# At Issue In a Massachusetts Town, the Value of Two-Thirds

#### timothy posted more than 4 years ago | from the all-those-in-favor-and-then-some dept.

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.

## Counting people? Round up! (1)

## CannonballHead (842625) | more than 4 years ago | (#31947606)

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.

## Re:Counting people? Round up! (1)

## afaik_ianal (918433) | more than 4 years ago | (#31947670)

The only law I've ever had to deal with similar to this (see my nick for a caveat here) says that for certain things to pass, you need "not less than a two thirds majority". That's pretty cut and dried. Two thirds of 206 is 412 / 3. 136 is 408 / 3. Seems pretty clear to me.

## Re:Counting people? Round up! (5, Insightful)

## lgw (121541) | more than 4 years ago | (#31947676)

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?

## Re:Counting people? Round up! (1)

## CannonballHead (842625) | more than 4 years ago | (#31947794)

Hmmm, after looking at it again it looks like they *are* rounding up/ceiling.

The issue is that they were rounding up an integer that was too small..

(in other words, you're right, hehe)

## Re:Counting people? Round up! (0)

## Anonymous Coward | more than 4 years ago | (#31948198)

No, they weren't.

## Re:Counting people? Round up! (0)

## Anonymous Coward | more than 4 years ago | (#31947826)

they were told there would be no math?

## Is our calculator society showing? (2, Insightful)

## Motard (1553251) | more than 4 years ago | (#31947832)

Really? Long division has been lost to the ages?

## Re:Is our calculator society showing? (3, Insightful)

## Bigjeff5 (1143585) | more than 4 years ago | (#31948156)

It's not even a long division problem, it's a basic math problem.

It's trivial to multiply 206 by 2/3 on a calculater, and it in no way involves any decimal figure until the result is shown.

206 * 2 = 412. 412/3 = 137.3~, or 137r1 via long division.

It's pretty clear, the law requires a 2/3 majority, and 137 is not even a 2/3 majority, let alone 136. This is maybe third or fourth grade level math here people, and it's kinda sad that there is even any confusion about it. .66 is not 2/3, it's a little less than 2/3 and it does not count if the law says 2/3.

## Re:Counting people? Round up! (5, Insightful)

## Gudeldar (705128) | more than 4 years ago | (#31947884)

## Re:Counting people? Round up! (0)

## Anonymous Coward | more than 4 years ago | (#31948186)

Yeah.

What they are doing is similar to wantonly saying, "lets just use a very small value of 206: 200" Then, you have just eliminated 6 votes from the total, and faked moving the proportion closer to 100%... in all fairness, some smart cheater there "forgot" using a "smaller value of 137" to somewhat even the score both ways, even if that's still not exactly the issue.

I think somebody needs to teach them that .66 != 2/3

And also teach them about significant digits. Point 66 has only 2. Number 206 obviously needs 3. But in applied math, you need balance by forcing both mantissas to either 2

or3 digits or there will be a large margin of error.## Re:Counting people? Round up! (0)

## Anonymous Coward | more than 4 years ago | (#31948202)

yeah that's very important.

So is this:

http://www.youtube.com/watch?v=c_l1FLHAPHI&feature=related

Stop giving them your data people, please!

## Re:Counting people? Round up! (4, Insightful)

## spazdor (902907) | more than 4 years ago | (#31947678)

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.## Re:Counting people? Round up! (1)

## jedidiah (1196) | more than 4 years ago | (#31947688)

You would think that an "accountant" would know that 2/3 is actually .66666... and gets rounded to .67 at two digits.

## Re:Counting people? Round up! (1)

## TheCarp (96830) | more than 4 years ago | (#31947900)

Actually, thats not even correct. Its a repeating number, but, its wrong to round in the middle of an operation. You always round the final value, not the intermediary value. You take 2/3 and then round, not round and then multiply.

-Steve

## Re:Counting people? Round up! (0)

## Anonymous Coward | more than 4 years ago | (#31948094)

... means "repeating"

## Re:Counting people? Round up! (1)

## idontgno (624372) | more than 4 years ago | (#31948132)

How about, you multiply by 2 and then, at the end, divide by 3.

That leaves the repeating decimal part at the very end of the calculation, where you can "round the final value" like you suggest.

