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At Issue In a Massachusetts Town, the Value of Two-Thirds
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.
can't these people do simple math?
2 / 3 = 0.66666666...
106 / 236 = 0.660194175
Whats the problem here? It didn't pass.
Rounding is not relevent here. They need 2/3 * 206 votes to pass. 137 is less than that value. 138 is more than that value.
137 votes fails to be more than 2/3 of 206. Why would rounding even be a topic for discussion?
Socialism: a lie told by totalitarians and believed by fools.
Yeah, this strikes me as a pretty trivial problem to solve.
If the process requires the approval of 2/3 of the voters or more, then the lowest whole number that satisfies this requirement is the lowest number of votes which can pass the motion.
Fucking duh, Massachusetts.
DRM: Terminator crops for your mind!
Did the Town Clerk and Town Accountant ever work for Verizon?
Clearly 70 times 2 is greater than 136 Therefore there is NOT a 2/3 majority. The matematics of politics, however, is not like the math we all know and love....
is irrational
Significant figures are important. In this case, the 2/3rds rule, being a constant, MUST be taken to at least 3 digits.
Uh.. how about not expressing an infinitely repeating number as a finite value?
(206 * 2) / 3 = 137.33~ = 138 votes to meet the minimum
Not that hard. Significant digits don't come into play. The value of two thirds is 2/3, not some decimal value.
"Our two-party system is like a bowl of shit looking at itself in a mirror." - Lewis Black
The ratio of 2/3 to 1/3 is 2:1. In order for a measure to pass by a two-thirds vote, the majority must have more than twice as many as the minority. 136 is less than two times 70, so the vote does not pass.
"How to Do Nothing," kids activities, back in print!
137 votes does not give you 2/3rds. It is less than 2/3rds. If the law requires 2/3rds, in what situation would 137/206 be sufficient?
Put it this way - put the equation into C++ and compile and see how it comes out.
if( 137/206 >= 2/3 )
votepass;
You need 138 for that equation to be true.
Most folk'll never lose a toe, and then again some folk'll...
You're complicating it.
(206 * 2)/3 = 137.333
Why use 0.66xxxx whatever when you don't have to?
The engineer pulls out his calculator, types in the results, and gives the answer.
The mathematician goes to the whiteboard, and writes a proof for the answer.
The politician whispers, "What do you want the answer to be . . . ?"
Schroedinger's Brexit: The UK is both in and out of the EU at the same time!
Really? Long division has been lost to the ages?
>>the results were 136 for, 70 against. The vote required 2/3 approval to
the question: is 136 / 206 >= 2 / 3 ??
is the same as: is 3*136 >= 2 * 206 (multiple each side by 206 * 3)
or: is 408 >= 412
or: DID NOT PASS
Date on the article is April 30th, 2009.
So, does anyone know if basic math skills prevailed?
When information is power, privacy is freedom.
I think somebody needs to teach them that .66 != 2/3
Put it this way - put the equation into C++ and compile and see how it comes out. if( 137/206 >= 2/3 ) votepass;
Nope. That will always evaluate true. (You're invoking integral division, not real numbers.) You wanted:
if (137.0 / 206.0 >= 2.0/3.0 ) votepass;
Uh.. how about not expressing an infinitely repeating number as a finite value?
Well, if you know how to count, it doesn't really matter.
How do you determine the area of a circle with a radius of 25.0 units, without "expressing an infinitely repeating number as a finite value"?
You can use 3.14 to get a reasonable degree of accuracy. Using 3 will introduce too much error in your result, and using 3.14159 is just silly because you can only be sure of 3 digits anyway from your measurement of the radius. There's usually a whole course on this when you take any science major.
Seven puppies were harmed during the making of this post.
The scariest part is their accountant is the one who things .66 is 2/3. I'll bet their books are ALL MESSED UP
...unless you have fractional people.
Well, that's not exactly unprecedented in American politics.
three fifths of all other Persons
Momentarily, the need for the construction of new light will no longer exist.
um... /. stripped my decimal points...yeah, that's it...
Most folk'll never lose a toe, and then again some folk'll...
I just did it myself in Python and it is a rounding issue:
206/3*2 = 136
206./3*2 = 137.333333333334
If you round the division down then do the multiplication, you get 136.
pft, clearly you've been taught wrong. 2/3 is really .666666. Duh.
You're both wrong, 2/3 is two divided by three. To make 2/3 of any number, you multiply it by two and divide it by three. It's not hard, and no decimal will ever be as accurate.
The 100% accurate answer is 137 and 1/3.
Security is mostly a superstition... Avoiding danger is no safer in the long run than outright exposure. - Helen Keller
As Barbie says, "Math is hard, let's go shopping!"
