Politics and Statistics--Drink Coffee Before Reading

This week's column contains not one, but two, eye-glazing topics, politics and statistics. Consider yourself warned. The editor's headline is a bit over the top; instead, my point is that there's no technological "solution" to vote counting, only reducing the number of errors. And none of the current systems quite approach what industry calls "Six Sigma" quality (or at least they did back in the days that we worshipped business), and in tight races, that margin of error may exceed the margin of victory. My advice to candidates: Try to win by more than one vote.

EVEN HIGH-TECH OPTICAL SCANNERS CAN SKEW ELECTION RESULTS
East Valley Tribune, September 29, 2002

The GOP primary for the newly redistricted District 11 state Senate seat pitted incumbent Sen. Sue Gerard (about whom I cannot say enough good things) and current Rep. Barbara Leff (about whom I shall say nothing). Both Leff and Gerard spent over $120,000, and the race was as tight as expected -- a lesson in how votes count.

Out of more than 18,000 votes cast, Leff beat Gerard on election night by 27 votes. The margin was so tight that the winner had to wait for some 30,000 miscellaneous Maricopa County ballots, from people who had requested an early ballot but didn’t mail it in time, or who otherwise had cast a questioned ballot -- ballots which could have come from any party or legislative district in the county.

On Sunday, the Maricopa County Recorder’s Office announced that Leff still had won, now by 37 votes. The “late ballots” increased her margin by 11 votes, while changing the results of an equally-close race in the GOP House primary. The final initial count showed a 38-vote margin.

(In the District 11 GOP House race, Steve Tully and Steve May seemingly had won the two spots, with Deb Gullett finishing third by 13 votes. The late ballots, however, changed the results, with Gullett overtaking May by 58 votes.)

The Leff-Gerard race fell within the 50-vote margin requiring a full recount. The automatic recount didn’t change the result, only the margin. Leff now won by 60 votes. But the automatic recount, despite not changing the outcome, was statistically fascinating.

Maricopa County votes using optical scanning technology, with voters marking ballots by completing an arrow with a pen. Optical scanners “read” each ballot and tally the votes. In an official recount, elections officials, as required by statute, run the ballots through a different machine. Nobody expected any difference in the result, because nobody expects machines to disagree.

In the recount, county officials use their “best” scanner, which means the most sensitive. The “better” machine detected a surprising number of missing votes, for both candidates, missed by the “regular” machines.

The official vote totals from the regular count and the recount, tracking the 5 possible results, are shown on the graph: a vote for Gerard; a vote for Leff; an “undervote,” where a ballot did not indicate a vote for either; a “write-in” ballot, where a voter wrote in a third person, and an “overvote,” where the voter voted for both candidates, either by completing both arrows or by write-in.

[I can't get the chart (not a "graph") to reproduce in Blogger, so here are the raw numbers:

Official Count: Gerard 8,402; Leff 8,439; Undervote 1,339; Write-In 49; Overvote 18.

Recount: Gerard 8,441; Leff 8,501; Undervote 1,235; Write-In 50; Overvote 20.]

Both the official count, and the recount, showed 18,247 total ballots. In the recount, Gerard gained 39 votes, but Leff gained 62 votes, a net gain of 23.

Note two interesting facts. First, 1,235 people in an upscale district who bothered to vote in a low-turnout primary didn’t vote in a high-profile state legislative race.

Second, notice the drop in the number of undervotes -- 104 votes for both candidates ignored in the official count. Despite our faith in optical scanners, the official count missed 104 valid votes out of 18,247. The result didn’t change, but our state-of-the-art machines missed 0.126 percent of the votes.

That’s not much of an error rate -- unless the election is close. Say, like in Florida in 2000, where out of more than 5.8 million votes cast, an error rate of 0.126 percent means 7,300 uncounted votes, more than a dozen times more than Bush’s announced margin of 537.

Democracy is an approximation. A mandate may be merely the margin of error. And congratulations to the winners.