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-instant-runoff-v1.

Configuration fingerprint (SHA-256): ae933b2937b81fc44b32662649ae3f161b7401486ad91c6d4f9b3f8c7e5e0bac.

Counting rule: instant runoff.

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: instant-runoff RAIRE assertion audit (comparison form). Public seed: condorcet-cvrs-irv. Risk limit 10% (used in the audit math).

Plain-language configuration (check against statute intent):

Configuration version: condorcet-cvrs-instant-runoff-v1

Fingerprint (SHA-256): ae933b2937b81fc44b32662649ae3f161b7401486ad91c6d4f9b3f8c7e5e0bac

Election: A made-up three-candidate Condorcet contest, one row per ballot, counted under instant runoff

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: instant runoff.

Tiebreak: not used under this counting rule.

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 instant runoff, 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.

Round 1

Ballots counting this round: 300.

Ballots counting for nobody: no candidate marked 0; ran out of rankings 0; two or more marks at one rank 0.

More than half of 300 is 151.

Ames has 180 votes, more than half of 300, and is elected.

Outcome

Ames is elected: after 1 round, 180 of the 300 ballots still counting rank Ames above every candidate left.

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 RAIRE assertion audit for Instant Runoff Voting (Blom, Stuckey, and Teague, RAIRE: Risk-Limiting Audits for IRV Elections, 2019), in comparison form. Each assertion is the Kaplan-Markov product (Lindeman and Stark 2012 III.B; Stark 2010 super-simple comparison) for the assertion assorter. It is not a Condorcet pairwise audit.

An instant-runoff contest whose reported winner is Ames is confirmed by k = 2 RAIRE assertions. Here n is 3 candidates.

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 instant-runoff 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 instant-runoff winner: Ames. Record winner on the committed CVRs: Ames.

Ballots N (every committed CVR): 300. Max overstatement per ballot u = 2. Inflator gamma = 1.03905. Diluted margin m for each assertion is computed from the committed CVRs: m = (nW - nL) / N. 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).

Assertions (margins from the committed CVRs):

Public seed: condorcet-cvrs-irv

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 read, paper 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 instant runoff. 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 instant runoff. The outcome stays. Outcome status: audit-confirmed. A risk-limiting audit on the record confirmed this reported outcome at the stated risk limit.