributing to the final result of the unlimited-ranking election is about the same as the number that narrowed the field from 22 to 3 in the limited-ranking election.

This suggests an additional way to compare two-round runoffs and RCV. In this election, a two-round runoff would ignore the wishes of 76% of voters when it narrows the field from 22 to 2. (The top 2 candidates only received 24% of the first-round vote in this election.)

With unlimited-ranking RCV, 74% of voters helped narrow it down to two, just about all voters helped in this process at earlier stages, and we know quite clearly that 26% simply don't have a preference between the remaining candidates.

By limiting choices to 3, we lose the contribution of another 18% of voters in this final stage, but again many of those contributed earlier, and this is much better than the 50% of voters who have a preference but are ignored if the field is narrowed to two in a single round. It is this distortion that usually creates the biggest problems with two-round runoffs. In the 2002 French presidential election, the top two candidates each had less than 20% of the vote, and one of the two was so strongly opposed that he only gained 1% in the runoff. RCV would have performed much better in this case, even when limited to 3 rankings.

So, in short, with Ranked-Choice Voting we can be much more confident that the top two candidates in San Francisco's District 5 are the right ones, and that more voters have had an overall impact on the election, even if the number of final-round exhausted ballots ends up being equal to or higher than past decreases in turnout in the two-round runoffs.

If lots of San Franciscans complain about exhausted ballots after this election, I hope that we can use these arguments to direct them to solve this problem by adding more rankings and encouraging voters to use all available rankings, and not by reverting to two-round runoffs.