Signature Verification Sampling Compared: California’s 3% Random Sample and Colorado’s 5% Random Sample

Two states, two sampling designs, one question: what does a sample actually prove?

When a referendum or initiative petition is filed, the elections official does not begin by reading every signature. The first operational decision is how many signatures to check, and what to do with the result. That decision is a sampling design problem, and the two most instructive examples are California’s 3% random sample and Colorado’s 5% random sample. They look similar from a distance. Up close, they differ in projection formula, duplicate treatment, and what happens when the estimate lands near the qualification line.

This is not a question of which state is stricter. It is a question of what each rule does when the margin is thin, and what each jurisdiction publishes so the projection can be audited.

California: the projection formula is written down in regulation

California’s random-sample methodology is set out in Title 2, Division 7, Chapter 5 of the California Code of Regulations, sections 20510 through 20540. The regulation is unusually explicit, which makes it useful for anyone designing or auditing a verification process.

Section 20521 defines the sample: signatures selected at random using a computerized random numbers generator, drawn so that every signature filed with the elections official has an equal opportunity to be included. The percentage sampled is set by the Elections Code section governing the petition type, not by the regulation itself.

Section 20530 then specifies the projection steps in order:

1. Identify the random sample percentage from the applicable statute and apply it to the petition.
2. Verify the signatures in the sample and count the valid ones.
3. Divide valid signatures by total sample signatures, computed as a percentage to two decimal places.
4. Multiply the raw count by that rate and round up to the nearest whole number.

Withdrawn signatures are treated as invalid if they are drawn in the sample. That matters because a signer may withdraw before filing under Elections Code sections 43, 4089, 5352, and 27304, and the regulation routes that withdrawal into the validity rate rather than excluding it from the sample.

The duplicate-signature adjustment

Section 20531 adds a step that a simple validity-rate projection would miss. The official divides the raw count by the sample size to get a per-signature value, computes a duplicate weight from that value, multiplies the weight by the number of duplicates found in the sample, and rounds up. Section 20532 then subtracts that estimated duplicate count from the projected valid total.

The effect is asymmetric. A duplicate found in the sample does not merely count as one invalid signature; it is weighted to estimate duplicates across the whole petition. The regulation’s worked example in section 20540 shows the arithmetic: a raw count of 24,034, a 3% sample of 722 signatures, 516 found valid, and 2 duplicates in the sample. The uncorrected projection is 17,178. The duplicate adjustment subtracts 2,150, leaving a projected 15,028 valid signatures.

That is a design choice with operational consequences. Proponents who treat duplicate avoidance as a compliance nicety rather than a qualification strategy are misreading the formula. Under California’s rule, duplicates are penalized at scale.

What triggers a full check

The regulation describes the projection method but does not, in the retrieved text, set the band that triggers a full count. A San Diego County Registrar of Voters informational presentation describes the operational framing for statewide petitions: a 3% random sample is checked, and the projection is compared against thresholds. If the projection falls below 95% of the required number, the petition fails. If it exceeds 110%, the petition is successful. If it lands between 95% and 110%, a full check is triggered, every signature is verified until the required number is reached, and processing adds up to 60 days.

That presentation is a county informational document, not the statewide regulation, and it states on its face that it does not have the force of law. Treat the 95%–110% band as the operational description a county publishes, not as a citation to the Elections Code. The statutory basis for the 3% sample and the full-check trigger sits in Elections Code sections 9030 and 9031, which were not retrieved for this article and should be read directly before relying on the band as a statewide rule.

The design logic, however, is clear enough to state: a full-check band is a practical response to sampling uncertainty. It routes close cases to a complete count instead of letting a projection decide a narrow outcome. The cost is time. The San Diego presentation puts the added processing at up to 60 days, which can move a measure past a ballot deadline.

Colorado: a 5% sample reported against a 110% threshold

Colorado’s published record of a 2021 initiative shows the same basic architecture with different parameters. The Secretary of State’s November 18, 2021 release on Proposed Initiative #31, the state income tax rate reduction measure, reports that the petition submitted 215,365 signature lines and needed 124,632 valid signatures to qualify for the 2022 general election ballot.

The release states that the Elections Division reviewed a 5% random sample and projected 148,189 valid signatures, which it described as greater than 110% of the required number. The sample itself was 10,769 signature lines, with 7,410 accepted and 3,359 rejected. The release reports a projected percentage of required valid signatures of 118.90%.

The release cites Article V, Section 1(3) of the Colorado constitution and section 1-40-116 of the Colorado Revised Statutes as the governing requirements. Those provisions were not retrieved in full for this article, so the precise statutory language of the 5% sample and the 110% threshold should be read at the source before being relied on as a general rule. What the release does establish is how the projection was reported: as a percentage of the required number, alongside the raw sample counts, so a reader can see both the inputs and the conclusion.

