Approval voting in Fargo North Dakota, St.Louis Missouri, and versus IRV

1. Fargo

is the largest city in North Dakota. In a referendum held 6 November 2018, Fargo decided to change their electoral system from plurality to approval voting. Fargo thus became the first city in the USA to enact Approval. The vote was 30092 in favor of switching to approval versus 17282 against (64-36% among valid ballots). This was a "landslide" margin, greater than the biggest margin in USA presidential election history.

Text of the referendum-wording (image from actual ballot).

Fargo then held its first elections (to replace 2 of its 4 city commisioners) with the new system on 9 June 2020. The 2 winners John Strand and Arlette Preston were announced that same day.

Fargo's first mayoral election with the new system came on 14 June 2022. There also were 15 candidates running for the two open Council seats, won by Denise Kolpack and Dave Piepkorn with 42.5% and 38.7% approval, respectively. (Mean #approvals per voter: 3.07.)

But we'll only discuss the Mayoral race. It involved 7 candidates on ballot, exceeding Fargo's previous record high 6. Dr. Tim Mahoney won (re-elected) despite his rival Shannon Roers Jones dwarfing the other mayoral candidates in fundraising with almost $121,000. (The next biggest fundraisers in the mayoral race were Dabar with about $32,000 and Mahoney with about $29,500.) The previous time Mahoney had run for mayor, he'd been unopposed.

This seems to have been a success. Election results were announced the next day. The mean number of approvals 1.59 was compatible with, say, 41% approve-1 and 59% approve-2 ballots (not that I am claiming that was the distribution; I do not know the distribution and it also could have been, e.g, 60%, 21%, and 19% for approve-1, 2, and 3) which was considerably greater voter expression than old plurality-style voting for only 1. It was enough to get Mahoney majority-approval, a feat achieved by nobody else. If the voters regarded the election as a race between Mahoney, Preston, and Roers Jones with the other 4 regarded as clearly worse and without hope of winning, and with the "Big Three" having random numbers (sampled independently from some even-symmetric density) as utilities, then the voters' optimum strategy would be to approve the above-average among the "big three" i.e. 1.5 approvals per voter on average (and always either 1 or 2). If, however, it was "big four" not "big three," then optimum voting strategy would involve 2 approvals per voter on average and always 1, 2, or 3. These oversimplified models of Fargo's situation in fact produced predictions corresponding decently to reality (namely 1.59) suggesting Fargo's voters "got smart fast" about how to approval-vote intelligently.

The hope that approval would decrease the influence of cash on elections (by decreasing the usefulness of – through very expensive "conspicuous consumption" – showing you "had among the top 2 best chances to win" to convince voters that plurality-style votes for you would not be "wasted") seems validated by the fact the big money was not generating big approval.

The hope that approval would inspire more candidates to enter the race was validated by this being the greatest number (7) in Fargo history.

2. St.Louis

The Ballot question: "Shall the City of St. Louis adopt an ordinance to:

• establish an open, non-partisan system for elections to the offices of Mayor, Comptroller, President of the Board of Aldermen, and Alderman
• enable voters to choose all the candidates they wish in the open, non-partisan primary
• allow the top two candidates to then compete in a runoff general election?"

There also was a more detailed write-up not printed on the ballot, but available to referendum voters.

St.Louis's first election witb the new system came on 2 March 2021. The mayoral primary via approval voting was to choose two finalists from a field of four candidates. Reed had raised the most money as of 22 Feb. with over $531,000, followed by T.Jones ($456,000) and Spencer ($432,600), with A.Jones far behind with only $19,468, most of it contributed by himself. The approval primary's winners were Tishaura Jones and Cara Spencer. Jones then won the 6 April general election over Spencer by 30166-27865, thus becoming St. Louis' first African-American female mayor. The 44571 voters approved an average of 1.56 candidates. That was enough to get Jones majority-approval, a feat achieved by nobody else, correctly making it seem likely she'd win the later general election. The results were announced the next day:

Again this seems to have been a "success," based on the same reasons as Fargo.

