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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.
It should at least be rounded, if not just simply rounded up (i.e., ceiling). It's talking about people; you can't have 3.5 people, so if you want "more than 3" people then you need to go up to 4 people.
It's the poster:
Truro zoning decision hinges on single vote
By Mary Ann Bragg
mbragg@capecodonline.com
April 30, 2009
Two thirds of this is approx 137.3. The vote must be greater than or equal to 137.3 to pass, than means 138 is required, unless you have fractional people.
can't these people do simple math?
2 / 3 = 0.66666666...
106 / 236 = 0.660194175
Whats the problem here? It didn't pass.
Significant figures are important. In this case, the 2/3rds rule, being a constant, MUST be taken to at least 3 digits. Otherwise why not just use 0.6 instead of 0.667 - that way all you need is 124 votes.
0.6 * 206 = 123.6
0.66 * 206 = 135.96
0.666 * 206 = 137.196
Mathematics should not be subject to politics. Some idiot legislators want to twist the law to get their stupid agenda passed. Instead they should call for a re-vote if their rules allow it, or ADMIT DEFEAT DAMN IT. This attitude makes a mockery of democracy.
Seven puppies were harmed during the making of this post.
2/3 != 0.66. In fact, 0.66 2/3. This is objective mathematical truth. Can we move on?
This doesn't seem that hard.
206 * (2/3) = 412/3 = 137 + 1/3
I'd side with the commenter that more than 136 votes are needed. Now, whether or not you truncate the decimal or round it, I'm not sure. In this case it doesn't matter though, it comes to 137 either way.
Obviously you can't have 1/3 of a vote.
"What do you despise? By this are you truly known." --Princess Irulan, Manual of Muad'Dib
/)
(136 / 206 == 0.660194174757281553398058252427181) is less than (2/3 == 0.66666666666666666666666666repeating)
The vote does not pass.
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....
The law states 2/3 is required, not .66 of the voters ... 2/3 of 206 is 137.3333333333333...
lets just round pi to 4 and get this mess over with
War isn't about who's right. It's about who's left.
Maybe Truro should vote on getting a town accountant who knows how to divide by three. Or, failing that, one that can round (2/3 doesn't round to 0.66!)
In[1]:= 136/206 >= 2/3
Out[1]= False
A few seconds with a calculator shows that 136/206 is less than two thirds. For the relentlessly pedantic, it works out to .66019... which is clearly less than .66666666...
Oliver's law of assumed responsibility: If you're seen fixing it, you will be blamed for breaking it.
Shouldn't they side with the "more accurate" definition of .666 than .66?
136/206 = 0.66019 137/206 = 0.66505 138/206 = 0.66990 2/3 = 0.66667 Clearly the measure does not pass with 2/3 of the vote. Even if you round off to 2 digits you would get 136/206 = 0.66, and 2/3 = 0.67, so it still doesn't pass.
is irrational
What is this, "Are you smarter than a 5th grader?" Wasn't it in Mass. where they
136/206~0.6602, less than 2/3. The measure did not pass.
I haven't kept up on Mass. politics, but hopefully the AG they're going to ask isn't Martha Coakley, who thought a glorified Lite-Brite was a bomb.
"National Security is the chief cause of national insecurity." - Celine's First Law
2/3*206 = 137.33333333333333333333333333333. Technically, 137 is less than two-thirds. If you need AT LEAST two-thirds, you need 138.
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!
By Mary Ann Bragg
mbragg@capecodonline.com
April 30, 2009
Only 357 days late: I hope the poster doesn't do anything time-sensitive for a living.
The Town Clerk and Town Accountant believe that since .66 * 206 is less than 136, the vote passes.
Wow. Haven't RTFA because it would scare me, but if the summary is even halfway correct then we may as well say 2/3 is just 0.6. They'd only need 123 votes to pass...
ok - 206 = total of yeas and nays.
.66?? who thinks like that... unless they are lazy and using a calculator. Even .666 puts it over 137, but "666" is a bad number ;-)
But
A grade school kid would quickly come up with "137 or more" without even getting into decimal places...