Why the reporting format matters

A projected valid-signature count alone is hard to audit. A projected percentage of the required number, paired with the sample size and the accepted and rejected counts, lets a reader reconstruct the arithmetic. Colorado’s release does that. The 7,410 accepted out of 10,769 sampled is a validity rate of roughly 68.8%, and applying that rate to the 215,365 submitted lines produces a projection in the range the release reports. The public can check the work.

That is a design feature worth naming. Sampling rules differ in their formulas, but they also differ in what they publish. A jurisdiction that releases only a yes-or-no sufficiency statement gives the public less to verify than one that releases the sample counts and the projection.

Comparing the two as sampling designs

The headline numbers, 3% and 5%, are the least interesting part of the comparison. Sample size affects precision, but the operational behavior of each regime depends on three other choices.

1. What the sample is projected against

California’s regulation projects a raw valid-signature count and then applies a duplicate adjustment. Colorado’s release reports a projected count and a percentage of the required number. Both approaches answer the same question, whether the petition clears the threshold, but they present the answer differently. A percentage-of-required framing makes the margin legible; a raw-count framing makes the arithmetic auditable step by step.

2. How duplicates are treated

California’s regulation weights duplicates found in the sample and subtracts the estimate from the projection. The retrieved Colorado release does not describe a duplicate-weighting step, and the statutory text was not retrieved, so no comparison of duplicate treatment should be asserted beyond what each source states. The safe observation is that duplicate handling is a design variable, and a jurisdiction that weights duplicates is making a different choice from one that does not.

3. What happens near the threshold

A full-check band is the mechanism that converts a statistical estimate into a complete count when the estimate is close to the line. The San Diego presentation describes such a band for California. The Colorado release describes a projection above 110% of the required number, which cleared the threshold without a full check. Whether Colorado has an equivalent intermediate band, and what triggers it, depends on section 1-40-116 and the constitutional provision, which should be read directly.

Practical implications for proponents and officials

Three operational lessons follow from the retrieved sources, stated as interpretation rather than as findings.

Duplicates are a qualification risk, not a paperwork issue. Under California’s formula, duplicates found in the sample are weighted and subtracted from the projection. A campaign that submits a large cushion of signatures but tolerates duplicates is exposing that cushion to a multiplier. Circulator training and pre-submission review are cheaper than a full check.

Withdrawals count against the sample. California’s regulation treats a withdrawn signature drawn in the sample as invalid. Proponents should track withdrawal requests before filing, because each one that lands in the sample reduces the validity rate.

A full check is a schedule risk. The San Diego presentation puts the added processing time at up to 60 days. For a measure aimed at a specific election, a projection that lands in the intermediate band can consume the remaining calendar. The design question for proponents is not only whether they have enough signatures, but whether they have enough margin to avoid the band entirely.

Frequently asked questions

Does California verify 3% of signatures on every petition?

The San Diego County Registrar of Voters presentation states that for statewide petitions a 3% random sample is checked under California Administrative Code 20521. The regulation itself sets the methodology and defers the percentage to the Elections Code section governing the petition type. Countywide, municipal, and district petitions may be verified by random sample or full check depending on the instructions the registrar receives.

What happens if the California sample projection is close to the threshold?

The San Diego presentation describes a full check when the projection falls between 95% and 110% of the required number, with every signature verified until the required number is reached. That band is described in a county informational document, not the statewide regulation, and should be confirmed against Elections Code sections 9030 and 9031 before being relied on as a statewide rule.

How large was Colorado’s sample in the 2021 Initiative #31 review?

The Secretary of State’s release reports a 5% random sample of 10,769 signature lines, with 7,410 accepted and 3,359 rejected, producing a projected 148,189 valid signatures against a requirement of 124,632.

Why does California adjust for duplicates but the comparison is not straightforward?

California’s regulation at section 20531 explicitly weights duplicates found in the sample and subtracts the estimate from the projection. The retrieved Colorado release does not describe a duplicate-weighting step, and the statutory text of section 1-40-116 was not retrieved. The two regimes should not be described as differing on duplicate treatment without reading the Colorado statute directly.

Sources

• California Code of Regulations, Title 2, Division 7, Chapter 5, sections 20510–20540, Election Petition Signature Verification Random Sampling Verification Methodology. California Secretary of State.
• San Diego County Registrar of Voters, Petitions Process informational presentation. sdvote.com.
• Colorado Secretary of State, News Release, November 18, 2021, Proposed Initiative #31 Qualifies For 2022 General Election Ballot. sos.state.co.us.
• Colorado Revised Statutes, Title 1, Article 40, section 1-40-116, and Colorado Constitution, Article V, Section 1(3), cited in the Secretary of State release; the full text was not retrieved for this article and should be read at the source.
• California Elections Code sections 9030 and 9031, cited in the San Diego presentation; the full text was not retrieved for this article and should be read at the source.