It's rank, all right – Part 5

If I've got some blood on me, it's because I've been deep in the weeds on how the votes will be counted in the crazy Portland City Council elections that are about to begin. There are a lot of thorns in that part of the garden.

I've gotten some of my questions answered, and so now I think I can walk through my hypothetical election in a council district a bit further, and run out numbers through several steps in the process. I'm still not sure I have everything 100 percent right, but I think I'm close enough to "show my work," as my first algebra teacher, Charles Rooney, used to say.

Here's my latest try:

Let's say in a race for three seats, there are seven candidates. (In the real races there are three or four times that many contenders, but I think I can figure everything out with only seven.) The first-choice votes are counted, and they are as follows:

First choice tally.

Because there were 1,000 first-choice votes cast, the number needed to win a seat is 251 – 25 percent plus one vote. That target never changes throughout the painful process we are about to undertake: 251 votes is needed to win a seat. That number is chosen because no more than three people can get to 251. This is quite different from how a winner is chosen in the mayor's race, which I've explained here.

And as you can see, CA got more than that, and wins one of the three seats, right off the bat. But the other two seats are still in play.

The next thing that happens is that because CA had "surplus" votes – more than the 251 it took to win – the second-choice votes of CA fans (that is, the 260 voters who chose CA first) are now going to count in favor of CB, CC, CD, CE, CF, and CG. But each of those second-choice transfers is going to be scaled back by applying a fraction that shows how much greater than the 251-vote threshold CA's first-choice total was.

The magic fraction that is going to tell us how much strength CA fans' second-choice votes should be given at this point is 9/260. That's because CA's first-choice vote total was only 9 votes greater than the 251 threshold, and CA got 260 votes altogether.

And so now we're going to take each CA fan's second-choice vote, multiply it by 9/260, and hand that fraction of a vote over to whoever that CA fan ranked in second place. If when that addition is done, any of the remaining six "active" candidates gets to 251, they win a seat.

But it turns out, on our hypothetical second-choice ranking, none of candidates CB through CG make it to victory. Here's the tally after the CA "surplus" business is taken into account:

Result after allocation of CA surplus.

At this point, I believe the official terminology is that Round 1 is over. You might note that not all the CA fans ranked a second choice. Only 235 out of 260 did. That's to be expected.

Okay then, now it's on to the next step, which is to eliminate the lowest vote-getter, CG. Sorry, CG fans, you lose. But you still count. We are now going to take out the ballots of all of the people who chose CG first (the CG fans), and see what their second choice was. If that was CA, we'll go on to their third choice. And once we have identified these next choices of the CG fans, we will add them to the totals of CB, CC, CD, CE, and CF.

But we're not done yet with this round. The other thing we have to do is get out the ballots of the 17 CA fans whose second choice was CG. We are going to identify the next choice (if any) on each of those ballots and add them, too, to the totals of CB, CC, CD, CE, and CF – but as before, only at their surplus fraction, which on these facts is small because CA came in only slightly above the threshold.

After we do this, we ask whether any of CB, CC, CD, CE, or CF have reached 251. If so, they win the second of the three council seats (or the second and third). But on our facts, it turns out that the votes coming out of the CG elimination don't push anyone over the top. CB and CC are still close to, but not actually, elected:

Result after elimination of CG and transfer of CG's votes.

I think the official jargon is that that's the end of Round 2. Notice, all the candidates got to keep the votes they picked up in the CA surplus. They will get to keep them through all the rounds until the candidate is either elected or eliminated. And the same goes for the votes they just picked up from the CG fans.

Let's take a breather. That's a lot to digest, and we still have only one winner. In the real elections, all this will be done by a computer in the Multnomah County elections office on inner Southeast Morrison Street, down by the strip club. I remember a Friday night in 1990...

But I digress. Let's get on to the next step, which is to eliminate CF. Sorry, CF fans, your favorite candidate, CF, will have to stay at their day job, or in their tent on the sidewalk, as the case may be. We are now going to take out the ballots of all of the people who chose CF first (the CF fans), and see what their second choice was. If that was CA or CG, we'll go on to their next choice. And once we have identified these next choices (if any) of the CF fans, we will add them to the totals of CB, CC, CD, and CE.

And we're not done yet with this round. The other thing we have to do is get out the ballots of the 8 CA fans whose second choice was CF. We are going to identify the next choice (if any) on each of those ballots and add them, too, to the totals of CB, CC, CD, and CE – but as before, only at their surplus fraction, which again, is small because CA got only slightly above the threshold.

No CG fans' votes were transferred to CF in the last round, and so we don't need to worry about that at this stage.

Okay, let's say we've done everything just described, and we get this (click on the image for a bigger version):

Result after elimination of CF and transfer of CF's votes.

Nobody's reached 251, and so we've got to do another round. I believe what we just did gets us to the end of Round 3. 

Now, in this next round, things are going to get serious. CE got 90 first-choice votes – there were 90 CE fans. We're probably going to be transferring a lot more votes this next time around than we have so far. So let's get going on that.

Sorry, CE fans, your favorite candidate, CE, is toast. But we are now going to take out the ballots of all of the CE fans, and see what their second choice was. If that was CA, CF, or CG, we'll go on to their next choice. And once we have identified these next choices (if any) of the CE fans, we will add them to the totals of CB, CC, and CD. We're down to just the three of them now, for the two remaining positions on the council. If any of them hits 251, they win a seat.

Similarly to what we did in previous rounds, we must also get out the ballots of the 5 CA fans whose second choice was CE. We are going to identify the next choice (if any) on each of those ballots for CB, CC, or CD, and add them, too, to the totals of CB, CC, and CD, but as before, only at their wimpy surplus fraction, 9/260. 

That's as far as I've gotten, and I hope it's right. But now I have questions. What about that 1 CG fan's vote that got transferred to CE in Round 2? And what about that 1 CF fan's vote that got transferred to CE in Round 3? Do we take those two ballots out and look for each of those voters' next choice among CB, CC, and CD? I suspect yes, but I'm not sure about that. Time to stop and chase that one down.

But as you can see, the fans of CE, the fifth place finisher in the first round and ultimately a failed candidate, could now push one of the three remaining contestants over the top. That would leave two candidates jostling for the last seat, and the outcome there could depend on the surplus vote of the candidate that the CE fans get across the finish line.

Notice, too, that none of the CB fans, CC fans, or CD fans have had their second or later choices counted, or even looked at, yet.

I'll progress further when I've got my latest question answered. But the big picture is that this is a terrible morass, convoluted and undemocratic, and it should never have been adopted. I'm determined to play along knowledgably while we suffer under it, but we all need to work to get it changed, and soon.

UPDATE, Oct. 14: I've gotten my questions answered, and completed the counting, here.

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