Guest Tony Tatman Posted May 20, 2015 at 09:43 PM Report Share Posted May 20, 2015 at 09:43 PM Our 9 member board will be voting on a new code of regulation soon that requires a 2/3 vote to pass. Is the correct number required to pass 6 votes or7? 2/3 of 9 is six but .667% of nine comes out to more then 6. Which calculation is correct? Link to comment Share on other sites More sharing options...
Dan Honemann Posted May 20, 2015 at 09:49 PM Report Share Posted May 20, 2015 at 09:49 PM Our 9 member board will be voting on a new code of regulation soon that requires a 2/3 vote to pass. Is the correct number required to pass 6 votes or7? 2/3 of 9 is six but .667% of nine comes out to more then 6. Which calculation is correct? See FAQ #5. Link to comment Share on other sites More sharing options...
Edgar Guest Posted May 20, 2015 at 10:07 PM Report Share Posted May 20, 2015 at 10:07 PM Is the correct number required to pass 6 votes or 7? It might be neither (and it's certainly not 7). Some members might be absent and some members might abstain (i.e. choose not to vote). A vote of 1-0 would meet the requirement for a two-thirds vote. As would a vote of 6-3. All that's needed is at least twice as many "yes" votes as "no" votes". Link to comment Share on other sites More sharing options...
Gary Novosielski Posted May 21, 2015 at 03:54 AM Report Share Posted May 21, 2015 at 03:54 AM Our 9 member board will be voting on a new code of regulation soon that requires a 2/3 vote to pass. Is the correct number required to pass 6 votes or7? 2/3 of 9 is six but .667% of nine comes out to more then 6. Which calculation is correct?Neither. It does not depend on the size of the board, but on how many are present and vote.For a 2/3 vote to pass, there must be at least twice as many Yes votes as No votes. So 6-3 is sufficient. But so is 2-1 or 1-0Abstentions and absentees make no difference as long as a quorum is present. Link to comment Share on other sites More sharing options...
Richard Brown Posted May 21, 2015 at 04:21 AM Report Share Posted May 21, 2015 at 04:21 AM The easiest way to know if you have a two thirds vote, though, is what Edgar Guest said: "Twice as many yes votes as no votes". No need for all the mental gymnastics unless the vote requirement is two thirds of the members present or two thirds of the entire membership. Then you have to do the math. The link Mr. Honemann provided will help you with that. Link to comment Share on other sites More sharing options...
SaintCad Posted May 21, 2015 at 01:53 PM Report Share Posted May 21, 2015 at 01:53 PM As a math major I just would like to point out to the OP that 2/3 does NOT equal 0.667 which is why you got two different results. Link to comment Share on other sites More sharing options...
Gary Novosielski Posted May 21, 2015 at 02:25 PM Report Share Posted May 21, 2015 at 02:25 PM As a math major I just would like to point out to the OP that 2/3 does NOT equal 0.667 which is why you got two different results.But in a group of less than 10 000 people, the number 0.666667 should give you acceptable results--but still not as good as multiplying by 2 and dividing by 3... or just using the "at least twice as many Yes votes as No votes" rule, which yields a value of True or False, rather than a fraction. Link to comment Share on other sites More sharing options...
Shmuel Gerber Posted May 21, 2015 at 09:40 PM Report Share Posted May 21, 2015 at 09:40 PM But in a group of less than 10 000 people, the number 0.666667 should give you acceptable results--but still not as good as multiplying by 2 and dividing by 3... or just using the "at least twice as many Yes votes as No votes" rule, which yields a value of True or False, rather than a fraction. So if 9 votes are cast, a two-thirds vote is 6.000003? Link to comment Share on other sites More sharing options...
Richard Brown Posted May 21, 2015 at 09:41 PM Report Share Posted May 21, 2015 at 09:41 PM So if 9 votes are cast, a two-thirds vote is 6.000003?I certainly hope not!!! Link to comment Share on other sites More sharing options...
Shmuel Gerber Posted May 21, 2015 at 09:48 PM Report Share Posted May 21, 2015 at 09:48 PM Our 9 member board will be voting on a new code of regulation soon that requires a 2/3 vote to pass. Is the correct number required to pass 6 votes or7? 2/3 of 9 is six but .667% of nine comes out to more then 6. Which calculation is correct? As a math major I just would like to point out to the OP that 2/3 does NOT equal 0.667 which is why you got two different results. Not to mention that it doesn't equal 0.00667 (or .667%). Link to comment Share on other sites More sharing options...
Richard Brown Posted May 21, 2015 at 09:53 PM Report Share Posted May 21, 2015 at 09:53 PM But Mr. Novosielski's suggestion to multiply by 2 and then divide by 3 does work.... as does multiplying 9 by .6666666. But the most accurate is obtained by multiplying by 2 and dividing by 3. Or just making sure you have twice as many yes votes as no votes. Link to comment Share on other sites More sharing options...
