By the numbers alone, Councilman Carl DeMaio’s initiative should have been cleared for a place on the November ballot: A sample count of petition signatures suggested that the measure had more than enough support to pass the required threshold.

But the rules don’t work that way. Under state law, the registrar of voters had to do a bit of extrapolation. Actually, a lot of extrapolation.

Thirty out of the 4,033 signatures in the sample count were duplicates. Thanks to a complicated mathematical formula required by law, the registrar estimated that each of those 30 signatures indicated that about another 1,000 of the total 134,441 submitted signatures were also duplicates.

The formula sliced about 32,000 signatures off the total. Combined with another finding from the sample count (that about 20 percent of the signatures were invalid), the formula prevented the estimated total valid signatures from meeting the required threshold.

Wait, what? Hang on. I’ll explain the math in a few paragraphs. First, a look at the big picture.

At the moment, the initiative — which would dramatically change city contracting and outsourcing rules — isn’t going on the ballot. The registrar of voters did a sample count and estimated that more than 59,000 of the 134,441 submitted signatures — nearly half — are invalid, meaning it doesn’t have enough to make the threshold of 96,834 signatures.

Today, DeMaio asked for a full count of the petition signatures and agreed to pay $152,000 for the cost. But as Deborah Seiler, the registrar of voters, told us yesterday, there isn’t enough time to complete a full count before the August deadline to put an initiative on the ballot. Seiler reiterated her concern about timing in an interview this afternoon.

Still, initiative spokeswoman Jennifer Jacobs said the measure’s supporters will push for a full count. “We’re not going to walk away from all these people who signed,” she said. “We feel like there’s a fluke and a glitch that happened here.”

Let’s get back to examining the counting system.

To put their measure on the ballot, supporters of the initiative needed to gather signatures from 15 percent of San Diego’s registered voters. That’s 96,834.

The supporters submitted 134,441 signatures. The registrar of voters office tested a randomly chosen sample of 4,033 signatures. (The registrar does a sample count to avoid the huge expense of verifying all the signatures.)

Of those, 3,212 were deemed valid. That’s 79.64 percent. If 79.64 percent of all the 134,441 signatures were valid, that number would be 107,068 — more than the required 96,834.

But there was that catch. A catch that hacked the estimate of around 107,068 signatures (more than enough) to 74,732 (not nearly enough).

Under state law, a sample count must impose a penalty for each duplicate petition signature, said Seiler, the registrar of voters. (When there’s a duplicate, one counts and the other doesn’t.)

The penalty is imposed through a mathematical formula and is “used by every jurisdiction that I know of” in the state, Seiler said.

In this case, the formula required the registrar to take those 30 duplicate signatures into account and remove about 32,341 signatures from the total estimated number of valid signatures. The formula determined that each duplicate signature found in the small batch is a sign that about 1,000 lurk amid all the signatures in total.

Sieler said finding that many duplicates is “unprecedented.”

“Having 30 duplicates in a sample like this is kind of a first. It’s very unusual to have that high number. Normally we would have two or three or four,” she said.

Generally, she said, the people who circulate petitions are aware of the heavy penalty for duplicates and try to avoid them.

So why does this unusual penalty for duplicates exist?

I’ve been calling experts around the state but haven’t been able to get a good answer yet. But one possibility is that there’s an assumption that a check of the rest of the signatures will find many more duplicates because those who signed the petition in the sample count were only checked against each other.

Jim Lackritz , a statistician and associate dean at San Diego State, said that would make sense.

Consider, he says, a hypothetical 300 petition signatures. In the first batch of 100, there’s a single duplicate. So you’d estimate that 1 percent of all 300 signatures are duplicates, right? Wrong.

The second group of 100 might have one duplicate but then a second one that matches with someone from the first group. (Cross-checking would turn this up.) And the third group of 100 might have three duplicates thanks to cross-checking. In total, the duplicates would (presumably) be more than 1 percent.

“My guess is that when the formula was developed, they probably had a mathematician or statistician work on it,” he said. “If it was not appropriate, it would have been challenged.”

— RANDY DOTINGA

Scott Lewis

Scott Lewis oversees Voice of San Diego’s operations, website and daily functions as Editor in Chief. He also writes about local politics, where he frequently...

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