Hands Up Republicans - You've been RCVed!

RCV attends the 2023 Utah County Republican Convention

Turtle: “If you give me a little head start, I will win!”

Achilles: “You will surely lose, my friend.”

Zeno: “That’s a paradox!”

Schrödinger : “Stop bickering. I need the three of you to come to the polls and vote against me to make me win, as I am currently losing. Quick!”

(Excerpt from: “Schrödinger’s Voter” - a Pulitzer winning book, yet to be written and published by an author yet to be determined)

I heard news that the number of municipalities in Utah using Ranked Choice Voting (RCV) is dwindling (from 23 towns in 2021 to 12 in 2023, see references at the bottom). That’s good news for almost everyone. Looking back to 2018, I suspect that Utah’s then-governor Gary Herbert as well as key legislators were quick to adopt this 100-years-old-and-broken voting method thanks to the fact that Utah GOP has been using it in their conventions for years prior. For many, usage proves. Occasionally, I, too, hear the “been used for years” adage as a counter-argument to a host of issues RCV brings to the table. One has to wonder: has anyone looked into Utah GOP convention election data and checked them for sanity?

((Cricket Sounds))

Well, maybe what we don’t know, can’t hurt us. But time’s up for blissful ignorance: We have received ranking data from the recent Utah County Republican Convention and analyzed them in depth. Here are our findings.

In Brief

We analyzed 22 races from the Utah Republican Party convention. Of these, 19 were Instant Run-Off Voting (IRV) races (excluding 3 races that had 2 candidates). Note that IRV is a term interchangeable with RCV. Although imprecise, RCV is a term pro-IRV advocates use to popularize this counting method.

Finding #1

Out of the 19 IRV races, 9 serious pathologies were detected:

• 3 races had Non-Monotonicity Paradox, aka “more is less” paradox, in which giving more votes to a winner causes the winner lose. This paradox has been first described by Fishburn and Brams in 1984.

• 3 races had Participation Failure Paradox, aka “voters better stay at home” paradox, in which had certain voters showed up to vote against a loser, the loser would win (Fishburn and Brams, 1984). This is also why Turtle’s, Achilles’, and Zeno’s votes are helpful to Dr. Schrödinger.

• 3 races had a Condorcet Failure, aka “consensus winner loses.” Consensus winner is a candidate who defeats every other candidate in head-to-head comparison. An election method that fails to elect the consensus winner is considered undesirable.

That’s 9 out of 19. I am recalling a quote from the pro-IRV lobbyist Rob Richie (Fairvote.org) comparing the likelihood of these paradoxes with that of a meteorite striking the Earth.

Finding #2

IRV delivered two races with a spoiler. A spoiler is a candidate who is not a winner but whose dropping out changes the outcome of the election. Remember, “eliminating the spoiler effect” has been one of two major selling points pushed by the pro-IRV lobby (Utah Ranked Choice Voting and Fairvote.org). Here is what URCV website says:

and, as a reminder, the meaning of the word “eliminate”:

Yet, two spoilers were found in 19 IRV races thus disproving URCV’s claim.

Finding #3

We found percentages of invalid ballots to be considerably smaller than seen in Utah County municipal elections in 2021. This is certainly good news for voters (see discussion below).

The amount of pathologies and spoilers should rattle the GOP out of their sopor. Election outcomes are only as good as the vote counting method that produced them. Pro-IRV advocacy famously dismisses the relevance of the paradoxes as “hypothetical,” “theoretical,” and “incredibly-rare-virtually-never-happening.” If we only count the most outrageous monotonicity and participation failures, we’ve observed 6 of them in just 19 races. Including consensus failures, it is 9 in 19. Regular readers may recall that we have found 4 serious paradoxes in the 2021 Utah County Municipal IRV Elections and 2 in the Alaska special election in 2022. Why is there such a discrepancy to the lobby’s claims? Perhaps we are just the first who actually looked for them without being on a special interest’s payroll.