Dan Honemann Posted May 21, 2015 at 10:02 PM Report Share Posted May 21, 2015 at 10:02 PM But the most accurate is obtained by multiplying by 2 and dividing by 3. Oh, yeah? I say you gotta' first divide by 3 and then multiply by 2. Link to comment Share on other sites More sharing options...
Richard Brown Posted May 21, 2015 at 10:06 PM Report Share Posted May 21, 2015 at 10:06 PM Oh, yeah? I say you gotta' first divide by 3 and then multiply by 2. Well, with a committee of 9 they both seem to work. I'll leave it to the math majors to sort this out! Of course, we've already had one math major lead us astray. . . . Link to comment Share on other sites More sharing options...
Edgar Guest Posted May 21, 2015 at 10:09 PM Report Share Posted May 21, 2015 at 10:09 PM But the most accurate is obtained by multiplying by 2 and dividing by 3. So, to find two-thirds of nine you first multiply nine by two to get eighteen? What significance does eighteen have? What you want to do is first find the value of the denominator (i.e what size the pieces are) and then multiply it by the numerator (i.e. how many pieces you have). Link to comment Share on other sites More sharing options...
Richard Brown Posted May 22, 2015 at 12:02 AM Report Share Posted May 22, 2015 at 12:02 AM So, to find two-thirds of nine you first multiply nine by two to get eighteen? What significance does eighteen have? What you want to do is first find the value of the denominator (i.e what size the pieces are) and then multiply it by the numerator (i.e. how many pieces you have).Well, I'm just quoting Gary Novosielski, but it works....at least with a board of nine. Try it. 2 x 9 = 18. Divide 18 by 3: You get 6. Six is two thirds of 9. But, then, Dan Honemann's formula works, too.,... at least for a board of 9. Like I said in the other post, I'm leaving it to the math geniuses (who told us that .6666667 works when it doesn't) to figure it out. Link to comment Share on other sites More sharing options...
Shmuel Gerber Posted May 22, 2015 at 12:02 AM Report Share Posted May 22, 2015 at 12:02 AM But Mr. Novosielski's suggestion to multiply by 2 and then divide by 3 does work.... as does multiplying 9 by .6666666. So if 9 votes are cast, a two-thirds vote is 5.9999994? Link to comment Share on other sites More sharing options...
Richard Brown Posted May 22, 2015 at 12:19 AM Report Share Posted May 22, 2015 at 12:19 AM So if 9 votes are cast, a two-thirds vote is 5.9999994?No. According to FAQ # 5, which you co-authored, it would be 6, right? http://www.robertsrules.com/faq.html#5 But, isn't that better than using Gary's formula of .6666667, which gives you 6.000000.3... or 7, as two thirds of nine? I'm gonna leave it to the mathematicians, including the one who told us to use .6666667, to sort this out. And I'll stick to hoping I have twice as many yes votes as no votes and hope that if I run across a case where the threshold is two thirds of those members present or two thirds of the entire membership, using both .6666666 and .6666667 both yield a clear winner. I have a hunch that Gary's other formula of multiplying by 2 and dividing by 3 might work, too. Or Dan's formula of dividing by 3 and multiplying by 2. And I'll hope that the yes votes are at least twice the combined number of people present who either didn't vote or voted no. C'mon, you mathematicians: Settle this!!! Link to comment Share on other sites More sharing options...
Shmuel Gerber Posted May 22, 2015 at 12:57 AM Report Share Posted May 22, 2015 at 12:57 AM No. According to FAQ # 5, which you co-authored, it would be 6, right? http://www.robertsrules.com/faq.html#5 But, isn't that better than using Gary's formula of .6666667, which gives you 6.000000.3... or 7, as two thirds of nine? I'm gonna leave it to the mathematicians, including the one who told us to use .6666667, to sort this out. And I'll stick to hoping I have twice as many yes votes as no votes and hope that if I run across a case where the threshold is two thirds of those members present or two thirds of the entire membership, using both .6666666 and .6666667 both yield a clear winner. I have a hunch that Gary's other formula of multiplying by 2 and dividing by 3 might work, too. Or Dan's formula of dividing by 3 and multiplying by 2. And I'll hope that the yes votes are at least twice the combined number of people present who either didn't vote or voted no. C'mon, you mathematicians: Settle this!!! I thought it was fairly well settled already. For one side of a question to obtain two-thirds of the vote, it must have double the number of votes of the remaining side(s), since two-thirds to one-third is a ratio of two to one (2/3 : 1/3) = (2 : 1). Also (and I am sorry to say that this requires no math beyond the elementary-school level),two-thirds of a number N is equal to (2÷3)×N, which is equal to (N×2)÷3, which is equal to (N÷3)×2.So you can multiply by 2 and then divide by 3, or divide by 3 and then multiply by 2, or -- and here's a concept -- actually just multiply 2/3 by the number. It is not possible to exactly represent a fraction of two-thirds by any finite number of decimal digits, but if all you're looking to do is determine what the whole number of votes needed to meet a two-thirds threshold is, this really shouldn't present any difficulty. Link to comment Share on other sites More sharing options...