Whereas your suggestion "take 2/3" means you start out with the repeating decimal whose approximation was the source of the problem.

In other words, the root of the problem is the idea of an absolute-precision decimal rendition of "2/3". You haven't escaped it. By doing this division first, you're stuck arbitrarily choosing some approximation for your intermediate value, just like the folks you're criticizing.

## Re:Counting people? Round up! (1)

## ferrocene (203243) | more than 4 years ago | (#31947902)

pft, clearly you've been taught wrong. 2/3 is really .666666. Duh.

## Re:Counting people? Round up! (2, Insightful)

## Anonymous Coward | more than 4 years ago | (#31948020)

The scariest part is their accountant is the one who things .66 is 2/3. I'll bet their books are ALL MESSED UP

## It's not the accountant I'm worried about (0)

## Anonymous Coward | more than 4 years ago | (#31947634)

It's the poster:

Truro zoning decision hinges on single vote

By Mary Ann Bragg

mbragg@capecodonline.com

April 30, 2009

## basic math (1, Informative)

## Anonymous Coward | more than 4 years ago | (#31947636)

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.

## Re:basic math (4, Informative)

## QRDeNameland (873957) | more than 4 years ago | (#31948024)

...unless you have fractional people.

Well, that's not exactly unprecedented in American politics.

three fifths of all other Persons [wikipedia.org]

## not quite 2/3 (5, Insightful)

## rla3rd (596810) | more than 4 years ago | (#31947640)

2 / 3 = 0.66666666...

106 / 236 = 0.660194175

Whats the problem here? It didn't pass.

## Re:not quite 2/3 (3, Informative)

## siwelwerd (869956) | more than 4 years ago | (#31947848)

## Re:not quite 2/3 (0)

## Anonymous Coward | more than 4 years ago | (#31948042)

Easier said than done, sometimes.

## Re:not quite 2/3 (2, Insightful)

## vikingpower (768921) | more than 4 years ago | (#31948148)

## Re:not quite 2/3 (1)

## thoughtsatthemoment (1687848) | more than 4 years ago | (#31948060)

## Re:not quite 2/3 (1, Insightful)

## Anonymous Coward | more than 4 years ago | (#31948078)

Regardless of personhood status, it's really hard to argue a fetus is voting age.

## Re:not quite 2/3 (0)

## Anonymous Coward | more than 4 years ago | (#31948160)

What about 137 and a slave? The Constitution says they count for 3/5 of a person.

## Re:not quite 2/3 (1)

## Herkum01 (592704) | more than 4 years ago | (#31947870)

106 / 236 = 0.660194175Evidently an article on math and/or writing skills is needed on slashdot as well...

## Re:not quite 2/3 (0)

## Anonymous Coward | more than 4 years ago | (#31947872)

rhetorical questions, rla3rd

## Re:not quite 2/3 (3, Funny)

## complete loony (663508) | more than 4 years ago | (#31947906)

## They can do simple math! (Probably) (1)

## Oxford_Comma_Lover (1679530) | more than 4 years ago | (#31947972)

> 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.)

## Re:not quite 2/3 (2, Interesting)

## mysidia (191772) | more than 4 years ago | (#31948110)

"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:not quite 2/3 (0)

## Anonymous Coward | more than 4 years ago | (#31948140)

Very obviously this sort of calculation should be done by multiplying everything by 3.

136 in favor: 3*136=408

70 against: 3*70=210

206 total: 3*206=618

2/3 of 618: 412

The vote passes if the number of in-favor votes multiplied by three is 412 or more.

## Learn 2 math (1, Insightful)

## Dunbal (464142) | more than 4 years ago | (#31947646)

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.

## Re:Learn 2 math (1)

## Monkeedude1212 (1560403) | more than 4 years ago | (#31947746)

They shouldn't be using any amount of signifigant digits. Simply put, 0.6 and 0.66 and 0.666 are all less than 2/3. Only equal to or greater than 2/3 allows a pass. It was close, but no cigar.

## Re:Learn 2 math (1)

## teh moges (875080) | more than 4 years ago | (#31947934)

## Re:Learn 2 math (3, Informative)

## amicusNYCL (1538833) | more than 4 years ago | (#31947754)

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.

