At Issue In a Massachusetts Town, the Value of Two-Thirds 449
An anonymous reader writes "In Truro, Massachusetts (a town on Cape Cod), a zoning decision came up for vote, where the results were 136 for, 70 against. The vote required 2/3 approval to pass. The Town Clerk and Town Accountant believe that since .66 * 206 is less than 136, the vote passes. However, an 'anonymous caller' noted that a more accurate value of 2/3 would require 137 (or perhaps even 138 votes) for the measure to be considered passed. The MA Secretary of State and State Attorney General are hard at work to resolve this issue." Updated 20100422 23:55 by timothy: Oops! This story is a year old (rounding up), which I didn't spot quickly enough. Hope they've got it all worked out in the meantime.
Re:not quite 2/3 (Score:2, Interesting)
"2/3 majority" does not mean 0.666666666666666666666666667 of the voters.
It means that 3 times the number of supporters must be at least twice the total number of voters.
Re:Counting people? Round up! (Score:1, Interesting)
Simple because if you only take 2/3 as 0,66 0,66 * 206 = 135.97
So, 136 would have been enough to pass.
If you take one more decimal, 0.666 * 206 = 137.196
So, 138 would have been needed to pass.
All they need to do is create ONE more votant to get up to 207 and they wont have that problem again.
EVER.
Re:Easy, no fractions or decimals needed (Score:3, Interesting)
They could never have (with their current number of seats) 140 to 70. It would have to become 140 to 66, to match their 206 total.
Re:Counting people? Round up! (Score:3, Interesting)
I don't know much about python, but if you're using Integer data types, you're taking the wrong approach. I assume Python implicitly converts 206 to an integer, and that division of integers results in integers. 206.0 would be currency if not an actual float, then, making the results floats.
But the best way to calculate fractional multiplication is get all of your multiplications done first, then do a single division. The last thing you want is a rounding error, so you do it last and it's the last thing you get!
206 * 2 / 3
2/3 of 206 is the same as 2/3 times 206, so you can write it as 2/3*206 if you like. But always do division last and remember order of operations doesn't apply to multiplication and division (aka do it in any order and it comes out the same).
Order of operations DOES matter, significantly, when rounding. Take 40 percent of any number, using integers, compared with 50 percent. 40 percent of 20 for example:
40 / 100 * 20 = 0
50 / 100 * 20 = 20
You can get better results if you move the division later, because rounding is the thing you do *last*. In order of operations, rounding is always last. So don't let your formula round until the last possible moment:
40 * 20 / 100 = 8
50 * 20 / 100 = 10
Applying this gives us 206 * 2 / 3
I don't know if you were trying to be funny or make fun of python, but people don't know how to do simple math, and your example and the article, although a year old (unless the year is a typo), don't help.
The complementary problem (Score:2, Interesting)
The more mathematically literate would note here that the complement of requiring 2/3 to pass is that if *more than* 1/3 vote against it should fail.
70 people voted against. 206 people voted in total. 70 is a third of 210 therefore it is more than a third of 206. Therefore the vote fails. Q.E.D.
I'm a CPA and... (Score:3, Interesting)
Re:not quite 2/3 (Score:3, Interesting)
i was taking this basic 'intro to' math class. i got the first exam back, and most of my answers were marked incorrect when i knew they were right. the supposedly correct answers were written on my test and some were relatively close, while some were not. perhaps you can guess where this is going.
i asked the teacher what was up and as she was checking my test, i saw her answer sheet had her work shown on it and realized quickly what the problem was. yes, she had rounded all the fractions to two place decimals as she went, introducing sometimes large errors to the final answer when many fractions were involved. one of the correct answers was actually an integer and she had a decimal! lolwut?
the test was copied straight out of a book and had an answer key of it's own. i showed this to her and that the books answers were the same as mine and tried to explain what she was doing wrong, but she just didn't understand.
anyway, i dropped that class asap.
Re:This is a year old... (Score:3, Interesting)
Yup. The Massachusetts Attorney General reviews all Town Meeting articles, and usually takes a few months to certify the results as valid and legal. This one would have been pretty obvious, but there were a bunch of other articles to review from the same meeting, and there are several hundred towns, so the number of articles pending review could easily be several thousand.
Re:Counting people? Round up! (Score:3, Interesting)
Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons.
So each non-free person (slave) counted as 3/5 of a person...
That's Article 1, Section 2. It was later modified by The 14th Amendment, Section 2, to lose the fraction but still "excluding Indians not taxed".
Re:basic math (Score:3, Interesting)
Since the original post is so brief, it's difficult to determine its intent. However, the usual intimation of such quotes is to imply that the 3/5ths valuation was immoral because slaves should have been counted fully, i.e., as 5/5ths.
But this is exactly counter to the various political goals of the time: the northern colonies, who were more generally against slavery (yes, there was still slavery in the North, but I'm describing averages) wanted the slaves to not be counted at all, while the southern colonies demanded that they count as a full person.
The reason? The census -- and it was only the census for which this definition was intended -- determined how many representatives each state could send to Washington. Northern, and sorta generally anti-slavery colonies, wanted to not count the slaves at all; if they're not fully-enfranchised citizens, why should the 'owners' get the Federal advantage of the extra legislative muscle that the extra census count would provide?
The southern colonies, on the other hand wanted slaves fully counted so as to maximize the pro-slavery clout that the South might exert through the additional members in the House of Representatives.
So, the old saw that evaluating slaves as "3/5ths human" is both a gross misrepresentation of the original intent (it had nothing to do with their status as human beings), and of the political impact of this count: the politically correct view would be to count them as zero, thereby depriving the slave-holding states of the census advantage.
Re:It's not that silly (Score:3, Interesting)
Whatever it is, you're going to need rules. Bad rules are bad. Good rules are good.
Perhaps all laws should have a lifetime. Constitutional laws might last for say 50 years (so that most people get to enjoy some symbolic "renewal" celebration).
The other "lesser laws" cannot last as long. If there are too many laws for legislators to keep renewing, there are too many laws for people to follow.