In the past years, GOP voters, candidates, winners as well as losers were RCV-ed into an unspoken convolution of logical paradoxes. Time to look for alternatives?

The Human Side

Before giving a little more detail below, let me transcribe the 9+2 paradoxes into plain English sentences using true candidates’ initials. Enjoy!

Non-monotonicity:

SD21 (Seat 1): Had at least 12 voters up-ranked (i.e., changed their votes in favor of) the winner WH, WH would have lost.

SD23 (Seat 2): Had at least 1 voter up-ranked winner BB, BB would have lost.

SD25 (Seat 2): Had 9 up-ranked winner CH, the winner would have lost.

Participation Failure:

SD21 (Seat 1): Had at least 27 voters showed up to bottom-rank LN (loser), LN would have won.

SD21 (Seat 2): Same as above, but this time at least 30 new LN-bottom ranking voters needed…

SD24 (Seat 1): Had at least 33 voters showed up ranking loser KG bottom, KG would have won.

Condorcet (Consensus) Failure:

SD21 (Seat 1): KC was Condorcet Winner, but WH won.

SD23 (Seat 2): LB was Condorcet Winner, but BB won.

DS25 (Seat 2): KE was Condorcet Winner, but CH won.

Spoilers (Loser-Dropout):

SD23 (Seat2): If MM dropped out, original winner (BB) would have lost to LB.

SD25 (Seat 2): BS dropping out will make original winner (CH) lose to KE.

In Depth

Congratulations your stamina are impressive, you’ve made it here without an additional penguin comic or a commercial break.

The Table below shows basic statistics of the 22 RCV races from the Republican Convention.

The data comprises 6 districts each with a varying number of seats to fill. As can be seen, these are relatively small races (column “#Candidates”). Procedurally, a single ballot is used for an entire district. To fill each seat, the IRV algorithm is run multiple times (as separate IRV races), every time removing the winner of a previous seat thus reducing the number of candidates by one (same method is used in Utah municipal elections). We record the average ballot length (if last rank position is empty we complete automatically to full-length ballot). These lengths indicate that voters tended to rank most candidates (likely motivated by the high number of seats available). As mentioned before, the numbers of discarded and impure ballots are low in comparison to those observed in municipal elections where regular voter population is involved (see Table 1 in our report as well as definition of “discarded” and “impure” there). Our understanding is that the ballot format at the Convention differed from ballots used in Utah’s municipal RCV races - perhaps this suggests an improvement is possible. Note that we have rectified single-gap (undervote) ballots as per Utah’s election code, before recording discardment and impurity rates.

The table below summarizes the findings on the counting side, including paradoxes (highlighted in red) :

Please refer to our municipal IRV technical report (pages 4-6 and Table 2) for exact definitions of each column. In 4 of the 19 IRV races the winner differed from what would have been a plurality winner. Besides the 9 serious paradoxes, the column “2nd-winner-misidentification (SWM)” may be of interest as it lists cases where a runner-up candidate for seat N does not win the next race for seat (N-1). There are 7 SWM cases. SWMs can potentially cause a voter’s vote to be cast for one and the same candidate multiple times in spite of multiple seats being filled (example: “I voted in a 2-seat election but my ballot has never been read past my first candidate in both seat races, and my candidate lost in both”), to which many object as unfair.

Conclusion

Every time real data is looked at, we become collectively wiser (whichever way things turn out). However, it is surprising that so little looking has been done so far.

“Let the Sunshine In!”

Acknowledgement

We thank Wendy Hart (Utah Election Integrity) for sharing the 2023 Convention dataset!

References:

23 towns participated in the municipal election cycle of 2021 (source: Deseret News October 26, 2021)

12 towns remain in 2023 (source:  https://vote.utah.gov/current-election-information/, Question 11)

Additional Notes:

• Some ballots IDs were duplicates (ie. non unique). For analysis, we have replaced those ballot IDs with hash strings to enforce uniqueness. This note may be relevant to those who wish to perform their own analysis.