## 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.
## Counting people? Round up! (Score:2)

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! (Score:5, Insightful)

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: (Score:2)

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: (Score:3, Insightful)

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.

## Spltting hairs, are we? (Score:5, Insightful)

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.

## Re:Spltting hairs, are we? (Score:5, Funny)

Under my proposed law, during the years between 16 and 21 noninclusive, the probability of being chargeable, upon discovery, with underage drinking shall be determined by interpolation through a truncated logistic function. n'hey.

## It's not that silly (Score:5, Insightful)

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).

## Re: (Score:3, Insightful)

There are even better reasons to draw sharp, arbitrary lines - to make the outcome of the law predictable. If the line between between old-enough-to-drink and not-old-enough-to-drink was fuzzy, or the court was required to decide if you were mature enough to drink, it would be almost impossible for the individual to determine when it was safe to drink.

## Re: (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.

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

Really? Long division has been lost to the ages?

## Re:Is our calculator society showing? (Score:4, Insightful)

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:Is our calculator society showing? (Score:5, Insightful)

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.You know good and well these assholes were the kids who used to ask "Why will I ever need to know this stuff in real life?" when they were kids.

Well, you stupid asses, this is why.

LK

## The math was correct (Score:4, Funny)

We're all missing part of the story. 136 is a 2/3 majority when you're dealing with very large values of 136.

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

## I'm a CPA and... (Score:3, Interesting)

## Re: (Score:2)

They should not even have used .66 ... .67 would have been much better :)

## Re:Divide 2 by 3 on a financial calculator (Score:5, Insightful)

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.

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

206/3*2 = 136

206./3*2 = 137.333333333334

If you round the division down then do the multiplication, you get 136.

## Re: (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

## Re: (Score:3, Funny)

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.

## Don't Round--Truncate! (Score:5, Funny)

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!

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

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.

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

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: (Score:2)

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

## Re: (Score:2)

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: (Score:2)

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 cho

## Re: (Score:2)

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

## Re: (Score:3, Informative)

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.

## Re: (Score:3, Funny)

The 100% accurate answer is 137 and 1/3.

So this is a midget voting?!?!

## Re: (Score:2)

You would think any dumbass would know how to multiply fractions on a calculator - it doesn't take any fancy functions, just a very very basic understanding of what a fraction is.

When it says 2/3, you use 2/3, not a decimal of anything. (206*2)/3, that's it. Done. The answer is 137.3~, and it's as accurate as is humanly possible. The only number of voters that satisfies the 2/3 majority requirement is 138.

## Re: (Score:2, Insightful)

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

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

I think this is a symptom of a generation raised with calculators...

## Re: (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 Art

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

2 / 3 = 0.66666666...

106 / 236 = 0.660194175

Whats the problem here? It didn't pass.

## Re:not quite 2/3 (Score:4, Informative)

## Re: (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 dec

## Re: (Score:2, Insightful)

## Re:not quite 2/3 (Score:4, Funny)

## Re: (Score:2)

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

## Re:not quite 2/3 (Score:4, Funny)

## They can do simple math! (Probably) (Score:2)

> 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 n

## Re: (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:not quite 2/3 (Score:4, Funny)

can't these people do simple math? 2 / 3 = 0.66666666... 106 / 236 = 0.660194175 Whats the problem here? It didn't pass.

Me and my Pentium beg to differ.My pentium begs to differ.

## Fractions (Score:2)

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: (Score:2)

So, really, they need 138 votes.

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

## Re: (Score:3, Informative)

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: (Score:3, Informative)

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: (Score:2)

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

## Re:Fractions (Score:4, Funny)

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

## Re: (Score:2)

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: (Score:2)

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 (Score:2)

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

The vote does not pass.

## Re: (Score:3)

The vote does not pass.

Are they going to hire Gandalf to tell then the news?!?

## hmmm (Score:2, Funny)

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

## Political Mathematics (Score:5, Insightful)

## Mathematica says... (Score:2)

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

Out[1]= False

## you've got to be kidding me (Score:2)

## Is the math really that hard? (Score:2)

## this whole story (Score:5, Funny)

## Re:this whole story (Score:5, Funny)

I disagree. This is a prime example of rationality.

## Seriously? (Score:2)

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].

## Easy, no fractions or decimals needed (Score:5, Insightful)

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: (Score:2)

## Re: (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.

## Too easy perhaps (Score:3, Informative)

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.

## An accountant?? (Score:2)

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: (Score:2)

Why stop there? .6 rounded down is 0, so then they'd only need 0 votes to pass.

## must be using a calculator... (Score:2)

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.

## Ask an engineer, a mathematician, a politician (Score:5, Insightful)

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: (Score:2, Funny)

## Math and dates (Score:2)

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.

## use integers, damnit! (Score:5, Insightful)

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... (Score:5, Informative)

Date on the article is April 30th, 2009.

So, does anyone know if basic math skills prevailed?

## Re:This is a year old... (Score:5, Informative)

## Re: (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.

## An unforeseen problem. (Score:2)

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.

## FAIL! (Score:2)

## Why use decimals at all? (Score:2)

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.

## Aliens! (Score:2)

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/ [imdb.com]

## At issue on Slashdot, the Value of 2009 (Score:3, Funny)

## multiply by 2 then divide by 3 ... (Score:3, Insightful)

... gets 137.333...(repeating). So 137 votes is not even enough. 136 is clearly not.

## The Mass. AG did resolve this (Score:3, Informative)

From:

http://www.tnrta.org/docs/TNRTA-nwsltr-Fall09.pdf [tnrta.org]

## This article is a year old? (Score:4, Insightful)

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.

## Re: (Score:2)

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: (Score:2)

## Re:Learn 2 math (Score:4, Informative)

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: (Score:3, Insightful)

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 su

## Re: (Score:2)

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: (Score:2)

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 (Score:5, Insightful)

You're complicating it.

(206 * 2)/3 = 137.333

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

## Re: (Score:2)

You're complicating it.

136/206 = 0.660194...

This is clearly less than 0.666666...

## Re:Learn 2 math (Score:5, Funny)

Close, but no cigar.

(206 * 2)/3 = 137 1/3

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

## Re: (Score:2)

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: (Score:2)

"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 (Score:5, Insightful)

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

isa 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.

## Re: (Score:2)

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.

## Re: (Score:2)

MUST be taken to at least 3 digitsWhere are you getting this from? I'm slightly scared you got modded 5 for saying this.

As other posters have noted the validity of the relation of "# votes >= 2/3" is determinable without any need for cutting off 2/3 to some arbitrary decimal precision.

## Re: (Score:2)

## Re:basic math (Score:5, Informative)

...unless you have fractional people.

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

three fifths of all other Persons [wikipedia.org]

## Re: (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 colon