Did the 2022 Alaska congressional special election have a Condorcet winner, who was not elected?

Question

Does anyone know if Begich may have been the Condorcet winner? Nic Tideman emailed me a few days ago, asking me this question.

I sure as hell do not know unless we can get the records of the individual ballot data for 188,582 ballots. Does anyone know where to get it?

This table shows what we know so far and what is left to learn from ballot data:

     1st choice          2nd choice
Begich   53810
                    Palin    27053
                    Peltola  15467
Palin    58973
                    Begich     ??
                    Peltola    ??
Peltola  75799
                    Begich     ??
                    Palin      ??

We need to know 4 more numbers to really understand what the voters were saying in Alaska last month.

Polling showed Begich to be preferred over Peltola by 54 to 55% of voters, and after Begich elimination, 2nd place votes transferred to both of the other candidates, so it seems likely. Alaska Survey Research has the data on whether Begich was preferred over Palin, too, but did not publish that scenario and have not responded to my email about it yet. Of course polls are not 100% accurate. — endolith, Sep 06 '22 at 15:37
FairVote says "In the coming days, Alaska will certify results and release a full cast vote record, which will tell us how Palin and Peltola voters used their rankings and much more." I wonder if they feel nervous about the release. — endolith, Sep 06 '22 at 15:42
I’ve moved the conversation about how the votes were tallied to chat as it was becoming off-topic. If there is any confusion as to how the RCV votes in Alaska are counted/reported, please ask a new question. — CDJB, Sep 08 '22 at 21:08
Ranked Pairs. https://en.wikipedia.org/wiki/Nicolaus_Tideman — robert bristow-johnson, Sep 12 '22 at 15:02

robert bristow-johnson · Accepted Answer · 2023-06-12T16:35:16.547

12

Yes.

Based on the official cast vote records for the special election, Begich would have beaten Peltola head to head 52-48, and beaten Palin 61-39. However, he had fewer 1st choice rankings than the other two and was eliminated in the semi-final round as per Hare RCV tabulation rules.

It's Burlington 2009 Redux.

U.S. Representative (Special General)
Valid ballots: 188787, Overvotes 4208, Undervotes 3502, Ranking errors 5984
irvWinner: Peltola, Mary S.       h2hWinner: Begich, Nick
irvRound:                     1         2         3
       Peltola, Mary S.     74819     75795     90884
           Palin, Sarah     58400     58824     85613
           Begich, Nick     52598     53629
               Write-in      2970
h2h Matrix:                                                         margin

results for Begich, Nick:
         Begich, Nick   87332         Peltola, Mary S.   79260        8072
         Begich, Nick  100409             Palin, Sarah   63351       37058
         Begich, Nick  132080                 Write-in   12977      119103
results for Peltola, Mary S.:
     Peltola, Mary S.   79260             Begich, Nick   87332       -8072
     Peltola, Mary S.   90884             Palin, Sarah   85613        5271
     Peltola, Mary S.  108196                 Write-in    9360       98836
results for Palin, Sarah:
         Palin, Sarah   63351             Begich, Nick  100409      -37058
         Palin, Sarah   85613         Peltola, Mary S.   90884       -5271
         Palin, Sarah  109518                 Write-in   18047       91471

edited Jun 12 '23 at 16:35

answered Sep 09 '22 at 01:18

robert bristow-johnson

1,496
10
24

4

Can you provide a link of where you found this data. – Joe W Sep 09 '22 at 02:21
2

@JoeW https://www.elections.alaska.gov/election-results/e/?id=22prim Converted to text file here: https://www.karmatics.com/voting/alaskaspecial.txt – endolith Sep 09 '22 at 15:53
2

Thank you for that update, can you edit that into the question so it is easier for future readers to find? It is really useful to see this information to understand how ranked choice impacts actual elections. – Joe W Sep 09 '22 at 15:56
1