(206 X 2) / 3
Doing the long division, by hand yields 137 with 1 left over (e.g. 137 1/3) no arguing over decimal points. OTOH, this is law we are talking about, not math.
This issue is a bit more complicated than you think.
NOT
(2/3)*206=(412/3)=137.333333
Dont even need a calculator, just a pencil (or google)
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!
A 2/3 vote is easy to see if it passes. You must have at least 2x the number of 'yes' votes than 'no' votes. 136 to 70 fails because 136 is less than 140. It is as simple as that.
Also, this news is almost a year old. April 30, 2009 is the date on the article.
Really? Long division has been lost to the ages?
you need at least 137.33333 votes for the measure to pass. It did not equal or exceed this number. it did not pass.... I could have answered this when I was 8.
What's up with this box everyone has to think inside of or outside of? Why does there have to be a box?
>>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.
http://www.wolframalpha.com/input/?i=136%2F206%3E%3D2%2F3
Input:
136/206>=2/3
Result:
False
70/206 > 1/3, therefore 136/206 2/3
For a vote to pass it must win by a 2/3 majority
So therefore we can model this with an equation:
for a vote to pass true then y > 2x/3 where x = total number of votes cast, and y = total number of votes FOR the measure
So lets test y(136) > 2x(206)/3 and we find
THAT THE NAY'S HAVE IT! Yes we have just proved that 136 is NOT, i repeat, IS NOT equal to or greater than 2(206)/3
When there are more than 163 votes in total, going from 2 to 3 decimal places in the representation of 2/3 increases the number of votes required by one.
Perhaps choosing a repeating decimal in your definition of a majority is not very smart.
An integer approximation of a fraction is not equivalent to the fraction.
If you want to verify X is a 2/3 majority, of 206, the right way to do this is:
You start with the question, is a majority of at least 2/3 of 206 satisfied by X voters?
To answer, you express the underlying mathematical question, which is:
Is it true that X > (2/3) * 206 ?
Now, you could write this as X > 206*2/3 or X > 412/3
Then you have a problem, since 412 is not divisible by 3, you cannot express this as an integer.
Instead you arrive at the final question, using standard arithmetic operations... Your question is translated into 3 * X > 412 ?
Now you can affirmatively answer the question. for X = 136 voters, that many is enough to pass the motion, if and only if 3 times that number is greater than 412.
3 * 136 is 408.
So no. 136 voters is not sufficient to pass the bill.
We don't care exactly how many are required. We cannot determine that precisely in decimal notation, only give an approximation.
But we can very easily test if an integer number of voters satisfies the 2/3 requirement, by utilizing the above derivation.
> can't these people do simple math?
One guy made a stupid mistake. It doesn't mean someone can't do math, it just means he got one math question wrong--the failure wasn't so much the bad math, it was (1) the failure of him to check his math a second time when the vote came out as close as it did, and (2) the fact that they didn't have someone else check it.
It's okay to not notice an extra decimal place on a first approximation. It's not okay if it suddenly might matter because you're within a vote of not passing. When votes or scores actually make a difference, you have to either be especially rigorous or you have to make sure the information that actually makes the result indeterminate will never see the light of day. (The latter is only appropriate in a few cases, as where it doesn't change anything important and everyone thinks the decision has already been made. IT doesn't apply to zoning changes where millions of dollars are at issue. It might apply to some game scores.)
-- IANAL, this isn't legal advice, and definitely isn't legal advice for you. Also, Squee!
2/3 of 206 is 137.33333333... the town clerk and accountant fail at math. 66% is NOT the same as 2/3; in fact 2/3 would be 67% if you rounded it.
I've abandoned my search for truth; now I'm just looking for some useful delusions.
A lack of knowledge of mathematics is hazardous to your health, wealth, and well-being.
more cowbell
Robert's Rules requires that this motion would have failed, however, the chair at the time could have voted to break the tie. Whoever the chair is shouldn't have been so careless.