## Re:Learn 2 math (2, Insightful)

## Dunbal (464142) | more than 4 years ago | (#31947996)

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 [wikipedia.org] when you take any science major.

## Re:Learn 2 math (0)

## Anonymous Coward | more than 4 years ago | (#31948104)

"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"?"

Easily: pi * r ^ 2

That expresses the area of the circle EXACTLY.

That is why the law doesn't need to worry about degree of accuracy, because it expresses the MINIMUM votes to pass as an EXACT number: 2/3

If you have exactly 2/3 or greater votes, it passes. Fewer, it does not pass. No "degree of accuracy" required.

## Re:Learn 2 math (1)

## lgw (121541) | more than 4 years ago | (#31948112)

The analogy fails, though, as there's no error of measurement here. The area of a circle with a radius of "the integer 25" is 625*pi exactly, not some decimal measuement. 2/3s of 206 is 137+1/3 exactly, not some decimal measurement.

## Re:Learn 2 math (1)

## F'Nok (226987) | more than 4 years ago | (#31948178)

Your example has no relevance.

Significant figures are used whenever a measured value is involved, such as the 25.0 (three significant figures) in your example.

The article has

infinite precisionso significant figures areinappropriate.You cannot have 136.001 people. Ever.

There were 136 people,

exactly 136, which is to say: 136.00...The requirement is for 2/3 majority. That means 0.666...

Both of these have infinite significant figures, and both can be trivially used in this calculation without needing approximations.

Required vote:

206 * 2 = 412

412 / 3Actual vote: 136

Expressed with common factor

136 * 3 = 408

408 / 3What's not clear here?

The actual vote is lower, no approximations needed, no arguments about significant figures, and no pretending you know anything about significant figures when you can't identify the

appropriate situationsfor their use.## Re:Learn 2 math (1)

## amicusNYCL (1538833) | more than 4 years ago | (#31948190)

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"?

Pi is not a repeating number, it's an irrational number. When you're dealing with an irrational number the only way you can express it is by itself. Pi is pi, that's it. The only value equal to pi is pi. If you're using pi in a calculation, you don't use a fraction, you use pi. 22/7 is sometimes used to estimate pi, but that's not correct either.

Thankfully, legislative decisions are not based on irrational numbers, they are based on fractions.

## Re:Learn 2 math (5, Insightful)

## rolfwind (528248) | more than 4 years ago | (#31947788)

You're complicating it.

(206 * 2)/3 = 137.333

Why use 0.66xxxx whatever when you don't have to?

## Re:Learn 2 math (1)

## Citizen of Earth (569446) | more than 4 years ago | (#31948052)

You're complicating it.

136/206 = 0.660194...

This is clearly less than 0.666666...

## Re:Learn 2 math (0)

## Anonymous Coward | more than 4 years ago | (#31947856)

Mathematics should not be subject to politics.

Very very true.

Unfortunately, there is plenty of times law has attempted to define math.

A lil over a hundred years ago, Indiana passed laws to make pi be exactly 3.200000

http://www.agecon.purdue.edu/crd/Localgov/Second%20Level%20pages/indiana_pi_bill.htm [purdue.edu]

There was an april fools joke going around about 10 years back or so that Alabama did the same thing, and people got just as upset at the time since this has been done before by politicians so had less than no reason to think it was actually a joke.

## Re:Learn 2 math (1)

## vux984 (928602) | more than 4 years ago | (#31947926)

significant digits aren't really the issue at all.

2/3*206 = 412/3

137 = 411/3

138 = 414/3

411/3 = 412/3 so 138 is more than enough

## Re:Learn 2 math (1)

## vux984 (928602) | more than 4 years ago | (#31947954)

"411/3 = 412/3 so 138 is more than enough"

lol... slashdot does funny things when you use angle brackets (ie lssthan gtrthan signs)

try that again

411/3 is less than 412/3 so 137 is not enough

414/3 is more than 412/3 so 138 is more than enough

## Re:Learn 2 math (0)

## Anonymous Coward | more than 4 years ago | (#31947936)

The majority was FOR the decision, not against. They should just pass it.