@rbj how did you tally these? I've seen two other tallies that are broadly similar but don't match exactly. – endolith Sep 09 '22 at 17:02
(Neither 74819 nor 75795 match the 75799 in the original PDF, for example) – endolith Sep 09 '22 at 17:12
2

IOW, a Condorcet ranking of Begich > Peltola > Palin. – dan04 Sep 09 '22 at 21:19
3

@dan04 Which is called a "complete Condorcet order", I think. Burlington had one, too, and the Condorcet 2nd place candidate won there, too. – endolith Sep 09 '22 at 21:41
1

So from your numbers, 52% preferred Begich > Peltola and 61% preferred Begich > Palin (and 51% preferred Peltola > Palin)? – endolith Sep 09 '22 at 23:25
2

@endolith I did not tally these numbers. An acquaintance, Robbie Robinson, did. Those JSON files are a bitch to parse. – robert bristow-johnson Sep 11 '22 at 00:52
@robertbristow-johnson Yah everyone seems to have parsed them slightly differently, but they're all within a percentage point of each other. – endolith Sep 11 '22 at 02:49
2

@endolith When Nic Tideman passed this on to me, he said it did not include hand-counted ballots. with Hare RCV, i dunno how you can do hand-count ballots without getting their information entered into the same computer that the data of all of the other 180,000 ballots are already entered. – robert bristow-johnson Sep 11 '22 at 03:07
Do we know about November 2022? The CVR is published: https://www.elections.alaska.gov/election-results/e/?id=22genr – endolith Jan 01 '23 at 01:46

score 2 · Answer 2 · answered Sep 08 '22 at 06:55

TL;DR: It's possible that Begich was the Condorcet winner (with an overall Condorcet ranking of Begich > Peltola > Palin), but we can't know for sure without knowing everyone's second choices.

We also can't rule out the possibility of a non-transitive cycle where Begich beat Peltola, and Peltola beat Palin, but Palin beat Begich.

Assigning variables to your question marks, we get a ballot set of:

27053: Begich > Palin
15467: Begich > Peltola
11290: Begich
a: Palin > Begich
b: Palin > Peltola
58973-a-b: Palin
c: Peltola > Begich
d: Peltola > Palin
75799-c-d: Peltola

There are three pairwise contests to consider:

Palin vs. Peltola

This one is easy because it's the one that actually got counted. Peltola won, by a margin of 5240 votes.

91266: Peltola
86026: Palin

However, this contest has no bearing on whether Begich would be the Condorcet winner.

Begich vs. Peltola

The total vote count is:

53810+a: Begich
75799+b: Peltola

The result comes down to Palin voter's second choices (a and b):

Begich wins if a-b > 21989
Peltola wins if a-b < 21989

If all 58973 of Palin's first-choice voters expressed a second choice, then Begich would need at least 40482, or 68.6% of those votes, in order to win the pairwise contest.

For comparison, among voters who ranked Begich first, Palin got 63.6% of those ballots that expressed a second choice, or 60.7% of ballots if those who didn't make a second choice flipped a coin.

So Begich winning this contest would require Palin voters to have noticeably more party loyalty than Begich voters. But this would easily be explainable with a framing of Begich as a moderate candidate compared to more a more solidly right-wing Palin.

Begich vs. Palin

The total vote count is:

53810+c: Begich
58973+d: Palin

The result comes down to Peltola voters' second choices.

Begich wins if c-d > 2581.5
Palin wins if c-d < 2581.5

If all 75799 of Peltola's voters expressed a second choice, then Begich would need at least 40481, or 53.4%. This is a rather close contest, and it's hard to tell who would win.

//We also can't rule out the possibility of a non-transitive cycle// ---- ya, I know, though I think it's unlikely that very many Peltola voters would rank Palin as #2. — robert bristow-johnson, Sep 08 '22 at 14:54

Did the 2022 Alaska congressional special election have a Condorcet winner, who was not elected?

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