It's rank, all right – Part 2

Yesterday I started working on an overdue project: understanding the City of Portland's new "rank choice" vote-counting. I started with the relatively easy one, the mayor's race. But I quickly hit a snag, with a question that I couldn't answer by looking at slick, superficial websites on the subject.

At that juncture I went with my lawyerly instincts and dug out the city's actual election code, which I think answers just about every question I could think of. The code is posted here. So here's my hypothetical scenario again, and this time, with the help of the official rules rather than the for-dummies versions, I think I can trace the process all the way through to the end. 

Again, it's important to note at the outset that this post deals only with single-winner races, which this time around means the mayor, not the council. And these are my unofficial views of how this is going to work. At this point I'm asking anyone who reads this, and knows better, to correct me where I'm wrong.

Here goes.

Say there are six candidates for mayor, three mainstream and three, how shall I put this, wack jobs. I'll call them MS1, MS2, MS3, WJ4, WJ5, and WJ6, respectively. Let's assume that all the ballots that come in are properly marked, and no markings are invalid. Now assume that the voters' first choices are as follows:

Round 1 results.

Under the old system, MS1 and MS2 would move to a runoff. But those days are over, folks. We're rank and dank now.

Nobody's got more than 50% of the 3306 first-choice votes, and so it's on to Round 2. As I understand it, in Round 2, WJ6 is eliminated, and the WJ6 fans (those 100 who picked WJ6 as their first choice) now get their second choices counted. Assume that it just so happens that all the WJ6 fans name some candidate or other as their second choice, and that their second choices are split evenly among the other five cadidates. That gets us to this:

Round 2 results.

Still no majority, and so it's on to Round 3. 

But before moving past this point, what if, as is likely, some WJ6 fans don't name any choice other than their first choice, WJ6? What if the Round 2 scenario looks like this?

Round 2 alternate scenario results.

Well, still nobody's got a majority, but note that the total number of votes being counted just shrank. Instead of the 3306 votes we had in Round 1, this alternate version of Round 2 has only 3281 votes in it, because 25 WJ6 fans stopped ranking after their first choice. And so the number it takes to win just dropped from 1654 to 1641. With every successive round, as voters stop ranking lesser choices, the number needed to win gets progressively smaller.

Okay. So let's go back to our original scenario for Round 2: All the WJ6 fans picked a second choice, and all five remaining candidates got 20 each as the WJ6 fans' second choice. Now it's on to Round 3.

In Round 3, WJ5 gets bounced, and MS1, MS2, MS3, and WJ4 get to keep all the votes they've collected so far. Now WJ5's fans get their second choices counted. And as I understand it, the twenty WJ6 fans whose second choice was WJ5 now get their next choices counted. And by their next choices, I mean their next choices among the four candidates who are still in the running. Any WJ5 fan second-choice votes for WJ6 are disregarded, and those WJ5 fans' next choices, if any, are counted.

Let's say with that in mind, Round 3 shapes up like this:

Round 3 results.

Note that not every WJ5 fan cast a second-choice (or later-choice) vote for MS1, MS2, MS3 or WJ4. Of the 101 WJ5 fans, 22 either didn't rank a second choice at all or ranked only WJ6 as their second or later choice. And so only 79 votes from the 101 WJ5 fans made it into Round 3.

And of the 20 votes that WJ5 had picked up from WJ6 fans in Round 2, only 15 cast a later vote for MS1, MS2, MS3 or WJ4. And so five of the WJ6 fans are out of the game in Round 3 and the rest of the way.

Note, too, that with those voters dropping out of the picture, the number of votes needed to get a majority decreased again. There were 3306 first-choice votes, but here in Round 3, there are only 3279 votes counted. And so now a majority is only 1641, not 1654.

But still, nobody has that majority, and so now we're on to Round 4.

In Round 4, WJ4 gets bounced, and all of WJ4's Round 3 votes get redistributed. MS1, MS2, and MS3 hold on to what they'e collected so far.

The WJ4 fans get their votes transferrred to their next choice (if any) for MS1, MS2, and MS3. The 25 WJ6 fans who had their votes transferred to WJ4 (20 in Round 2 and 5 in Round 3) also get those votes transferrred to their next choice (if any) for MS1, MS2, and MS3. And the 25 WJ5 fans who had their votes transferred to WJ4, in Round 3, also get those votes transferrred to their next choice (if any) for MS1, MS2, and MS3.

