It's rank, all right – Part 4
I should have my head examined, but I'm actually trying to figure out how votes are going to get tabulated in the upcoming Portland City Council elections. In each district, there will be three winners, but there aren't three separate races. Instead, a gigantic cast of bobbleheads is thrown at the hapless voters, and the results are to be determined using a most peculiar version of "rank choice" voting.
The whole thing is ridiculous, but the game has begun. And before anybody plays along, they ought to know the rules. I'm trying.
And I'm not getting too far before becoming stuck. The following is as far as I've been able to penetrate. I may not have even this little bit right. Those in the know, please correct me where I'm wrong.
Here's my hypothetical situation. 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:
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.
Okay, here's where it starts to get a little batty. Apparently the next thing that happens is that because CA had "surplus" votes – more than the 251 it took to win – some of 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.
At this point, this is all so ridiculous that I want it repealed. But I soldier on, because I want to understand it. Stupidity can be fascinating.
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 these numbers and on a 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:
Notice that of the 260 CA fans, 25 of them didn't rank a second choice. That's their prerogative, and in Portland, it's important not to rank anyone that you don't want to win. If they're terrible, leave their row blank!
Given the results in this second table, the lowest vote-getter, CG, now gets eliminated, and CG fans' next-choice votes, for anybody other than CA, get added to the total for those later-choice candidates.
But here's where I get stuck, and I have a couple of questions. When we go to this next step and transfer the CG lower-ranked choices, do CB, CC, CD, CE, and CF get to keep the transferred votes from the CA "surplus"? And does the CA "surplus" that got transferred to CG now get transferred to CB, CC, CD, CE, and CF as a result of the CG elimination?
If anybody knows, please clue us all in.
* * * * * * * * * *
But even at this point, notice that a CA fan has essentially voted more than once, whereas the other six candidates' fans have not. This is "democracy"?
Look at it this way: If CA's first-choice vote is way over the threshold, the second-choice votes of the fans of any other candidate might not count. If you can stand it, picture the result under this alternative set of facts: CA gets 500 votes out of 1,000, and so every CA fan's second choice is worth almost half a vote.
In the meantime, I think I've found an error on the county elections website regarding a different issue. But I'll keep that one under wraps for now. One mess at a time.
I’ve seen about a dozen “real” simulations. In EVERY case, the top 3 in the first round end winning overall. Makes the whole ranking thing seem like a silly waste of time.
ReplyDeleteIn the last simulation shown here, the no. 3 first-choice vote getter loses to the no. 4.
DeleteThanks for publishing these and working through them.
ReplyDeleteI don't really follow you though on how you got to 251 - 25 percent. If I divide the total number of votes which is 1,000 by three people seeking those votes, I get 333.33. Clearly that's an evenly divided vote count and doesn't make sense but I just don't understand how you got to 251 etc.
Wasn't my idea. Those are the rules set by the clowns in the charter commission car. Where they got their marching orders from, I'll never know, but it sure wasn't from anywhere in Oregon.
DeleteIt’s not hard to figure out if you approach it with an open mind. If three seats are available, and If three people get 25%+1 votes each, then the most that the next candidate can garner is 25%-3 votes — so for practical purposes, you say that the threshold for winning a seat is 25%. If you seated four candidates instead of three, the threshold would be 20%+1 vote (i.e., 100/(N+1) seats).
DeleteHere's what evveryone forgets: it's 25% of the TOTAL vote...which means that the computations will keep skittering around as the votes come it. In a previous election, the USPS fell down onn the job and final votes were very late. But the county will be updating its returns every day at 8PM...and elections head Scott says that canndidates leading in those reports might change day to day.
ReplyDeleteAs he says, the county does not declare "winners." Media--god help us--does. The county only counts votes. As for the mathematical gyrations above, one question to ask of the county's vote-counting software: is it "open source?" Can any citizen actually see the algoritm that will be fractionating the "surplus" votes?
Finally, thanks to Jack for mentioning the mantra: if you don't want someone to win, don't rank them. First mentioned in...why bother with the citation.