Holy shit, it's not that complicated!
The law requires a majority of 2/3 or more.
(206*2)/3 = 137 1/3
137 is less than 137 1/3, so 137 is not a 2/3 majority.
138 is greater than 137 1/3, so 138 is a 2/3 majority.
Done. You can keep the 138 figure on hand to remind yourself, but it isn't necessary, just do 206 * 2/3 to get the minimum number of votes needed. It isn't hard.
This story and some of the posts have really been pretty sad, half the people on slashdot are perpetuating the same error the clerk made, they are simply doing it more accurately. The other half have come up with convoluted ways to check whether a number meets the criteria.
Christ, just multiply by 2/3 and be done with it, it's not hard.
Security is mostly a superstition... Avoiding danger is no safer in the long run than outright exposure. - Helen Keller
The 100% accurate answer is 137 and 1/3.
So this is a midget voting?!?!
how long until
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.
I don't believe in rounding. I truncate. It helps to always win 2/3 majority votes:
2/3 is 0.66666... Truncated to integer = 0
Total voters: 206
To win the vote, we require at least: 206 * 0 = 0
Therefore any number of affirmative votes constitutes a 2/3 majority.
Numbers don't lie!
The vote does not pass.
Are they going to hire Gandalf to tell then the news?!?
how long until
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.
... most of my co-worker's (most of whom couldn't even pass the pretty easy test), definitely wouldn't understand that level of "math", much less that logical expression
No, they definitely didn't round up, they truncated a number that was never accurate to begin with. 206*2/3 takes a half second longer to punch in than 206*0.66, if that. Why were they ever using 0.66 to begin with?
The law says 2/3, use 2/3. It's not hard.
Security is mostly a superstition... Avoiding danger is no safer in the long run than outright exposure. - Helen Keller
Close, but no cigar.
(206 * 2)/3 = 137 1/3
Why use 0.66xxxx whatever, when you don’t have to?
Any sufficiently advanced intelligence is indistinguishable from stupidity.
I don't know much about python, but if you're using Integer data types, you're taking the wrong approach... 206 * 2 / 3
This story would be much more interesting if they did use integer division as 2 / 3 * 206. In fact since the law didn't declare the type for number_of_votes, I suggest we fall back to fortran conventions.
We're all missing part of the story. 136 is a 2/3 majority when you're dealing with very large values of 136.
... gets 137.333...(repeating). So 137 votes is not even enough. 136 is clearly not.
now we need to go OSS in diesel cars
From:
http://www.tnrta.org/docs/TNRTA-nwsltr-Fall09.pdf
How refreshing to see one comment where someone does not show off their amazing multiply-by-two-thirds skillz.
No. A majority vote requires 50% + epsilon to pass. However, a 2/3 vote typically requires that the majority must have at least twice as many as the minority, not "more than twice as many". Which is to say, if there are three people voting, only two voting yea passes the bill, not three.
Support a few technologists in Washington.
But I think it's amusing to say the least -- splitting hairs on a vote.
Really, the who notion of voting is severely flawed from a mathematical point of view. One extra vote makes all the difference between whether or not a bill is implemented. What is the intrinsic importance of making it 2/3rds? Why not 3/4ths? 1/2? 5/8ths? What is the significance of 2/3? Seems arbitrary.
But then, that is the difference between law and mathematics, I suppose. 20 years and 364 days old, you're too young to drink, it's illegal, and there are sanctions. 20 years and 365 days -- 21 years old, and it's perfectly legal. But what is the significant difference in a person at 20 years 364 days vs. 20 years 365 days? Is there some sort of "maturity switch" that is magically flipped? Do the gods of time descend upon you and bestow you with something special?
We humans make so much ado over meaningless arbitrary demarcations. Life situations are fuzzy and spread out, not the digital of "on/off". It all seems rather a bit silly! Splitting arbitrary hairs without real meaning.
Ruby Neural Evolution of Augmenting Topologies
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.
Generating news isn't simple. You have to investigate, contact the sources, write the article, correct it, publish it in a readable way, etc, etc.
Agregating news isn't that hard. All you have to do is check the source, the date and place of the article, if it's serious and still relevant, write a small summary (or cut and past it from the article) and submit. Not that hard at all. Google news does a better job than Slashdot at it. A damn perl script does a better job than 20+ slashdot editors. Even Fark is doing better than slashdot. If you post some old copypasta on the randomness and caos that is /b/, it'll be spotted instantly. The 13 year old kids at /b/ do a better job than slashdot's team of editors.
