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EMENDATION
We reported the Cape Cod town council that couldn't decide whether a vote of 136 to 70 met the requirements of a two thirds majority. A couple of our readers said no. For example, Montana legislator Brady Wiseman writes:
"This question comes up often in state legislatures, where some supermajority of those present and voting requires the calculation. In this case, the calculation is: 206 x 2/3 = (206 x 2)/3 = 137.3333. So the actual 2/3 majority vote is 138, since 137 is fractionally less than 2/3 of 206."
Vemene did a similar calculation adding the thought that "The officials need to put away their calculators and learn to work arithmetic with good, old-fashioned fractions and their own brainpower."
"This question comes up often in state legislatures, where some supermajority of those present and voting requires the calculation. In this case, the calculation is: 206 x 2/3 = (206 x 2)/3 = 137.3333. So the actual 2/3 majority vote is 138, since 137 is fractionally less than 2/3 of 206."
Vemene did a similar calculation adding the thought that "The officials need to put away their calculators and learn to work arithmetic with good, old-fashioned fractions and their own brainpower."
posted by TPR | 12:51 PM
2 Comments:
But it's bog-standard practice to round DOWN fractions less than 0.5, Sam! Therefore Wiseman isn't very. Nor is Vermene.
Furrfu! And I'm all but innumerate.
Thinking it over, I realise there's another, simpler way to look at it.
The requirement that the majority be 2/3 means that the proportions of yes:no be 2:1 (2 thirds yes, 1 third no)
So we can double the No vote (70 ) to see what the minimum Yes vote would have to be: 140. The Yes vote would have to be 140 or more when the No vote is 70.
Or, we can cut the Yes vote in half to see the upper limit for the No vote: 136 divided by 2 is 50+15+3 (half of 100 + half of 30 + half of 6) therefore 68. The No vote would have to be 68 or fewer for a Yes vote of 136 to be 2/3.
136 is less than 140, and 70 is more than 68, so the measure was insufficiently supported.
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