CVRs name Baird the Ranked Robin winner, paper elects Ames: evidence account

How the sample was chosen

This seed names no sealed machine records and no published box list. This account does not show the sample was chosen before anyone could see the ballots.

The contest

Title: CVRs name Baird the Ranked Robin winner, paper elects Ames

Candidates: Ames, Baird, Cortez.

Records in this count: 20.

Ballot file: condorcet-wrong-winner

Source: Synthetic fixture: committed CVRs all rank Baird first, simulated paper all rank Ames first.

The machine's reported Ranked Robin winner is Baird, who wins every matchup on the CVRs. A hand count of the paper would elect Ames. A comparison-form assertion audit at 10% risk must go to a full hand count.

Where the records sat:

One stack of 20 records. There is no ballot manifest of sealed containers.

No container custody was supplied.

What was configured

Configuration version: condorcet-wrong-winner-ranked-robin-v1.

Configuration fingerprint (SHA-256): 6dd15194e147ec0d1f3a2e729ad800f312268159fbdf57af8d8d9df63c0892bf.

Counting rule: Ranked Robin.

Tiebreak announced: most matchups won.

Ballot rules used: Two or more marks at one rank end the ballot there; 2 ranks in a row left blank end the ballot; a candidate marked again lower down counts as a rank left blank.

Ballot file: condorcet-wrong-winner. A third party with this file can rerun the count.

Audit: Ranked Robin assertion audit (comparison form). Public seed: condorcet-wrong-winner. Risk limit 10% (used in the audit math).

Plain-language configuration (check against statute intent):

Configuration version: condorcet-wrong-winner-ranked-robin-v1

Fingerprint (SHA-256): 6dd15194e147ec0d1f3a2e729ad800f312268159fbdf57af8d8d9df63c0892bf

Election: A made-up three-candidate contest whose machine records name the wrong winner

A demonstration configuration over synthetic committed CVRs. No real election was counted under it.

The machine records name Baird the Ranked Robin winner. The simulated paper elects Ames.

Contests and candidates:

A made-up three-candidate contest, machine records wrong (condorcet-wrong-winner): Ames; Baird; Cortez.

Counting rule: Ranked Robin.

Tiebreak when nobody wins every matchup: most matchups won.

Ballot rules (how marks become a ranking):

Two or more marks at one rank: the ballot counts up to that rank and no further.

A candidate marked again lower down: that rank counts as a rank left blank.

2 ranks in a row left blank: the ballot counts up to there and no further.

A mark for anyone not on the ballot: a mark, so the rank is not blank, but never a vote.

Audit risk limit: 10%. A risk-limiting audit that runs under this configuration stops when the sample confirms the outcome at that limit, or sends the contest to a full hand count.

How a ballot is counted and how an audit stops are fixed by this version. Changing any of the lines above requires a new version id.

The count

What follows is the counting account under Ranked Robin, including every intermediate step.

What was counted

Ballots in this count: 20.

Ballots from: Synthetic fixture: committed CVRs all rank Baird first, simulated paper all rank Ames first.

The machine's reported Ranked Robin winner is Baird, who wins every matchup on the CVRs. A hand count of the paper would elect Ames. A comparison-form assertion audit at 10% risk must go to a full hand count.

How the marks on a ballot were read:

Two or more marks at one rank: the ballot counts up to that rank and no further.

A candidate marked again lower down: that rank counts as a rank left blank.

2 ranks in a row left blank: the ballot counts up to there and no further.

A mark for anyone not on the ballot: a mark, so the rank is not blank, but never a vote.

The rankings the ballots form, and how many ballots form each. A candidate a ranking does not name is ranked last on those ballots.

Head to head

Every candidate is set against every other. A ballot counts in a matchup when it ranks one of the two above the other. A candidate a ballot never ranks is ranked last on that ballot, tied with every other candidate it never ranks, so such a ballot has no preference between them.

Outcome

Matchups won: Baird 2 of 2; Ames 1 of 2; Cortez 0 of 2.

Baird is elected because more voters prefer Baird to each of the other candidates than the other way round.

Records with no mark, by contest and by machine

At the close of polls, the share of records with no mark in each contest, by contest and by machine. Leaving a contest blank is a voter's right; an outlier below is a question about the ballot or the machine, not a verdict.

The audit

This is the Condorcet-winner assertion audit in Blom, Stuckey, Teague, and Vukcevic, Risk-Limiting Audits for Condorcet Elections (2023), section 3, in comparison form. Each assertion is the Kaplan-Markov product (Lindeman and Stark 2012 III.B; Stark 2010 super-simple comparison) for the pairwise assorter. It is not an instant-runoff / RAIRE audit.