Why use decimals at all?
206*2/3=137.3333333333(repeating)
Since I have yet to see a third of a person, that means you need 138 votes.
206*2/3=137 and 1/3. 136 is too little!
2/3 = .66666666666666666667
136/206 = .66019417475728155339 < 2/3 .66504854368932038834 < 2/3
137/206 =
You have to go to 138/206 to get >= 2/3
... debating this issue. Clearly, if only it was handled by a bunch of reasoned individuals like us, that would not happen.
Lrn to math?
In the case of 2/3rds... .66 is not the proper equivalent, because the truncated value (.006666...) is greater than .005 and you have to round UP
So, the proper value for 2/3rds in this case would be .67, which yields 138.02, which is easily rounded to 138 people
I swear, we need some sort of remedial math training for politicians, that can be the only explanation for the fact that they continually pass unfunded mandates while cutting taxes. That might be a great way to get re-elected, but it is a damn poor way to balance the books
Wherever You Go, There You Are
Geez...50 comments and NONE of them make mention that Truro, Mass not too long ago lost their Postmaster. Not to mention the entire contingent of postal employees is ineligible to vote!
http://www.imdb.com/title/tt0120912/
Learning HOW to think is more important than learning WHAT to think.
...that 2/3 = 0,7 for large values of 2 ??
Religous speak to God. Insane are spoken to by God. When all shut up, one can finally hear Shostakovich in peace
Why bother with a less than accurate value at all? Why not multiply by 2, then divide by 3. The result is 137.333... Clearly 2/3rds of 206 is, when rounded, 137.
And for the folks that don't like the thought of rounding 1/3 of a vote, why don't they either add 2 seats or eliminate one so that rounding doesn't complicate things?
Just a thought.
*** *** You're just jealous 'cause the voices talk to me... ***
They must be seeing too much TV and watch 2-1/2 Men when they do watch TV.
Let alone two people at the same time.
Clearly this had been made up.
206 * 2 / 3 = 137.3...
Less than 137.3? No pass.
More than 137.3? Pass.
136 votes is not above 137.3, so it fails...
There's a much easier way to know whether a 2/3 vote has passed: There must be at least twice as many votes in favor as there are opposed. 136-70 fails. 137-69 fails. 138-68 passes. This matches up with the real math, since you can't have a fraction of a vote (in the normal case), so in order to get 137-1/3 votes, you must have 138.
This answer brought to you by your friendly neighborhood Professional Registered Parliamentarian member of the National Association of Parliamentarians.
Disinfect the GNU General Public Virus!
As Barbie says, "Math is hard, let's go shopping!"
Set your calculator to 2 decimal places.
Hell on Unix, use bc. 2/3 is multiply by 2 & divide by 3
206 / 3 = 68
68 * 2 = 136
Not to mention 0.66 anywhere.
Typically financial calculators are limited to 2 decimal places, some will even throw away the figures beyond the 2nd place. 2/3 = 0.66 They can prove the answer is 136. They can do the calculation in front of you and you can see it on the screen. If you've been taught that the computer or calculator is gospel, the result is 136.
Deleted
As long as we're rounding to two decimal places, .67 is a better approximation of 2/3 than .66
206 * .67 = 138.02
A person can't cast just 2 percent of his or her vote, so it's clear that 139 votes are required!
5/4 of all politicians don't understand math.
Table-ized A.I.
count the individual votes, the most votes win. forget about trying to figure out if it's a 2/3 majority.
if you really need to inisit on describing it as a fraction, its 106/206 ;)
If you mod me down, I will become more powerful than you can imagine....
They took time off from sucking each other off to actually vote?
Notice, those are the same people who take your taxes and then distribute them to the "best" use they can find for them, after of course, taking as much as they can for themselves. Have a nice day.
This is Massachusetts. I expect that kind of thing from Kansas or Texas, but a state known for technology and universities?
Table-ized A.I.