## Re:Learn 2 math (1)

## siwelwerd (869956) | more than 4 years ago | (#31947986)

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

Significant figures has absolutely nothing to do with it. They are for making measurements in a non-discrete space. All that's going on here is counting--there's no error, so no need for significant figures. Why on earth would you approximate a constant anyways? In any event, your rule for 'at least 3 digits' is completely arbitrary and useless. With enough votes, one could show that taking 'at least 3 digits' would still yield an incorrect result.

## That's not difficult (0)

## Anonymous Coward | more than 4 years ago | (#31947648)

2/3 != 0.66. In fact, 0.66 2/3. This is objective mathematical truth. Can we move on?

## Fractions (1)

## nmb3000 (741169) | more than 4 years ago | (#31947656)

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.

## Re:Fractions (1)

## pluther (647209) | more than 4 years ago | (#31947728)

So, really, they need 138 votes.

137 137 1/3, therefore it wouldn't pass.

## Re:Fractions (-1, Troll)

## Anonymous Coward | more than 4 years ago | (#31947770)

Obviously you can't have 1/3 of a vote.

What about midgets?

## Re:Fractions (2, Informative)

## ferrocene (203243) | more than 4 years ago | (#31947784)

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.

## Re:Fractions (2, Informative)

## Imagix (695350) | more than 4 years ago | (#31947888)

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;

## Re:Fractions (1)

## bnenning (58349) | more than 4 years ago | (#31947904)

Better put a decimal point in those numbers, otherwise you're confirming that 0>=0.

## Re:Fractions (0)

## Anonymous Coward | more than 4 years ago | (#31947960)

Did you actually try that? 0 would be enough to pass using that.

## Re:Fractions (3, Funny)

## ferrocene (203243) | more than 4 years ago | (#31948046)

um... /. stripped my decimal points...yeah, that's it...

## Re:Fractions (1)

## amicusNYCL (1538833) | more than 4 years ago | (#31947786)

137 votes is not "at least 2/3" of 206, 138 votes is "at least 2/3". 137 votes is still less than 2/3. This isn't difficult.

## Re:Fractions (0)

## Anonymous Coward | more than 4 years ago | (#31947816)

right, you can't have 1/3, and the law says two thirds majority. The lowest number that is greater than 137 1/3 is 138, 137 is not a two thirds majority.

## Re:Fractions (1)

## Idarubicin (579475) | more than 4 years ago | (#31947840)

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.

Nope, it doesn't. The correct answer is 138 votes to pass. As you noted, 206 times 2/3 is 137

plus one third. 137 votes is less than two thirds of 206; it therefore doesn't pass either.(If the supermajority calculation is confusing, consider a conceptually-easier simple majority (1/2) case. In the hypothetical case of 101 voters, a pass is 51 votes - being the first integer

greater than50.5 - not 50.)Why is this hard?

## It's simple (1)

## Monkeedude1212 (1560403) | more than 4 years ago | (#31947674)

(136 / 206 == 0.660194174757281553398058252427181) is less than (2/3 == 0.66666666666666666666666666repeating)

The vote does not pass.

## hmmm (2, Funny)

## Anonymous Coward | more than 4 years ago | (#31947680)

Did the Town Clerk and Town Accountant ever work for Verizon?

## Political Mathematics (5, Insightful)

## WahCheng (1543195) | more than 4 years ago | (#31947692)

## Math is hard. (1)

## ZHaDoom (65485) | more than 4 years ago | (#31947694)

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

## Re:Math is hard. (1)

## iammani (1392285) | more than 4 years ago | (#31947762)

## maybe.... (0)

## Anonymous Coward | more than 4 years ago | (#31947702)

Maybe Truro should vote on getting a

town accountantwho knows how todivide by three. Or, failing that, one that can round (2/3 doesn't round to 0.66!)## Mathematica says... (1)

## Gavin Scott (15916) | more than 4 years ago | (#31947706)

In[1]:= 136/206 >= 2/3

Out[1]= False

## Wolfram Alpha says... (0)

## Anonymous Coward | more than 4 years ago | (#31947908)

http://www.wolframalpha.com/input/?i=136%2F206%3E%3D2%2F3

Input:

136/206>=2/3

Result:

False

## you've got to be kidding me (1)

## roc97007 (608802) | more than 4 years ago | (#31947716)

## Accuracy (1)

## chemicaldave (1776600) | more than 4 years ago | (#31947722)

## Is the math really that hard? (1)

## AaronPSU777 (938553) | more than 4 years ago | (#31947732)

## this whole story (5, Funny)

## jarrodlikesmath (1795858) | more than 4 years ago | (#31947734)

## Re:this whole story (0)

## Anonymous Coward | more than 4 years ago | (#31948082)

Arguing about it is cathartic. Right? Agree with me on this one thing, dammit.