A Ranked Robin contest whose unique winner W beat every other candidate is confirmed by k = n-1 pairwise assertions "W beats C". Here n is 3 and k is 2.

Overall risk limit 10% (0.1). Each assertion is a Kaplan-Markov test at that same 10%. The contest confirms only when every assertion has a P-value bound at most 0.1. A wrong Condorcet winner falsifies at least one assertion, so the chance of confirming it is at most 10%. That is the SHANGRLA intersection of assertions, not a Bonferroni split of the risk across the k tests.

A risk-limiting audit does not prove the outcome is right. It has a large chance of forcing a full hand count when the outcome is wrong. If the outcome is right, this test cannot change it.

Reported Ranked Robin winner: Baird. Condorcet winner on the committed CVRs: Baird.

Ballots N (every committed CVR, including those with no pairwise preference): 20. Max overstatement per ballot u = 2. Inflator gamma = 1.03905. Diluted margin m for an assertion W vs C is computed from the committed CVRs: m = (nW - nC) / N, where nW is CVRs ranking W above C, nC the reverse, and N includes no-preference. U = 2 gamma / m.

Each draw multiplies that assertion's P-value bound by (1 - 1/U) / (1 - o / (2 gamma)). Stop an assertion when its bound is at most 0.1. Stop the contest and count every ballot by hand when any assertion cannot confirm (remaining ballots cannot save it, a 2-vote overstatement pattern blows the bound, or the draw cap is hit without confirming).

Ranked Robin matchups on the committed CVRs:

Assertions (margins from the committed CVRs):

Public seed: condorcet-wrong-winner

A sealed CVR commitment was not required or verified for this account. Do not read this run as proof the CVRs were fixed before the seed.

Ballot 1 is the first CVR. One shared sample with replacement, SHA-256 of "seed,draw,attempt" mapped onto 1 through 20. Each draw is classified for every unfinished assertion.

The hand read of each drawn ballot is simulated from the per-ballot paper ranking on the fixture (the CVR ranking, when paper is omitted). That is a fixture, not a sealed container. A live audit replaces each simulation with a person reading the paper at that place.

Ballot manifest:

No container custody was supplied.

Draws (CVR pairwise read, paper pairwise read, overstatement o, running P-value bound per assertion):

Per assertion:

At least one assertion cannot confirm at this risk limit, so the audit stops sampling and every ballot is counted by hand. The full reading follows.

The full hand count

The sample could not confirm Baird at the 10% risk limit.

The record read here is the paper held for each of the 20 ballots, not the machine records the audit was comparing them against.

Ballots read: 20.

The reading counts them under Ranked Robin, the rule this contest was counted under. What follows is that reading, step by step, so a reader holding the published ballots can rework it.

Each paper is read from the record file, as the sampled papers were. That is a fixture, not a sealed container. A live hand count replaces every one of these readings with a person reading the paper.

The full hand count: what was counted

Ballots in this count: 20.

How the marks on a ballot were read:

Two or more marks at one rank: the ballot counts up to that rank and no further.

A candidate marked again lower down: that rank counts as a rank left blank.

2 ranks in a row left blank: the ballot counts up to there and no further.

A mark for anyone not on the ballot: a mark, so the rank is not blank, but never a vote.

The rankings the ballots form, and how many ballots form each. A candidate a ranking does not name is ranked last on those ballots.

The full hand count: head to head

Every candidate is set against every other. A ballot counts in a matchup when it ranks one of the two above the other. A candidate a ballot never ranks is ranked last on that ballot, tied with every other candidate it never ranks, so such a ballot has no preference between them.

The full hand count: outcome

Matchups won: Ames 2 of 2; Baird 1 of 2; Cortez 0 of 2.

Ames is elected because more voters prefer Ames to each of the other candidates than the other way round.

The outcome the record supports

The full reading of the record elects Ames. That reading is the outcome that stands, in place of the reported winner Baird. Outcome status: full-hand-count. The audit sent the contest to a full hand count of the record; the hand count, not the machine total, is the outcome.

What was found

Decision: full-hand-count.

Every draw whose paper disagreed with its machine record (overstatement o not 0):

Custody: none supplied. No container custody chain was recorded or verified.

Why it stopped

Decision: full-hand-count.

The sample could not confirm Baird at the 10% risk limit.

The full reading of the record elects Ames. That reading is the outcome that stands, in place of the reported winner Baird. Outcome status: full-hand-count. The audit sent the contest to a full hand count of the record; the hand count, not the machine total, is the outcome.