[repost from the OpenStreetMapUS blog]

The OpenStreetMap US board elections for 2019 have completed! As an election observer, I was tasked with making sure the elections were impartial and not unduly influenced, and that the vote counting was done properly.

This was an unusual election in that we had two separate questions:

The first question was to fill the open seat vacated by Maggie Cawley, who resigned to take on the role of Executive Director. The second question was a simple confirmatory vote of approval for the remaining four board members. Given that there was no election held for the board back in March (because only five candidates were nominated for five open seats), the board decided it was appropriate to hold a confirmatory vote since we were already holding an election anyway for the open seat.

The results of the election are as follows:

The existing board members were confirmed overwhelmingly, with 98 voting “yes” and 6 voting “no”. In the final round of ranked choice voting Minh Nguyễn was elected to the open seat. Congratulations Minh!

Analysis

If you don’t care about the nerdy mechanics of this Ranked Choice Voting election, you can stop reading now. But if you’re interested in a deeper analysis of the results, read on:

For OpenStreetMap US elections, we use Ranked Choice Voting (RCV), which means that each voter has the opportunity to rank all the candidates in order of preference. When RCV is used to elect multiple seats at the same time, it’s also known as Single Transferable Vote (STV), and when it’s used to elect a single seat (as was the case in this election), it’s sometimes called Instant Runoff Voting (IRV).

Under Instant Runoff Voting, if no candidate has a majority of the votes at first, the candidate with the fewest votes is eliminated, and the votes for that candidate are then transferred to the second choices on those ballots. After the transfer, if there is still no candidate with a majority, then the cycle repeats: the remaining candidate with the fewest votes gets eliminated, and their votes are transferred to the highest-ranked candidate on those ballots that is still in the running. This process continues until a candidate reaches a majority of votes, or until there is only one candidate left standing.

Under our system of Ranked Choice Voting, voters are not required to rank all the candidates, so it’s possible that their ballots will become “exhausted” if there are no more candidates still in the running that have been ranked by that voter.

Here is the graphical output from the OpaVote vote tallying software, which shows the results at each round of counting.

This IRV election had some interesting characteristics. First of all, there was no majority winner until the final round, showing the necessity of using Ranked Choice Voting. Had we used a single-round plurality voting system (often called First Past the Post), the leading candidate could have won a seat on the board with only 29% of the votes. In the end, the final tally was very close, with Minh Nguyễn finishing with 51.7% of the vote compared to Daniela Waltersdorfer’s 48.3%.

Another interesting feature of this election was that Nguyễn was 2nd place in the early rounds of voting, only to come from behind to win in the final round. This is exactly the kind of outcome that IRV is designed to make possible, but in most cases where IRV is used in practice, generally the leader in the first round of voting ends up winning in the final round. It is only when there are two (or three) evenly matched candidates that IRV vote transfers end up making a difference.

In the final round, we can see that IRV guarantees a majority winner, with Nguyễn having 51.7% to Waltersdorfer’s 48.3%. But this was only a majority of votes that were still in play at the final round: almost 15% of the ballots were “exhausted” in the final round, meaning that those voters did not rank either Nguyễn or Waltersdorfer on their ballots. If we include those exhausted ballots in the totals, then Nguyễn got 44% of the vote compared to Waltersdorfer’s 41%. But we can still say that Nguyễn won a majority of the voters who still had a preference in the final round.

One last interesting feature of this election is that Nguyễn and Martijn van Exel were tied for 2nd place in the second to last round. Under the IRV rules we used for this election, in order to decide which candidate to eliminate when there is a tie, we look back into the previous rounds to see which candidate was ahead. Since Nguyễn was ahead of van Exel in every previous round, we use that information to decide that van Exel should be eliminated.

Alternative scenarios

But some variations on IRV rules (for example, the rules used by the cities of San Francisco and Oakland) specify that tied candidates should be eliminated randomly. For large civic elections with hundreds of thousands of votes, that’s probably fine because exact ties are extremely rare. But in our OSM elections it’s better to use our more deterministic way of breaking ties, since they are likely to happen more often.

But what if we had used these random-tie-breaking rules and if Nguyễn had lost the coin flip, then what would the outcome have been if it was Waltersdorfer and van Exel in the final round?

If we look at the raw votes file, we can examine the ballots and see what would have happened in this alternate scenario. See here to learn how to understand the .blt file format used by OpaVote.

To figure out what the tally would be in the final round between two candidates, we can ignore the rankings for all the other candidates, and merely look at the relative ordering of the two finalists on each ballot.

So, if Nguyễn had been eliminated instead of van Exel, we find that there are 43 ballots that ranked Waltersdorfer ahead of van Exel, and 49 that ranked van Exel ahead (with 12 exhausted ballots). So had van Exel not been eliminated in the tiebreaker in the second-to-last round, he would have gone on to win overall.

Again, this shows that in an election between three evenly-matched candidates, small differences in the rankings can produce surprisingly different outcomes.

Condorcet winner

IRV is not the only alternative voting method out there, and one of the other possible voting techniques is the Condorcet Method. From the voter’s point of view, Condorcet is similar: on your ballot you rank candidates in order of preference. But unlike IRV where we progressively eliminate candidates in a series of runoffs, under Condorcet we would look at each possible head-to-head matchup of the candidates, to find out which candidate would beat every other candidate.

If you spend enough time learning about alternative election methods, you’ll eventually hear one of the few criticisms of IRV, which is that it can sometimes fail to elect the candidate who is the “Condorcet winner”.

In our election, Nguyễn narrowly defeated Waltersdorfer in the final round, but had we used different tie-breaking rules, then van Exel would have been the one to narrowly defeat Waltersdorfer. So this left me wondering: is it possible that van Exel was the Condorcet winner, but our IRV election failed to elect him?

The way to find that out is to see who would have won in a hypothetical head-to-head matchup between Nguyễn and van Exel. Note that there are no IRV rules that would have resulted in this matchup in the final round; Waltersdorfer was ahead in every round of counting until the end, so there is no way she would have been eliminated earlier, resulting in this matchup.

If we look at the raw ballots again, we find that there are 57 ballots where Nguyễn was ranked ahead of van Exel, and 38 where van Exel was ahead of Nguyễn (with 9 ballots that did not rank either one of them). So Nguyễn would win the head-to-head matchup, making him the clear Condorcet winner, as well as the IRV winner.

Final thoughts

Again, I’d like to congratulate Minh for winning election to the OpenStreetMap US board, and I’d also like to congratulate all the other candidates who ran. One of the great things about Ranked Choice Voting is that we don’t have to worry about the “spoiler effect”, whereby one candidate choosing to run could end up splitting the vote and causing another like-minded candidate to lose. Under the RCV system, there’s no harm in having many candidates running; if anything, more candidates brings more attention to our elections and builds a healthier democracy within OSM. So for those candidates who didn’t win this time, don’t be discouraged! We hope you’ll stand again for election next year!