Town Officials and Journalists Unclear On Fractions:

Cape Cod Times reports:

[Headline:] Truro zoning decision hinges on single vote

Voters narrowly approved one of four zoning amendments late Tuesday night at the annual town meeting. But town officials were still looking at the exact vote count on that article yesterday.

In a vote of 136 to 70, voters passed a new time limit on how quickly a cottage colony, cabin colony, motel or hotel can be converted to condominiums....

The exact count of the vote — 136 to 70 — had town officials hitting their calculators yesterday. The zoning measure needed a two-thirds vote to pass. A calculation by town accountant Trudy Brazil indicated that 136 votes are two-thirds of 206 total votes, said Town Clerk Cynthia Slade.

Brazil said she used the calculation of .66 multiplied by 206 to obtain the number.

But using .6666 — a more accurate version of two-thirds — the affirmative vote needed to be 137 instead of 136, according to an anonymous caller to town hall and to the Times.

Slade said that she called several of her colleagues to see how they calculate a two-thirds vote, and the answer varied widely. In Provincetown, Town Clerk Doug Johnstone uses .66. But Johnstone said he'd never had a close vote where it might matter.

A spokesman from the Secretary of State's office was not available to comment yesterday.

Slade said she will let the state Attorney General's office decide on the correct count, as part of their normal review of town meeting decisions....

Now let's be careful here, since there are so many problems here that it's easy to miss some. (I assume, by the way, that the article is correct in saying that a two thirds vote is required to pass the amendment, which the Truro Charter seems to confirm.)

1. Voters didn't "narrowly approve[]" the amendment; they narrowly disapproved it. It doesn't matter what the town official says; 136 is not 2/3 of 206. [UPDATE: The reporter e-mails me, in response to a query, "the article is considered to have passed by town meeting. but it will be reviewed (as all general and zoning bylaw articles are) by mass. attorney general before it is enacted." But whatever the town authorities might have said, the voters didn't narrowly approve the amendment — their vote fell short of the legally required 2/3.]

2. The affirmative vote needed isn't 137, since 2/3 of 206 is 137.333..., which means 137 is less than 2/3 of 206. The affirmative vote needed is 138.

3. Therefore, the zoning decision didn't "hinge[] on [a] single vote" — even if the one vote had changed, so the total would be 137 to 69, still not 2/3. To pass with 206 people voting, two voters would have had to switch sides.

4. I realize this item is a bit pedantic, but .6666 isn't a more accurate version of two-thirds. There is only one 2/3, not multiple versions. .6666 is a more accurate approximation to 2/3 than is .66.

5. If you need to calculate 2/3 on a calculator, there's no need to choose an approximation of two-thirds — you can just multiply by 2 and divide by 3.

6. But beyond this, who needs "an anonymous caller to town hall and to the Times," or even a calculator here? If you need 2/3 ayes (and assuming, as the article does, that this is 2/3 of those who cast a vote, not 2/3 of those present), then the only question is whether there are at least twice as many ayes as nays. 136 is less than two times 70, so 136 is less than 2/3 of the total.

7. It's not just one town, but two! And the answers in different towns "varied widely," so who knows what else is going on there?

8. They need the state Attorney General's office to multiply 2/3 in Massachusetts.

9. Finally, the best part — this was supposedly done by the town's accountant. Hey, a lawyer I could understand, but shouldn't the accountant be the one person who knows better?

Thanks to Adam Bonin for the pointer.