Gary Novosielski Posted May 22, 2015 at 01:17 PM Report Share Posted May 22, 2015 at 01:17 PM So if 9 votes are cast, a two-thirds vote is 5.9999994? Yes. Count the votes. Any vote that exceeds that number is sufficient to approve a motion that requires a 2/3 vote.. Now you might quibble that a vote equal to that technically would not, since it is less than two thirds. But my guess is that you will either get more or fewer votes than 5.9999994.. If you happen to get exactly that number, we'll burn that bridge when we come to it. Link to comment Share on other sites More sharing options...
Dan Honemann Posted May 22, 2015 at 01:57 PM Report Share Posted May 22, 2015 at 01:57 PM Yes. Count the votes. Any vote that exceeds that number is sufficient to approve a motion that requires a 2/3 vote.. Now you might quibble that a vote equal to that technically would not, since it is less than two thirds. But my guess is that you will either get more or fewer votes than 5.9999994.. If you happen to get exactly that number, we'll burn that bridge when we come to it. Continuing with this frivolity, I hereby declare that 5.9999994 is not two-thirds of 9. (It's a little too windy to go fishing.) Link to comment Share on other sites More sharing options...
SaintCad Posted May 22, 2015 at 04:09 PM Report Share Posted May 22, 2015 at 04:09 PM Now just suppose our bylaws allow us to split our vote and I vote 0.9999995 yes and 0.0000005 no. Then it may get more than 5.9999994 votes but not 2/3. Moral of the story: don't try to round 2/3. Take the number of voters and multiply by 2 and divide by 3. On a side note: Gary was a math major too? Link to comment Share on other sites More sharing options...
Gary Novosielski Posted May 22, 2015 at 04:34 PM Report Share Posted May 22, 2015 at 04:34 PM Oh, yeah? I say you gotta' first divide by 3 and then multiply by 2. Not so fast. Mathematically they're equivalent, but see below. And by the way, it's worse than simply not being able to represent 1/3 in decimal. If you use a computer or calculator, the numbers are internally represented in binary. Many (most) decimal fractions cannot be exactly represented in binary. The number 2/3 can't be represented in either, but neither can common decimals like, for example, 0.1 will yield the repeating "bicimal" 0.0001100110011001100110011001100110011.... Division creates a loss of precision in the least significant digit(s) and multiplication can magnify the error, so it's better to multiply first and divide last. That's an area where pure mathematics and computer science part company. Link to comment Share on other sites More sharing options...
Josh Martin Posted May 22, 2015 at 06:46 PM Report Share Posted May 22, 2015 at 06:46 PM Not so fast. Mathematically they're equivalent, but see below.And by the way, it's worse than simply not being able to represent 1/3 in decimal. If you use a computer or calculator, the numbers are internally represented in binary.Many (most) decimal fractions cannot be exactly represented in binary. The number 2/3 can't be represented in either, but neither can common decimals like, for example, 0.1 will yield the repeating "bicimal" 0.0001100110011001100110011001100110011....Division creates a loss of precision in the least significant digit(s) and multiplication can magnify the error, so it's better to multiply first and divide last. That's an area where pure mathematics and computer science part company.Yes, but if someone is using a decent calculator or computer, then they can simply multiply the number by 2/3, so there is no need to worry about any of this. Doing it in steps is more helpful when someone is calculating it by hand. Link to comment Share on other sites More sharing options...
Gary Novosielski Posted May 22, 2015 at 06:49 PM Report Share Posted May 22, 2015 at 06:49 PM Yes, but if someone is using a decent calculator or computer, then they can simply multiply the number by 2/3, so there is no need to worry about any of this. Doing it in steps is more helpful when someone is calculating it by hand.There never was any need to worry about it, and no need to start now. But unless you have a 2/3 key on your calculator, you'll need to multiply it by 2 / 3, which will actually multiply by 2 and then divide by 3. Or you can multiply by ( 2 / 3 ) which will first divide 2 by 3 (giving an imprecise result) and multiplying by that. Most calculators actually carry out their math two or three digits beyond what they show you, and round off, so nearly all of the time none of this will be detectable. Link to comment Share on other sites More sharing options...
Richard Brown Posted May 22, 2015 at 08:20 PM Report Share Posted May 22, 2015 at 08:20 PM Yes, but if someone is using a decent calculator or computer, then they can simply multiply the number by 2/3, so there is no need to worry about any of this. Doing it in steps is more helpful when someone is calculating it by hand.Well, I guess I'm using indecent calculators because none of mine have a 2/3 key. They've never offered me the option of watching anything indecent, either, so I guess they are really cheap, indecent calculators! Maybe I need to try pushing some more buttons. . . . Link to comment Share on other sites More sharing options...
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