Not even hard. And there shouldn't be any decimals in there. The correct formula is (206*2)/3, yielding 137 and 1/3rd. So 137 votes fails (137 < 137&1/3rd), 138 passes (137&1/3rd < 138). Not all math is done in decimal notation, and they taught me how to do math with fractions way back in elementary school.
Any integer less than 138 is less than 2/3rds of 206. I could have told you this when I was 5.
See what you get.
But yeah.
Deleted
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!
Cut everyone in three pieces.
That's the easiest solution ever.
no math, no rounding, no court. done.
What they really need to do is have a special vote on what the definition of 2/3 should be for this past vote. Then a problem with a straightforward mathematical solution like this one can be replaced with a heavily politicized one, just like every other problem these days, resulting in a distortion in logic that we will live with for years.
You know what the real issue here is?
We, the Slashdot crowd ridicule the vote-counters for their mistake, yet there are over 100 posts and responses arguing the point. We ridicule them for what they did then, even as we do it now.
Government's idea of a balanced budget: take money from the right pocket to balance...oh who am I kidding?
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
Town Clerk: "The results until now are 137 for, 68 against."
Last man in the room: "Well... I'm 1/3 inclined to vote for, 2/3 against..."
Town Clerk: "Vote passed!"
It's refreshing Timmothy bothered to update the entry for the oversight.
Nevertheless, I think the quality of story selection has been diminishing a good bit here. Is it a revenue shortfall? If so, post a little story - tell us so that more will whitelist the URL for ads (or perhaps even subscribe). You've done good over the years to build loyalty, let me tell ya. Yous guys are an institution for us geeks and nerds of all stripes. Keep it that way.
Fuck systemd. Fuck Redhat. Fuck Soylent, too. Wait, scratch the last one.
From TFA: "A calculation by town accountant Trudy Brazil indicated that 136 votes are two-thirds of 206 total votes, said Town Clerk Cynthia Slade." Sadly, their city directory still lists her as town accountant.
It's perfectly rational, sadly. It's not natural, but it's perfectly rational.
We are talking about 2/3 here, you know.
We're all missing part of the story. 136 is a 2/3 majority when you're dealing with very large values of 136.
Who remembers their class on fractions?
Which is bigger? 2/3 or 136/206?
First, get a common denominator by multiplying each side by the denominator of the other...
2/3 * 206 = 412/618
136/206 * 3 = 408/618
Remember that the ratio hasn't changed (ie 2/3 = 412/618).
Since 412/618 > 408/618, then 2/3 > 136/206.
Notice how there aren't any decimal places involved, nor any rounding. I finally understand why my teachers insisted I learn how to do this by hand before I just plug it into a calculator.
... gets 137.333...(repeating). So 137 votes is not even enough. 136 is clearly not.
now we need to go OSS in diesel cars
...corruption more than stupidity. What's the bet the town clerk and town accountant were investors in the development the re-zoning would allow?
From:
http://www.tnrta.org/docs/TNRTA-nwsltr-Fall09.pdf
Instead of using Political Mathematics, they could have used Corporate Project Management Mathematics, where:
The society for a thought-free internet welcomes you.
The accountants only see dollar signs, and they always throw out the penny. Some tax forms let you round down to the nearest dollar. It's not a lot of money.... maybe a cup of coffee or two over the course of a few years. I'll take a cup of coffee in exchange for having the laws not pass. Most laws are dreck anyway.
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.
There are so great explanations of how to find wether or not the vote passes, I wish I was as smart as you guys. Thanks for explaining to me, I had no idea when reading the article what they did wrong but now I know.
A true programmer answer consist in using discrete math, otherwise there SHALL (SHALL as defined by RFC 2119) inevitably be issue with some junior programmer unaware of the limitations of floating-point numbers and unable to use a correct error margin etc.
A true programmer thinks this way:
Is 136 > 206 * / 3 ?
Becomes:
Is 136 * 3 > 206 * 2 ?
No, 408 ain't greater than 412.
Problem solved.
You guys seriously s*ck as programmers and I don't want you on my team (oh, I may have made a typo, have fun with it, but my point stays ;)
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?
