Alaska 2022 · 201 — the vote math, round by round¶

You've read the plain-language 101. Now we count it exactly: the IRV transfers, the exhausted ballots, the head-to-head grid, and the two pieces of vocabulary that name what happened — Condorcet winner and center squeeze. All numbers are the reduced 200-voter model; the real election is the same story ~943× bigger.

Run it: bv2213_k3fmwv_alaska_2022.yaml · live BV counts: results ↗.

The ballots¶

Every voter's ranking, as nine groups (a "preference profile"). Read Palin>Begich>Peltola as "ranked Palin 1st, Begich 2nd, Peltola 3rd"; a single name is a bullet ballot that ranked only that candidate:

Voters	Ranking
50	Peltola > Begich > Palin
25	Peltola (only)
5	Peltola > Palin > Begich
36	Palin > Begich > Peltola
23	Palin (only)
4	Palin > Peltola > Begich
29	Begich > Palin > Peltola
16	Begich > Peltola > Palin
12	Begich (only)

200 voters. Add up the first names in each row: Peltola 80, Palin 63, Begich 57.

RCV-IRV, counted¶

Round 1 — first-choice totals:

	Votes
Peltola	80	hopeful
Palin	63	hopeful
Begich	57	fewest → eliminated

Transfer Begich's 57 ballots to each voter's next choice still standing:

Begich > Palin > Peltola (29) → Palin
Begich > Peltola > Palin (16) → Peltola
Begich only (12) → no next choice → exhausted (leaves the count)

Final round:

	Votes
Peltola	80 + 16 = 96	elected
Palin	63 + 29 = 92
(exhausted)	12

Peltola wins 96–92. Notice the denominator: 96 out of 200 ballots cast is only 48% — a "majority" of the surviving 188 ballots, not of everyone. Those 12 exhausted ballots quietly shrank the finish line. (More on that in 301.)

The head-to-head grid¶

Now the other question: every one-on-one matchup. Read each cell as for – equal – against (from the row candidate's view):

                    |    Peltola    |    Begich     |     Palin     |
        Peltola  >  |      ---      | 84 - 23 - 93  | 96 - 12 - 92  |
        Begich   >  | 93 - 23 - 84  |     ---       |107 - 25 - 68  |
        Palin    >  | 92 - 12 - 96  | 68 - 25 -107  |     ---       |

Read the Begich row:

Begich vs Peltola: 93 – 84 → Begich wins. (The right wing, plus Begich's own voters, prefer the center candidate to the left one.)
Begich vs Palin: 107 – 68 → Begich wins big. (The left wing prefers the center candidate to the right one.)

Begich wins every matchup. A candidate who beats each rival head-to-head is the Condorcet winner — the "beats-everyone," consensus candidate. Alaska had one (Begich), and RCV-IRV didn't elect him. That's a Condorcet failure.

Naming the mechanism: center squeeze¶

Why did IRV miss him? Look back at Round 1: Begich had the fewest first choices, so he was eliminated before any head-to-head mattered. The broadly-liked centrist is knocked out early precisely because "everyone's acceptable second choice" earns few firsts. That specific pattern — the middle candidate eliminated between two wings despite beating both head-to-head — is the center squeeze. It is an IRV-specific flaw: it comes from eliminating on first-choice counts, not from ranked ballots themselves.

The same ballots, four ways¶

Because the model carries scores too, we can count the identical electorate four ways:

Method	What it rewards	Winner
Choose-One (Plurality)	most 1st choices	Peltola (80)
RCV-IRV (Hare)	most 1st choices, with elimination	Peltola (96–92)
Ranked Robin	most head-to-head wins	Begich
STAR	highest scores, then a head-to-head runoff	Begich

The two methods that eliminate/count on first choices pick Peltola; the two that read the whole ballot pick the Condorcet winner, Begich. IRV is the lone method here that fails him — the center-squeeze signature. (Ranked Robin uses the same ranked ballots as IRV; only the counting rule differs.)

Challenge your understanding¶

Q1. Recompute the final round: after Begich is eliminated, where do his 57 ballots go, and what's the final tally?

Begich's ballots: 29 go to Palin (`Begich>Palin>…`), 16 go to Peltola (`Begich>Peltola>…`), and 12 exhaust (bullet `Begich` only). Final: Peltola 80+16 = **96**, Palin 63+29 = **92**. Peltola wins 96–92, with 12 ballots exhausted.

Q2. From the grid, who is the Condorcet winner, and what are the two margins that prove it?

**Begich.** He beats **Peltola 93–84** and **Palin 107–68** — a majority in each one-on-one matchup, so he beats *everyone*. That's the definition of a Condorcet winner.

Q3. Peltola "won a majority" in the final round. Why is calling her a majority winner misleading?

Her 96 votes are a majority only of the **188 ballots still active** after 12 exhausted. Against all **200** ballots cast she has **48%**. Ballot exhaustion shrinks the denominator, so IRV's "majority" can be a minority of the actual electorate — a *majoritarian failure*.

Q4. Ranked Robin uses the exact same ranked ballots as RCV-IRV, yet elects a different winner. How is that possible?

Because they *count* the ballots differently. RCV-IRV eliminates on first-choice counts round by round (which cuts Begich in Round 1). Ranked Robin instead tallies every head-to-head matchup and elects whoever wins the most — which is Begich, who wins both. Same ballots, different tabulation, different winner. "RCV" names the ballot; "IRV" and "Ranked Robin" are two ways to count it.

Q5. Which of the four methods failed the Condorcet winner, and what's the name for the pattern?

**Choose-One** and **RCV-IRV** both failed him (both elected Peltola). For IRV specifically, the pattern — a broadly-preferred centrist eliminated early on first-choice counts despite beating everyone head-to-head — is the **center squeeze**.

Ready for the hard part? 301 — the full pathology set, and is this even fair to STAR?