Changing Hawaii

By Diane Yukihiro Chang

Monday, December 4, 2000

Researcher at
UH solves dimpled
chad dilemma

HERE'S an understatement: The presidential election is a close one. It's so close, in fact, that the votes of a single state -- Hawaii's arch-rival in tourism, Florida -- are going to determine the victor.

It's so, so close that the key determinant may rest on whether or not to count "chads," those little pieces of paper that voters are supposed to decisively perforate when they pick a candidate.

Sometimes, for whatever reason, a vote isn't punched through completely. This results in a hanging chad (still partially attached to the ballot), a pregnant chad (slightly bulging) and a dimpled chad (where there's a discernible imprint).

So when Lee Altenberg of Kihei, Maui, learned that the canvassing board in Palm Beach County, Fla., was going to count a dimpled chad as a bona fide vote ONLY if there was another dimpled chad on the ballot, he was annoyed.

Altenberg, 43, has a Ph.D. in mathematical genetics. He is a researcher and adjunct assistant professor in information and computer sciences for the University of Hawaii. He knows numbers and probabilities.

Therefore, in an hour's time, he wrote a two-page paper titled "Can Single Dimpled Chads Reflect Voter Intent?" and faxed it off to Democratic Party headquarters in both Hawaii and Florida.

No, Altenberg isn't a Democrat. In fact, he says he's voted for more Republicans since moving to Maui in 1994 than anytime in his life.

It's just that Palm Beach County doesn't know what it's doing. "It's the civic duty of scientists to get involved in open debate when it can contribute to clarifying the public's understanding of the truth," says Altenberg.

Check out his explanation:

"(Palm County's) reasoning seems intuitive: If all the other votes on the ballot were clearly perforated, then a single dimpled chad must not be an intended vote, but is more likely caused by a voter's decision not to finally make that vote.

"This might seem to make sense and has been argued by people objecting to the counting of the dimpled chads. However, this reasoning is flawed.

"If on rare occasion a voter casting a vote accidentally dimples a chad instead of perforating it, then the vast majority of ballots that have dimpled chads will have exactly one dimpled chad, with the other votes on the ballot being clear perforations.

"Therefore, to restrict the count of dimpled chads only to those ballots that bear multiple dimpled chads will exclude the vast majority of intended votes."

ALTENBERG continues by offering his analysis of dimpled chad distributions, complete with a really complicated mathematical formula and a table comparing the number of dimpled chads on a ballot with the fraction of ballots on which they'd likely occur.

For example, a single dimpled chad would appear on approximately .0913517 of ballots, two dimpled chads -- .00415235, three dimpled chads -- .000111848, etc.

The bottom line is this: Among all the ballots that have at least one dimpled chad, and in which they occur as accidents when a vote was truly intended -- fully 95.5 percent of them would ONLY have a single chad.

Ergo, Palm Beach County did exactly the opposite of what it was supposed to do.

Here's another understatement: Florida needs a few more Ph.D.s in mathematical genetics in its ballot-counting room. But it can't have ours.

Diane Yukihiro Chang's column runs Monday and Friday.
She can be reached by phone at 525-8607, via e-mail at, or by fax at 523-7863.

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