I wrote to the author of the original article and asked her if she knew how they resolved it. If I get a useful response I'll share it here for the unproductively curious.
You need to understand how the election works. This is not hidden paper ballot election. Rather, like in many small New England towns, you simply raise your hand.
The issue was a contentious one, an issue that has divided the town for a long time. Heated arguments were made for awhile and then the vote occurred. After the winning side was announced many people left the meeting. A voting irregularity was pointed out (and procedurally, it was done incorrectly, and a second ballot was (incorrectly) called for.) Now mind, many people on both sides of the issue had left. The moderator ran the vote again and the answer was unchanged. Note how error prone the entire process is.
Curiously, based on the verbal arguments, the issue could have passed with some fairly minor wording changes. (I was opposed to its passing so obviously I didn't point this out.) The same issue is not on a town warrant for this year. Rather, the selectman will be asking the townspeople if they want a paper ballot election to look into the issue. I'm a little surprised that the proponents didn't resubmit the question and just make sure they had their supports show up.
I'll post this now and get into the issue next.
Paul
There is something i do not understand :
let ' a ' be the number of votes for
and
let ' b ' be the number of votes against
the condition to pass is
a >= 2/3*(a+b)
it is equivalent to
1/3*a >= 2/3*b
which in turn is equivalent to
a >= 2*b
but then, it would require a >= 2*70 = 140 , and not 136 or 137 !! Where am I wrong ? Help me !
Seriously guys, this is a Christian nation. How can you expect people to go beyond .66? DO YOU UNDERSTAND THE RAMIFICATIONS?
'Political power grows out of the barrel of a gun.' - Mao Tse-tung
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).
I'm going to work out how much 2/3 of 206 is and then tell everyone what my calculator told me. I bet no one has thought of doing this yet and will appreciate the effort I put into this problem. I'm the sort of guy who's always on the look out for ways to contribute to this website.
and it tells me that 3,489,122 votes are needed.
Nullius in verba
If you need 2/3 to pass, then anything over 1/3 opposed defeats the measure.
Well, if 2/3rds is twice 1/3rd (it is...), then if the vote against is twice or more what the vote for is, the measure is defeated.
The vote was 136 for, 70 against. 70 is more than half of 136.
The nays have it.
Had the vote against been 68, that's exactly half of 136 - the yeas have it. Of course, if the total of votes were the same, then from a total of 206 votes, 137 for leaves 69 against. 69 is half of 138. Woops, the nays have it still. But 138 for leaves 68 against. Half of 138 is 69. Not enough no votes. The yeas prevail. This method avoids rounding, and satisfies the 2/3-1/3 formula.
Is this simple enough for ya?
This is only complicated because in this case 137.3 votes carries the measure, but we don't count fractional votes, even in Massachusetts. So it takes the extra .7 of a vote, or 148 whole votes, to approve the measure.
This wouldn't have happened in Maine, where we dislike Augusta sticking its nose into town business. But then we left the Commonwealth in 1820, for several reasons.
deleting the extra space after periods so i can stay relevant, yeah.
2/3 votes are defined as passing if the number of votes in favor is greater than or equal to twice the number of votes against. Period. No need to dick around with fractions at all. Take the number votes against and double it. Is that greater than the number of votes in favor? Yes. it is defeated. No. It passes. So double 70... 140. That is greater than 136. So defeated. In the original vote however... 64 against doubled is 128 which is less than 139 and so it passes. I'm not certain why they needed a recount at all?
Other things that people screw up: It is the count of votes in favor and against that matter. It has nothing to do with the number of representatives. So the fact that at least three members didn't vote the first time doesn't matter. Also, there is never a need to call for or count "those abstaining." The fact that they did not vote in favor of or for against implies abstention. Abstention votes have no bearing on a motion. Lastly, as long as a quorum is reached (minimum number of representatives present is met) then it doesn't matter how many vote... You could have a quorum of 150 people and if only two vote in favor and 1 votes against while the remaining 147 have decided not to vote or have fallen asleep... the motion passes.