## Seriously? (1)

## msauve (701917) | more than 4 years ago | (#31947740)

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 [time.com] .

## You're kidding me! (0, Redundant)

## Antony-Kyre (807195) | more than 4 years ago | (#31947760)

2/3*206 = 137.33333333333333333333333333333. Technically, 137 is less than two-thirds. If you need AT LEAST two-thirds, you need 138.

## Easy, no fractions or decimals needed (4, Insightful)

## dpbsmith (263124) | more than 4 years ago | (#31947768)

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.

## Re:Easy, no fractions or decimals needed (1)

## MurphyZero (717692) | more than 4 years ago | (#31947942)

## Re:Easy, no fractions or decimals needed (1)

## Dan Morenus (179942) | more than 4 years ago | (#31947998)

## Even more worrying is this: (0)

## Anonymous Coward | more than 4 years ago | (#31947772)

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.

## An accountant?? (1)

## digitalhermit (113459) | more than 4 years ago | (#31947782)

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...

## Re:An accountant?? (0)

## Anonymous Coward | more than 4 years ago | (#31948208)

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...

We don't need that many digits. We can just use 0 instead of 0.6 or 0.66. Therefore any votes in favor, it passes!

## must be using a calculator... (1)

## NotQuiteReal (608241) | more than 4 years ago | (#31947796)

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.

## math is hard (0)

## Anonymous Coward | more than 4 years ago | (#31947810)

NOT

(2/3)*206=(412/3)=137.333333

Dont even need a calculator, just a pencil (or google)

## Ask an engineer, a mathematician, a politician (4, Insightful)

## PolygamousRanchKid (1290638) | more than 4 years ago | (#31947814)

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 . . . ?"

## Re:Ask an engineer, a mathematician, a politician (2, Funny)

## clintonmonk (1411953) | more than 4 years ago | (#31948130)

## Math and dates (1)

## imp (7585) | more than 4 years ago | (#31947830)

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.

## Math is simple. (1)

## thinktech (1278026) | more than 4 years ago | (#31947834)

## use integers, damnit! (4, Insightful)

## Paul Rose (771894) | more than 4 years ago | (#31947864)

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

## This is a year old... (4, Informative)

## Jah-Wren Ryel (80510) | more than 4 years ago | (#31947874)

Date on the article is April 30th, 2009.

So, does anyone know if basic math skills prevailed?

## logic (0)

## Anonymous Coward | more than 4 years ago | (#31947932)

70/206 > 1/3, therefore 136/206 2/3

## Basic math Anyone? (0)

## Anonymous Coward | more than 4 years ago | (#31947950)

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

## An unforeseen problem. (1)

## nuckfuts (690967) | more than 4 years ago | (#31947958)

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.

## Common mistake (1)

## mysidia (191772) | more than 4 years ago | (#31947964)

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

rightway 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*2/3orX > 412/3Then 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 isnot sufficientto pass the bill.We don't care

exactly how manyare required. We cannot determine that precisely in decimal notation, only give an approximation.But we can very easily test if an

integer number of voterssatisfies the 2/3 requirement, by utilizing the above derivation.## FAIL! (1)

## Locke2005 (849178) | more than 4 years ago | (#31948076)

## Lack of knowledge of mathematics (1)

## wonderboss (952111) | more than 4 years ago | (#31948086)

## Robert's Rule (0)

## Anonymous Coward | more than 4 years ago | (#31948138)

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? (1)

## h4rr4r (612664) | more than 4 years ago | (#31948142)

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.

## Well according to my calculator (0)

## Anonymous Coward | more than 4 years ago | (#31948168)

206*2/3=137 and 1/3. 136 is too little!