Happy Friday to a "Majority" of You
You know the feeling when you bought a car only to realize you need to pay extra to add steering wheel?
Yes, maybe a stretch but you can imagine how you would feel: cheated. It’s like when you are a voter and they just sold you Instant Runoff Voting (IRV):
“(IRV ensures) a true majority winner” (quote from utahrcv.com)
We are all human. “All those 37% winners are, you know, undemocratic!” the salesman stares into your eyes, and you feel moderately pressured. You want to close the door on him but he persists. “Let me demonstrate to you!” The well-prepared IRV pitch unfolds. First round. Elimination. Another round, and another. Just about when your attention starts leaving for the beach—voilà!—”We have a majority winner,” the salesman proclaims.
It’s Friday - time for light-hearted reading. My co-author Warren D. Smith and I decided to indulge in “true classlessness,” as he puts it, and prepared a comic strip illustrating some of missing steering wheels of IRV. Check it out. The story has math but we won’t abandon you now, read on!
Let’s take a look at the first election example devised by that smart penguin (yes, it’s a penguin, just ignore the antennas). The notation
9 B > C> A
means that 9 voters ranked three candidates as: B (top), C (second), and A (bottom). In this tiny IRV election it so happened that voters’ rankings came only in three patterns
9 B > C> A
8 A > B > C
7 C > A > B
Now, recall how IRV works: C’s tally is smallest → C gets eliminated. The next ranked candidate on those 7 “C-top” ballots is A and so A gets 7 votes transferred from C, upping her tally to 15. Now it’s just A-vs-B and the tally is clear: A has 15 while B only 9, A wins with 62.5%. That’s a good numerical majority. We will return to this type of majority later. Well, it’s been a fine day, until we started digging. Let’s reverse all ballots (first will be last, last will be first):
9 A > C> B
8 C > B > A
7 B > A > C
Now B is eliminated, transferring 7 votes to A, making A winner 16-vs-8 . Wait what?! If A, as the best candidate, had won with 62.5% previously, should she not be the worst candidate using reversed ballots? Not with IRV. The worst candidate is the best and the best is the worst. Adding insult to injury, both are majority winners. My understanding of “majority” just got a dent.
The second penguin example relates to the question: If a consensus (aka Condorcet) candidate exists, should we not elect him? In the recent Alaska special election, Begich beat both Peltola and Palin in head-to-head comparison (always reaching majority, by definition), yet he was eliminated by IRV in the first round. In Utah’s Moab, Luke Wojciechowski defeated all five city council opponents, yet IRV did not elect him (in that race). In Burlington, VT, a Condorcet candidate did not become mayor either.
You can see growing irritation on the other penguin’s face turning into frustration as the little trouble-maker points out that a candidate can win IRV in all precincts (with “true majority” - after all, the salesman is still at our doorstep), yet lose IRV after pooling all ballots centrally. OK, I give up: Which majority was the true one?
The comic highlights IRV’s “shifty” notion of majority. But these fundamental intricacies aside, there is actually a bigger fish to fry when it gets to IRV’s majority winners. There’s a fine print (you know the one where you must squint so bad you get a headache): IRV winner reaches a majority among voters only if (1) all voters’ ballots are valid, and (2) all voters’ ballots contain complete rankings. On the other hand, quoting the Salt Lake County Clerk’s website:
Voters may rank as many or as few candidates as they like
Same sentence can be found on Alaska Division of Elections’ website. Off you go voters - do your partial rankings. Let’s be honest, who is really up for ranking all nine candidates? You either fill it out partially or you mess it up. In the previously cited Moab race, the average ranking length was 3.3 candidates out of 6 (see Table 1 in our Utah report) and none of the 16 races had all ballots complete. The problem? Partial rankings often lead to ballot exhaustion (ballots running out of candidate choices). Exhausted ballots no longer count in IRV’s last round and so while an IRV winner may achieve “majority” among ballots that survived all those elimination rounds, he may fall short of “true majority” among all voters. This happens surprisingly frequently: Peltola won with 48.4% (47.5% if you account for discarded ballots) in the infamous Alaska special election. Three out of sixteen IRV races in Utah produced a non-majority winner (see Table 2 in our Utah report). Finally, Warren reminds me to mention:
Ah, so you are saying failing to reach majority wasn’t really a frequent problem, but now we have fixed that by adopting IRV that fails to deliver majority on so many levels that even penguins go nuts?
Yes. Happy Friday!