I will never live for sake of another man, nor ask another man to live for mine.
If the voter has a boner, round-up that one too.
And you know what, I think if they just got into a big nice orgy on the voter floor we could count the resulting pregnancies as a round-up or round-down based on gender of the babe/foetus; if it's a female then round-down because those obviously are inferior to the strength of a (round-up)male.
Maybe if someone had a parrot perched on their shoulder that would count as 1/10th a vote, so moar p-p-p-powerrr to voters with parrots on their shoulders. Head lice are inferior to someone with a toupee.
(2/3) of 206 = 137.333333
If there were only 204 members, two thirds would require exactly 136 "yes" votes. So adding two more members obviously requires at least one more "yes" vote to exceed the required number of votes to pass. In other words, if 136 yes votes are needed with 204 total members, then more than 136 are needed with 206 members.
This, my friends, is why the American educational system is so poor. The politicians don't want their constituents to be more intelligent than themselves, for fear of having their incompetence exposed.
And the measure didn't require 2/Pi votes.
> The 136 people don't include the woman.
So where do you get the 138th person from?
If there are one thousand voting, you only need 660 to pass.
If one million are voting, you only need 660,000 to pass.
If one billion are voting, you only need 660,000,000 to pass.
Their they're doing there hair.
The population is so dumbed down that simple fractions now leave them befuddled. The law calls for 2/3, not 66% or .66 or .6666 nor even .66666666666. Multiplied by two and divided by three. It's just not that hard! Back before calculators we even had these things called remainders that could be turned into fractions.
Before people surrendered all of their arithmetic skills to the calculator, fractions used to be carried through a computation until a result was produced or the denominator would go into the numerator evenly. The result was no rounding errors at all.
They could have avoided all the hair splitting and nit picking over what 1/3 of a person means if they did the math right in the first place.
This is the sort of question that might come up on a 5th grade math test and they all flunked. No wonder towns can't balance their budgets.
The law says 2/3. They used 66/100.
Sometimes it is easier to not use any "complicated" maths. If you need more than 2/3 of the votes to pass, that means that you need more than twice the votes of those who vote against it. You do not even need to do any calculations involving possible rounding errors. Just look at the "no" votes, multiply by 2, and compare to the "yes" votes. Are the "yes" votes more than that? Congratulations, you have more than 2/3 of the votes. No need to even calculated what EXACTLY 2/3 of the votes would be.
In this case: 136 "yes", 70 "no". 136 is less than 140, so the vote does not pass. Done.
Sorry to crosslink, but this guy had it right: http://politics.slashdot.org/comments.pl?sid=1628396&cid=31950218
"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."
Mod HIM, not me. Thanks.
Hmm. Need 2/3rds majority. You say 70 people voted against? Then you need 140 or more to vote for. Got 136? Oh well, looks like it fails. No need to worry about what 2/3rds of 206 is. Just simply see if at least twice as many people voted for the issue compared to the number who voted against.
20 years and 365 days may not mean someone is 21 years old, we have leap years to make it fun.
The zoning measure needed a two-thirds vote to pass
Is that what it said? Or did it say greater than 2/3? At least 2/3?
So 173 is not 2/3 and since you can't have a fraction of a vote, I'd say it takes 138 votes to pass.
.... I'm trying to decide if I would want to have a contract with them.
It might work to my favor.
To me its far easier to do this:
206 votes total, 2/3 to pass.. which means 1/3 against is the most that can vote against (since they don't mention abstentions and how abstentions are handled).
206 * 1/3 or 206/3 is 68 and 2/3... if more than that vote against it can't pass.
70 is more than 68 2/3 so the vote fails.
If it take their bad shortcut method and say 206 * 0.33 i get 67.98 which is also less than 70 so that vote fails.
jcochran said it similarly. if you think it passed than that means passed voters against * 2 = passed voters... its not.
