A made-up three-candidate Condorcet contest, one row per ballot: 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: A made-up three-candidate Condorcet contest, one row per ballot

Candidates: Ames, Baird, Cortez.

Records in this count: 300.

Ballot file: condorcet-cvrs

Source: Synthetic committed CVRs for the Ranked Robin comparison-form assertion audit. Invented for this package. No real election.

180 ballots rank Ames then Baird then Cortez, 60 rank Baird then Ames then Cortez, 60 rank Cortez then Ames then Baird. Ames wins both matchups 240 to 60, so Ranked Robin elects Ames without a tiebreak. Paper rankings are omitted, so they match the committed CVRs. This is a fixture, not a sealed container.

The grouped Alaska 2022 profile is not this file. Comparison-form needs 1:1 CVRs.

Where the records sat:

One stack of 300 records. There is no ballot manifest of sealed containers.

No container custody was supplied.

What was configured

Configuration version: condorcet-cvrs-ranked-robin-v1.

Configuration fingerprint (SHA-256): 3ba8975749c711f3b2088566f82abc9627c96767cd1beafd1b7e62fd003f570c.

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-cvrs. A third party with this file can rerun the count.

Audit: Ranked Robin assertion audit (comparison form). Public seed: 2026-08-29. Risk limit 10% (used in the audit math).

Plain-language configuration (check against statute intent):

Configuration version: condorcet-cvrs-ranked-robin-v1

Fingerprint (SHA-256): 3ba8975749c711f3b2088566f82abc9627c96767cd1beafd1b7e62fd003f570c

Election: A made-up three-candidate Condorcet contest, one row per ballot

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

Contests and candidates:

A made-up three-candidate contest (condorcet-cvrs): 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: 300.

Ballots from: Synthetic committed CVRs for the Ranked Robin comparison-form assertion audit. Invented for this package. No real election.

180 ballots rank Ames then Baird then Cortez, 60 rank Baird then Ames then Cortez, 60 rank Cortez then Ames then Baird. Ames wins both matchups 240 to 60, so Ranked Robin elects Ames without a tiebreak. Paper rankings are omitted, so they match the committed CVRs. This is a fixture, not a sealed container.

The grouped Alaska 2022 profile is not this file. Comparison-form needs 1:1 CVRs.

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: 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.

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: Ames. Condorcet winner on the committed CVRs: Ames.

Ballots N (every committed CVR, including those with no pairwise preference): 300. 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: 2026-08-29

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 300. 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:

Every assertion has a P-value bound at most 0.1, so the audit stops. The sample is strong evidence that a full hand count would elect Ames under Ranked Robin. The outcome stays. Outcome status: audit-confirmed. A risk-limiting audit on the record confirmed this reported outcome at the stated risk limit.

What was found

Decision: confirmed.

There were no CVR/paper disagreements in the sample.

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

Why it stopped

Decision: confirmed.

Every assertion has a P-value bound at most 0.1, so the audit stops. The sample is strong evidence that a full hand count would elect Ames under Ranked Robin. The outcome stays. Outcome status: audit-confirmed. A risk-limiting audit on the record confirmed this reported outcome at the stated risk limit.