Let's say that gets us here:

Round 4 results.

The number of votes needed to win keeps getting smaller, but still no one has a majority of that figure, and so it's on to Round 5, the final showdown.

At this point, MS2, who came in second in the first-choice voting, gets eliminated. (At 1070 total votes at the end of Round 4, MS2 is now coming in third.) And all of MS2's votes from Round 4 get redistributed. MS1 and MS3 hold on to what they'e collected so far.

I repeat: MS2 is out, and now it's MS1 vs. MS3. Interesting! The WJ4, WJ5, and WJ6 fans re-ordered MS1, MS2, and MS3 from where they stood in Round 1.

In Round 5, the MS2 fans get their votes transferred to their next choice (if any) for MS1 and MS3. All the various fans who got their votes transferred to MS2 in one of the previous rounds now also get their votes transferred to their next choice (if any) for MS1 or MS3. And with only two candidates left getting votes, barring a dead heat, one of them will get a majority of the votes counted in this last round. If it comes out as follows (click to get a bigger picture), MS3 wins:

Round 5 results.

In this scenario, the key is the later-choice votes of the MS2 fans. When MS2 got eliminated and MS2's votes were redistributed to MS1 and MS3, that essentially determined the outcome – especially those original MS2 fans. Up until then, it was up in the air.

In the final round, only 2963 votes were counted – 343 less than in the first round. It took 1483 or more to win. MS3 won.

Wow, I'm exhausted. Are you still there? Let's take a break for a few minutes and then come back and try to see what we've learned about all this craziness.

* * * * * * * * * *

Whew. So what can we divine from my scenario? First, it's important to realize that ranking someone your fifth or sixth choice (the lowest possible on the current election ballots) is not a vote against that person. Ranking a candidate as any of of your choices, no matter how low, does nothing but increase the chances that that person will win. If you don't want someone to win, don't blacken any circle on the row next to their name.

Second, notice that some people have all their choices counted. For example, in our scenario, say a voter ranked it WJ6-WJ5-WJ4-MS2-MS3. Their choices counted in Rounds 1, 2, 3, 4, and 5, although only their Round 5 vote controlled the final outcome. They got to keep trying again, five times in all, before they landed on the winner. People who started with MS2 as their first choice had their vote in play only in Rounds 1 and 5.

Third, although they call this mayoral vote-counting morass "instant runoff," it's not like a real runoff. In a real runoff, everyone gets to choose between the two finalists. As can be seen from this illustration, rank-choice doesn't get you there. In Round 5, only 2963 votes were counted. That means that 343 voters had no say in the final showdown between MS1 and MS3. And that's because, in keeping with the wisdom of the first point I just made, those voters didn't really want either MS1 or MS3 to win, and so didn't rank either of them.

Along those same lines, it's not hard to picture a scenario in which many people's second or later choices don't count at all. For example, say you have four mayoral candidates, and the first-choice voing comes in as follows:

Candidate 1 1005

Candidate 2 995

Candidate 3 201

Candidate 4 200

Total       2401

If all of the Candidate 4 fans' second choice is Candidate 1, Candidate 1 wins in the second round, with 1205 out of 2401, and Candidate 3 fans' second and later choices are irrelevant, even though Candidate 3 lost. (Candidate 2 fans' second and later choices are also irrelevant, even though Candidate 2 lost.)

* * * * * * * * * *

Having done this exercise, I'm as convinced as ever that rank choice voting is a solution in search of a problem. I think I understand the single-winner version of it now, and it's garbage. And from what I've seen of the goofy charter commission, not even well-intentioned garbage.

But we live with it. Don't rank anyone you don't want in office – leave the bad candidates blank – and hope for the best as this nonsense plays out. Be prepared to feel disenfranchised. And hope you live long enough to vote to scrap this foolishness at the next opportunity.

Having peered into the single-winner version of "rank choice," my next foray will be into the city council races. There, except when a vacancy is being filled, there will always be a pack of candidates running for three open seats simultaneously. In that environment, I'm sure the "rank" business will get even ranker. More on that soon. Right now the most important thing is to be sure that I got the mayoral version of this right. What am I missing?

UPDATE, Oct. 3: I now have it on very good authority that the math and the procedures discussed in this post are correct.

UPDATE, Oct. 17: My critique of rank-choice voting, in general and Portland-syle, is here.