I usually don't complain about article quality, dups, etc. I believe it's better to just let it go and move on. I say "hey, anyone can make a mistake". But it just gets worse everyday. We trust slashdot. We just spent a lot of our time discussing this issue, and trying to provide meaningful answers. It turned out to be an issue that happened almost a year ago. That is worse than reading slashdot on April 1st (at least you KNOW it's all bullshit on April fools day).
Even taking all the stupid trolls into account, this community is much more valuable than the site that is hosting it. Yes, we can be a bunch of assholes sometimes, but I believe this is still true: Slashdot's community is la creme de la creme of the Internet. Just tell me of any other place where you can get a high profile open source developer, a NASA researcher that has written code for the Shuttle, a guy from Star Trek, a lawyer that understands copyright law, one of the founders of Apple, the Father of quake, an employee from almost every single technology corporation in the world, plus a huge crowd of engineers, coders, technology enthusiasts, writers, philosophers, sysadmins, doctors, lawyers, politicians, and generally smart people. The Slashdot community is amazing. Unique. I can't think of any other place with such diversity and such a high concentration of people that matters. Don't get me wrong, I'm not saying that /. readers are some kind of superior race. I'm just saying that the distribution of people in /. isn't average. We certainly have less cab drivers and more world changers than any other community out there. What worries me, is that the the site hosting that community is not up to the task. I love Slashdot. I've been in here for a long long time, and I have no intention of leaving. This is an off topic comment, and it'll certainly be flagged as such ... But I just felt like sharing this lines with you. What can we do to improve this place? it is, after all, like a second home to many of us.
WTF am I doing replying to an AC at 5 A.M on a Friday night?
This is so incredibly simple that I can't believe I'm reading scores of responses about significant digits and rounding, etc. For a motion to be passed by a 2/3 majority, at least twice as many people have to vote in favour as those who vote against. Since 136 is less than 70*2, the vote fails. No calculator required, no consideration of significant digits. It's the kind of thing a reflective schoolchild should be able to reason out, frankly.
I think this is a symptom of a generation raised with calculators...
Give a man a match: warm him for an instant. Douse him in petrol and set him aflame: warm him for the rest of his life.
While drawing these arbitrary lines is silly, it is often far sillier to not draw them in the universe we live in.
Making silly arbitrary decisions is a necessary part of life. Life situations aren't that fuzzy except at the quantum level. Even little things like which hand to use, whether to breath in or out. And even if the Many Worlds Interpretation is correct, it's not that fuzzy in each path of the universe.
Say a car is about to hit you, you could jump either left or right to save yourself. The neurons in your brain are going to have to make a decision. Say you jump right, you think all the neurons participating in the decision wanted to go right? I doubt it, some would have wanted to go left. But you cannot satisfy all of them. You can't go both left and right, unless you wait for the car to split you in two.
Back to your question, there is no magical maturity switch. Some people never even become mature. So what? With our current technology we are not able to practically put you 60% in jail and 40% out of jail at the same time, just because you are actually "60% mature".
And it's costly to put in all the shades of gray for the different percentages of "maturity". Some countries do cater for a few categories: juvenile prisons, probation, etc.
So there are very many arbitrary lines in laws: when it's legal to abort a fetus/baby, when does a child become an adult.
There's definitely much silliness that should perhaps be fixed. For example, in many countries you might be legally considered old enough to sign up as a soldier, but not do other "adult things". This to me is silly. If you are going to be old enough to kill others and risk your own life, you should be considered old enough to do the other adult stuff. Otherwise, you shouldn't be considered old enough to be a soldier (unless the country is in such a bad/desperate state that you might as be allowed to be a soldier).
Interestingly, the U.S. Constitution was written with this passage about the census:
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".
You have the right to remain sentient. If you give up the right to remain sentient, you will be elected to public office
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.
Y'all screwed up.
2/3 majority in parliamentary procedure is taken as meaning there are at least twice as many votes for than against. That avoids the whole fractional vote issue, which is a nonsensical concept.
In this case there were 70 against, which means there would have to be at least 140 for. Thus the motion fails.
C'mon, people. This thing has to have happened more than a few times in the course of history.
Fucking duh, Massachusetts.
One feels obliged to note that because massachussetts is one of the only states in the world that has ANY practicing actual democracies (the federal government is a republic) . . . the state usually doesn't interfere in this sort of thing. Welcome to town government by the people. Usually it works better than this, but, actually, often it doesn't.
OR, you could not be retarded and just realize that a 2/3 majority means that the number of yes votes will be double the number of no votes or greater.
All you do is double count the no votes. If the measure still passes, it had a 2/3 majority.
It's not that fucking hard.