If the 4 candidates had had random numbers (selected independently from an even-symmetric density) as their utilities for each voter (an ultra-simplified model of the situation) then that voter's optimal strategy would have been to approve the candidates with above-average utility, which on average would be 2 approvals per voter. If however the "big three" were regarded by voters as having such random utilities while A.Jones was regarded by all voters as clearly less desirable and with no hope to win, then the optimum approval-voting strategy would be to approve the above-average members of the big three, while leaving A.Jones unapproved. Then you'd be approving only 1.5 candidates, on average. These predictions by over-simplified models in fact correspond well to what actually happened, which was 1.56 approvals per voter on average. So it would appear that St.Louis voters "got smart" about approval voting fast – at least based on this single election-datapoint.

3. Some confused and wrong propaganda spread by Steven Hill (and Don Saari...) about "bullet voting"

Hill in 2022 wrote, in an attempt to influence Seattle-2022 voters against approval by attacking the success of Approval Voting in Fargo:

For Fargo's mayoral election in June 2022, an opinion poll estimated that 60% of voters "bullet voted" (i.e. approved exactly one), despite there being seven candidates – meaning voters could vote up to seven times, once for each of those seven candidates – voters approved an average of just 1.5. [Actually it was 1.59, Hill rounded wrong.]

Hill then continued, trying similarly to attack St.Louis:

In St. Louis, we see a similar story. For its mayoral primary in March 2021 using approval voting, two finalists were selected from a field of four candidates. In the old pre-approval system, voters had a single vote. But in the approval voting election, despite voters having four approvals to use, voters approved an average of only 1.6 candidates. [This time Hill rounded 1.56 correctly.]

Then Hill helpfully explained what he claimed was the reason for that:

Another study found that 24% of voters said that the reason they approved of only one candidate was because they feared that voting for more than one would hurt their favorite candidate's chances. Fargo candidates quickly figured out this bullet voting dynamic, because it just makes practical sense when running under the rules of approval voting. So candidates began instructing their voters accordingly. Incumbent mayor Tim Mahoney during his reelection campaign said "I would probably bet that every candidate says just vote once." One of his challengers, Republican state representative Shannon Roers Jones, agreed saying, "It will be important for me to convey to people... that the most effective way to elect the person they care about is to vote only for that person." Election administrator Mike Montplaisir, who runs Fargo's elections, said that he also "voted for only one candidate – the candidate I wanted to win – because voting for anyone else is like taking a vote away from [my first choice]." He added, "You can game the system."

Those quotes demonstrate that Steven Hill, in addition to being a professional propagandist, also is an idiot. The reality is that we understand correct approval-voting strategy quite well and have for 40 years. Hill, however, never learned that, since reading and understanding voting theory just is not what he does.

And that correct theory tells us that sometimes "bullet voting" is a strategically good idea, and sometimes it is not. For example, suppose you, as a Fargo voter, liked Dabar best and Mahoney 2nd best. Were you well advised by the "experts" Hill and Montplaisir to approve Dabar only? Of course not. That would be the act of an idiot. Dabar had virtually no chance to win. The real battle was between Mahoney and Preston; and by following Hill's completely wrong advice you would merely idiotically sacrifice nearly 100% of your power as a voter to decide the election winner.

On the other hand, if your favorite candidate was Mahoney or Preston (presumably true for roughly 61% of Fargo's voters), then "bullet voting" could well have been a strategically-sensible move.

Fortunately, the voters in Fargo and St.Louis were smarter than those so-called experts, i.e. Fargo ignored their wrong advice and instead cast ballots which, at least as far as I can tell from the aggegrated statistics, closely resemble optimal approval-voting strategy. (If I had the full ballot-set, which I do not, then I could analyse this matter more deeply.)

The correct theory tells us that the strategically-correct number of "hoper" candidates for a voter to approve is on average going to be about C_hope/2 or a bit less, where C_hope is the number of candidates with realistic hopes to win. Plus, if there are "no-hopers" you prefer over the expected value of the winner among the hopers, approve them too. In Fargo C_hope≈2 to 3, so we expect an average voter to approve 1 to 1.5 hopers, plus all the no-hopers they like best (if any), which would add at least 0.4 approvals per voter on average. In net we expect (1 to 1.5)+0.4 approvals, i.e. 1.4 to 1.9. And in fact Fargo delivered 1.59 approvals per voter, entirely as expected. In short: Hill produced no evidence whatever that anything went wrong in Fargo. He merely cast aspersions to sow fear and doubt (a classic propaganda technique) but with no legitimate underlying basis for them.