This is also why I ensure that everyone agrees and records what they believe is the required number of voters for or against to pass / block a decision (when its not a majority wins decision with friends) BEFORE actually voting.
"Jazz isn't dead, it just smells funny" ~Frank Zappa
EdelFactor
They would pass the Tea-Party test though...
Baddabisssssh!! ;-)
"The 100% accurate answer is 137 and 1/3."
Really. I could swear 137*3/2 is 205.5, which is half a person less than 206. So this is not counting everyone fully. 137 is not enough if more people than 2/3 have to vote in favour (no pass, no blank votes).
206*2/3 = 137.33333.....
Since you can't have 1/3 of a person, 138 persons would have to vote in favour to meet these rather arbitrary voting conditions.
If the condition is that more than 1/3 have to vote in favour, you can even get a situation of equality, where it is still undecided.. Of course abuse in the voting process have been rampant all the time, so people being so weak at maths is a big plus for certain people who want to push things their way..
The debate is stupid.
Each vote has an equal value.
Rounding up or down will approximate the weight of each vote.
100/206=0.485436893, the proportional value of each vote.
So, 0.485436893*136=66.02 votes per 100 people in the population of 206.
66% is correct for 136 votes in a 206 population.
Unaccountable leaders are masters, and unrepresented people are slaves. How do US and EU fare?
"the first vote was close, counted as 139 in favor and 64 opposed. A recount was held that was tallied at 136-70"
Third world accuracy.
Or is it 2/3 world accuracy?
No brain, no pain.
this
The number FOR is TWICE or more than the number AGAINST. simple. 2 of every 3. duh. 136 is NOT twice 70; 137 is not twice 69; 138 is twice 68. simple.
This problem is not very difficult, because taking 2/3 from 206 gives you just 137+1/3. But can you subtract 0.999... from 1?
This thread is a good example of how our generation was taught math wrong. I'm talking about the +5 responders, not the people in the article. Most people in this discussion are saying that the number of votes needed is 137.33 based on multiplying 206 by 2/3. The fact that all of the upvoted responders used arithmetic belies the failure of our math education system. Arithmetic has its place, but not here. This is a simple number problem. 2/3 is twice 1/3, so the number of yea votes must be twice the number of nay votes. Obviously the vote failed because 136 is less than twice 70. Using arithmetic is unnecessary and overly complicates the issue. We don't need any discussion about repeating digits or order of operations. I think Lockhart said it best.
This is why people need to know fractions!!!! If only i could convince my college class that this was important. :(
It's not necessarily plain maths that is at issue, it may be the specific wording (which is not given in TFA).
It's easy for an article to say the "measure needed a two-thirds vote to pass" and for everybody to have an understanding that the vote requires at least a two thirds majority of the votes (which is the 138 yeas) but that's not necessarily the literal interpretation of what was written. For starters "needed a two-thirds vote to pass" may require 2/3 of the eligible voters to turn out in favour - our 206 does not include anyone abstaining...
It could also say that it needs a third to block the vote, 68.6recurring so 69 (back to our 137 yeas). But most people would still talk about this as what is required to pass the vote, people are inaccurate like that.
If it says "requireth no less than two yeas per one nays", everyone understands that's two out of three, 2/3 right? Wrong. You start with your nays to determine the number of requires yeas and it's 2:1 so if 70 voted nay they would need 140 yea.
One naturally assumes that a vote requiring a 2/3 majority requires a full two-thirds, i.e. rounding the required number of yea's up to the nearest whole. But assumptions should never be confused for facts.
But probably it does require the 2/3 majority, rounded up. The error here could well stem from careless use of technology. An accountant's calculator (the type which prints to a paper roll) round to two decimal places as they are used for currency, a good accountant will habitually utilise this rounding to his client's advantage whenever possible.
It is a false argument. A law requiring a two thirds vote is entirely different than a law requiring a .66 per cent vote. Solve it as it is written. Multiply the fraction two thirds times 206 and one gets the only correct answer 137.33 votes.Frankly I'm shocked that almost everyone didn't see the real issue.