A made-up three-candidate plurality contest: 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 plurality contest

Candidates: Ames, Baird, Cortez.

Records in this count: 1,000.

Ballot file: plurality-3

Source: Invented for this package. No real election.

Ames has 450 first choices (45%), Baird has 350 (35%), Cortez has 200 (20%).

Nobody has a majority, but Ames has a plurality. Used to test BRAVO ballot polling.

Where the records sat:

One stack of 1,000 records. There is no ballot manifest of sealed containers.

No container custody was supplied.

What was configured

Configuration version: plurality-3-plurality-v1.

Configuration fingerprint (SHA-256): 407e032fbe141e10dd87d95b6534df90ba9e1daa2ee7e41fb2ee83cedf010917.

Counting rule: plurality.

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: plurality-3. A third party with this file can rerun the count.

Audit: ballot-polling risk-limiting audit. Public seed: plurality-polling. Risk limit 10% (used in the audit math).

Plain-language configuration (check against statute intent):

Configuration version: plurality-3-plurality-v1

Fingerprint (SHA-256): 407e032fbe141e10dd87d95b6534df90ba9e1daa2ee7e41fb2ee83cedf010917

Election: A made-up three-candidate plurality contest

A demonstration configuration over committed fixture records. No real election was counted under it.

Audit risk limit is the 10% limit this package uses for risk-limiting audits; it is not a claim about any statute.

Contests and candidates:

A made-up three-candidate plurality contest (plurality-3): Ames; Baird; Cortez.

Counting rule: plurality (most first choices).

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 plurality, including every intermediate step.

What was counted

Ballots in this count: 1,000.

Ballots from: Invented for this package. No real election.

Ames has 450 first choices (45%), Baird has 350 (35%), Cortez has 200 (20%).

Nobody has a majority, but Ames has a plurality. Used to test BRAVO ballot polling.

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 count

Each ballot counts once, for the candidate it marks first.

Ballots counting for a candidate: 1,000.

Ballots marking no candidate: 0.

Ballots stopped by two or more marks at their first rank: 0.

Ames is elected with 450 first choices, more than any other candidate.

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 ballot-polling audit in Lindeman, Stark, and Yates, BRAVO: Ballot-polling Risk-limiting Audits to Verify Outcomes (2012). Risk limit 10%. It tests pairwise assertions for a plurality winner without a majority.

A plurality contest whose reported winner W does not have a majority is confirmed by k = n-1 pairwise assertions "W beats C" against every opponent C. Here n is 3 and k is 2.

Overall risk limit 10% (0.1). Each assertion is the 2012 Wald SPRT at that same 10% (confirm when T is above 9.9, full hand count when T is below 0.011). The contest confirms only when every assertion confirms. A wrong plurality 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 plurality winner: Ames, with 45.00% of 1,000 valid votes.

Tolerance t: 1.00%.

Plurality first choices on this file:

Assertions:

Multiply an assertion's T by the winner factor when the ballot votes for the winner, and by the loser factor when it votes for that opponent. A ballot voting for another candidate or showing no valid vote leaves that T unchanged. T starts at 1.

Public seed: plurality-polling

Ballots in the file: 1,000. One shared sample with replacement, SHA-256 of "seed,draw,attempt" mapped onto 1 through 1,000. Each draw is classified for every unfinished assertion.

The hand read of each drawn ballot is simulated from the ballot file. 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 (invalid ballots or votes for other candidates leave each unaffected T unchanged):

Per assertion:

Every assertion has T above 9.9, so the audit stops. The sample is strong evidence that a full hand count would elect Ames. 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.

This is a polling-form audit. It does not compare machine records to paper, so there are no CVR discrepancies to list.

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

Why it stopped

Decision: confirmed.

Every assertion has T above 9.9, so the audit stops. The sample is strong evidence that a full hand count would elect Ames. The outcome stays. Outcome status: audit-confirmed. A risk-limiting audit on the record confirmed this reported outcome at the stated risk limit.