And did anything go wrong in Fargo? No. Fargo produced one winner – Mahoney – with a massive landslide 65% approval rate, and all his rivals had ≤35% approval each, i.e. a massively clear demonstration that Mahoney was the right winner while the others were not. Approval Voting succeeded in making that essentially as massively clear as we could possibly hope for.

The fact that 1.59 was about the "right" average number of approvals per Fargo voter was demonstrated by this success. If all voters had, say, cast only 1 approval as Hill foolishly recommended, then we probably would have wound up with Mahoney getting about 41% approval and still winning, but it would not have been massively clear Mahoney was the "right" winner because neither he nor anybody else would have enjoyed majority support. If Fargo had gone in the other direction with, say, 2.5 approvals per voter, then we likely would have wound up with two majority-approved candidates, in which case, again, it would have been less-clear Mahoney was the right winner.

In St.Louis (for which as a 2-stage "approval plus 2-woman-runoff" election, actually the plain-approval strategy-theory did not apply, but this process was approximated by plain approval – especially since the runoff had "no effect," i.e. merely re-delivered the same winner as stage 1 – hence its strategy also was approximately the same) C_hope again was 2 or 3, and the theory predicts 1 to 1.5 approvals per average voter for "hoper" candidates, plus another 0.14 additional approvals per voter for the no-hoper A.Jones (plus some for the no-hoper Reed, if you, rather debatably, consider him a no-hoper). Again, the reality (1.56) agreed fine with the prediction (1.14 to 1.7). And again the fact that 1.56 was about the "right" average number of approvals per St.Louis voter was demonstrated by this success of St.Louis in producing exactly one majority-approved winner (T.Jones with 57%) with all her rivals getting ≤46% each.

Again, Approval Voting succeeded in making the "correctness" of its winner essentially as massively clear as we could possibly hope for, and the reason it did so was because the St.Louis voters approved just about the optimally right average number of approvals per ballot. If they'd approved 1.08 times more, or 1.14 times fewer, then St.Louis would not have enjoyed a unique majority-approved winner, and that clarity would have been lost.

Notice: in both Fargo and St.Louis, the voters automagically optimized their average number of approvals with ±3% or better relative accuracy! Impressed? I am.

Approval voting, if the voters employ optimum strategy, automatically tends to produce a unique majority-approved winner. (We warn you this is only a tendency, not a guarantee. But it worked in Fargo & St. Louis.) This fact (which is a consequence of the theory) allows you to tell almost immediately whether the voters in any given approval-voting election cast about the right average number of approvals, or whether they were fools like Hill.

Fargo and St.Louis' voters just naturally exhibited nearly optimal behavior, despite all the wrong advice Hill et al tried to spoon-feed them.

To summarize: Hill's entire complaint here was wrong-headed. If he'd ever read approval voting theory he'd have known that 40 years before he unwisely opened his mouth. And then the facts in Fargo and St.Louis conclusively refuted Hill's wrongness. Which he was too stupid to notice even then. This all is a success for Approval, and Hill in no way even came close to demonstrating anything wrong. All he did was sow fear and doubt. (But probably that was his goal, as opposed to any sort of voter education or theoretical or experimental correctness.)

4. Is Approval Voting more popular than Instant Runoff in USA?

Those landslide 64-36 and 68-32 margins for enacting approval in the USA's first two referenda on the matter ever (mean 66-34) are quite reassuring. It is interesting to compare them versus large referenda held contemporaneously in the USA trying instead to enact Instant Runoff Voting (IRV) or variants.

This is not enough data for statistical significance, but as far as it goes it suggests approval voting is more popular than the largest popular-vote-margin (24%) US presidential victories ever, which in turn are more popular than IRV, which finally is about equally popular as the average US presidential victory margin of 10.5% during 1920-2020.

And there is evidence that 10-level score voting would, if offered, be even more popular than approval.

5. Seattle

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