The Rivermont Referendum Petition
Rivermont (population 88,000; 62,400 registered voters) elects its council at large. A coalition wants to replace that with eight single-member wards and ranked-choice voting. The city charter allows citizen-initiated amendments if signatures equal 8 per cent of registered voters. The coalition filed 5,410 signatures. The clerk drew a random sample of 500 and found 71 invalid: duplicates, unregistered signers, and signers listing addresses outside the city. State law requires that if the invalidity rate in a sample exceeds 12 per cent, every signature must be checked; otherwise the sample result stands. Separately, a 2016 state statute pre-empts local changes to voting methods unless approved by the county board, and the state constitution requires "one person, one vote." The mayor wants the council to reject the petition outright on pre-emption grounds; two councillors argue that doing so would be illegitimate even if legal.
1. Compute the sample invalidity rate, determine whether a full check is required, and project whether the petition would qualify.
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Invalidity rate: 71 ÷ 500 = 14.2 per cent. That exceeds the 12 per cent threshold, so the statute requires a full check of all 5,410 signatures - the sample cannot be the final word.
Still, the projection is informative and can be given to the council as an estimate. If 85.8 per cent are valid, expected valid signatures are 5,410 × 0.858 ≈ 4,642, about 350 short of the 4,992 required (8 per cent of 62,400).
A rough 95 per cent interval: standard error of the proportion is √(0.858 × 0.142 ÷ 500) ≈ 0.0156, so the margin is about 1.96 × 5,410 × 0.0156 ≈ ±165 (slightly less with a finite-population correction). That gives roughly 4,480–4,810 - below the threshold across the whole interval.
Conclusion: the petition probably fails, but the clerk must still verify every signature, because the statute makes the sample a trigger, not a verdict. Estimating and certifying are separate acts.
2. Distinguish legality from legitimacy here. Should the council reject the petition on pre-emption grounds?
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Legality is whether a court would uphold the action. Legitimacy is whether the action is a defensible use of authority in a democracy that has promised citizens an initiative.
On legality, the mayor's case is mixed. The 2016 statute is a real constraint, but it channels the change through county approval rather than banning it, and the city has not yet asked the county. "One person, one vote" governs apportionment - wards must be roughly equal in population - not the choice between at-large and district elections, so that argument is weak.
On legitimacy, outright rejection before the clerk certifies the count would look like the council using a technicality to avoid a vote it might lose. The better course: complete verification, publish the result, and if the count qualifies, place the measure on the ballot with a clear statement of the pre-emption issue while simultaneously seeking county approval. If it does not qualify, say so on the count.
Lawful and legitimate usually overlap. Here the cheapest way to keep them together is process, not a unilateral ruling.
3. Why does the sampling method matter in this case, and what could bias the estimate?
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Because the sample is being used to decide whether the count is even examined, its design determines who gets a vote.
A simple random sample of signatures gives an unbiased estimate with the standard error computed above. But petition sheets are clustered: one circulator may have collected a page of duplicates or out-of-town addresses. If invalid signatures cluster by sheet, a signature-level sample understates the true variance - the design effect - and the 14.2 per cent figure could be less precise than it looks. Sampling whole sheets instead would require a cluster adjustment.
Other biases: a sampling frame built from the raw submission may include sheets later withdrawn; ambiguous cases (a name spelled differently from the roll) may be coded inconsistently, and the coder's judgement can drift. The 12 per cent trigger is also arbitrary - a true rate of 11.9 per cent passes without full checking.
The fix is procedural: publish the sampling frame, the coding rules, and the invalid categories, so the estimate can be audited.