"Best is Worst" problem with Seattle's 2022 proposal for "top 2 IRV open primary"

by Warren Smith, Oct 2022.

Seattle in 2022 proposed ("ballot proposition 1B") this system:

1. a "primary" election would be held using rank-order ballots (every voter permitted to rank every candidate regardless of party) to select two winners via an Instant Runoff (IRV) procedure.
2. Those two then would compete against each other is a later "general election" to elect just one of them.

The Instant Runoff procedure is: The candidate with fewest top-rankings is eliminated, reducing a C-candidate election to C-1. We then eliminate again to reach C-2, and so on, until only 2 candidates remain: Seattle's two primary-winners.

Now let's look at an example of that process in action. There are 20 voters and 4 candidates named "A," "B," "C," and "D." Here are the rank-order ballots:

C has the fewest top-rankings (1, as opposed to D=3, B=7, A=9) hence the IRV procedure eliminates C. Next, D has the fewest top-rankings (3, as opposed to A=10, B=7) so IRV next eliminates D. We are left with a perfect 10-10 tie between A and B, and the general election contenders thus are A and B.

The proponents of this IRV² primary system contend these two candidates A and B are (by far) the two best choices for Seattle, while C and D therefore are its two worst choices. Wonderful: Seattle gets good leaders, namely A or B.

But now let's investigate what would happen if all 20 voters reversed their preference orders. They sadly are now ordering their four choices worst-first instead of best-first. Hence then the IRV process presumably sadly will pick the two worst choices for Seattle. The reversed rank-order ballots:

Now the IRV process eliminates D, then C, again leaving a perfect 10-10 tie between A and B for "first" place.

The proponents of this IRV² primary system contend these two candidates A and B are (by far) the two worst choices for Seattle, while C and D therefore are its two best choices. This would be terrible: Seattle would get bad leaders, namely A or B.

Wait. What?

This bass-ackwards example – and this sort of phenomenon seems entirely realistic – shows one way Seattle's proposed IRV² primary system can contradict itself. As you can see, it can equally well deliver the two best choices for Seattle, or the two worst, to the general election, with no clue which is which.

If my election system delivers sub-optimal winners, I at least want to hope they aren't going to be the worst. But then if that same election system itself says they are the worst, but crams them down my throat anyway, that's really a bit much.

Good luck with that, Seattle!

You might want to decide who you think should be the 2 winners in the original election. If you care about my personal opinion, it is: the best pair actually would have been A & D, and the worst B & C. The "Pairwise preference matrix" is

showing that each member of {A,D} beats each member of {B,C} by at least a 12:8 majority, except that A doesn't "beat" B, but rather merely is pairwise-tied 10:10 with B. (Also A is pairwise-tied with D, and B with C.) No other candidates besides A and D enjoy this "beats or ties all others" property.

My view also is supported by the fact "Borda scoring" ranks the candidates in this order: D>A>B>C with scores D=41, A=35, B=28, C=19. Also, if we were to employ "approval voting" where each voter "approved" her top two candidates and disapproved her bottom two, then A+D would get 29 approvals, more than any other pair.

One reason IRV was unable to realize all that was the fact IRV always massively ignores much information on the ballots, while Borda and the Pairwise Matrix do not. This was a 2-winner example of IRV reversal failure.

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