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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?

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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.

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2 Answers 2

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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
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  • 4
    Can you provide a link of where you found this data.
    – Joe W
    Sep 9, 2022 at 2:21
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    @JoeW elections.alaska.gov/election-results/e/?id=22prim Converted to text file here: karmatics.com/voting/alaskaspecial.txt
    – endolith
    Sep 9, 2022 at 15:53
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    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 9, 2022 at 15:56
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    IOW, a Condorcet ranking of Begich > Peltola > Palin.
    – dan04
    Sep 9, 2022 at 21:19
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    @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 9, 2022 at 21:41
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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.

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    //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 8, 2022 at 14:54

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