Majority vote and two-thirds vote with odd number of members

[Guest Betty Thompson]

First question:  How do you calculate a majority (51%) for an odd number of members?  For example, 51% of 12 is 7 (50% is 6 and you need one more vote than 50%).  But, for 11, 50% is 5.5 members and one more is 6.5 or 7 when rounded up.  But, if you multiply 7 by .51, you get 5.61 which is 6 when rounded up.

Second question:  At what decimal point do you round up for a two-thirds vote.  For example, two-thirds of  12 is 8.0004, two-thirds of 15 is 10.005, two-thirds of 19 is 12.673, and two-thirds of 20 is 13.34.  For two-thirds of 19 and 20, I can see rounding up to 13 and to 14, respectively, but for 12 and 15, it seems that two-thirds should be 8 and 10, respectively.

Thanks, Betty.

[Joshua Katz]

12 minutes ago, Guest Betty Thompson said:

First question:  How do you calculate a majority (51%) for an odd number of members?  For example, 51% of 12 is 7 (50% is 6 and you need one more vote than 50%).  But, for 11, 50% is 5.5 members and one more is 6.5 or 7 when rounded up.  But, if you multiply 7 by .51, you get 5.61 which is 6 when rounded up.

 Second question:  At what decimal point do you round up for a two-thirds vote.  For example, two-thirds of  12 is 8.0004, two-thirds of 15 is 10.005, two-thirds of 19 is 12.673, and two-thirds of 20 is 13.34.  For two-thirds of 19 and 20, I can see rounding up to 13 and to 14, respectively, but for 12 and 15, it seems that two-thirds should be 8 and 10, respectively.

Thanks, Betty.

First answer: A majority is neither 51% nor "one more than half." It is simply "more than not." A majority of 12 is 7 since 7 in favor and 5 opposed is more in favor than opposed. A majority of 11 is 6 since 6 in favor and 5 opposed is more in favor than opposed.

Second answer: You do not round up for a 2/3 vote. To have a 2/3 vote, you must have at least 2/3 voting in favor. The easy way to calculate that is "twice as many as not." I don't know where your examples are coming from, perhaps calculator error, but 2/3 of 12 is just 8 (one third is 4), and 2/3 of 15 is just 10. Notice that, if there are 12 voting and 8 in favor, there are 4 against - twice as many in favor as against. The same is true if 15 vote and 10 are in favor. If 19 are voting and 12 are in favor, there will be 7 against - but 12 is less than twice 7, so the vote won't carry. On the other hand, if 13 are in favor, and 6 against, there are more than twice as many in favor as against, and so the vote will carry (assuming, of course, in both cases, than a 2/3 vote is necessary). 

[Hieu H. Huynh]

Also see FAQ #4 and #5.

[Atul Kapur]

J. Katz' answer covered what I was typing and beat me by 2 minutes

Edited May 23, 2018 at 04:05 AM by Atul Kapur, PRP "Student"

[Guest Who's Coming to Dinner]

16 hours ago, Guest Betty Thompson said:

two-thirds of  12 is 8.0004, two-thirds of 15 is 10.005.

NASA is not going to like hearing this news.

[Richard Brown]

16 hours ago, Guest Betty Thompson said:

First question:  How do you calculate a majority (51%) for an odd number of members?  For example, 51% of 12 is 7 (50% is 6 and you need one more vote than 50%).  But, for 11, 50% is 5.5 members and one more is 6.5 or 7 when rounded up.  But, if you multiply 7 by .51, you get 5.61 which is 6 when rounded up.

 

15 hours ago, Joshua Katz said:

First answer: A majority is neither 51% nor "one more than half." It is simply "more than not."

I suppose defining a majority as "more than not" might be an acceptable definition, but I much prefer the standard "more than half" as defined in RONR and other parliamentary authorities.  I think the term "more than not" is just too confusing, especially for readers who, by the very question, do not understand what a majority is.

Here is the definition of "majority" from page 400 of RONR, along with the examples used on that page:

"Majority Vote—the Basic Requirement
As stated on page 4, the basic requirement for approval of an action or choice by a deliberative assembly, except where a rule provides otherwise, is a majority vote. The word majority means "more than half"; and when the term majority vote is used without qualification—as in the case of the basic requirement—it means more than half of the votes cast by persons entitled to vote, excluding blanks or abstentions, at a regular or properly called meeting. For example (assuming that there are no voters having fractions of a vote, as may occur in some conventions):
    •    If 19 votes are cast, a majority (more than 9) is 10.
    •    If 20 votes are cast, a majority (more than 10) is 11.
    •    If 21 votes are cast, a majority (more than 10) is 11."   

[Joshua Katz]

3 minutes ago, Richard Brown said:

I suppose defining a majority as "more than not" might be an acceptable definition, but I much prefer the standard "more than half" as defined in RONR and other parliamentary authorities.  I think the term "more than not" is just too confusing, especially for readers who, by the very question, do not understand what a majority is.

 

I understand your point. My experience has been that explaining to lay audiences that a majority is "more than half" results in a significant number thinking, until corrected, that a majority vote is taken of those present. Saying "more in favor than against" or, colloquially, "more than not" has tended to result in people getting the point faster. YMMV.

[Richard Brown]

I agree with explaining a majority as "more in favor than against" (or "more yes votes than no votes"), but it is the term "more than not" that gives me pause.  I just don't think it adequately explains what a majority is.   When explaining a "majority vote" to laymen, I usually first say "it means more than half" or "more than half of the votes cast" and then follow that up with "more yes votes than no votes".  Or, if it's regarding an election, "more votes than all the other candidates combined". 

Likewise, when explaining a two thirds vote, I usually add that the easiest way to determine whether you have a two thirds vote is "that there must be twice as many yes votes as no votes" or "if you have twice as many yes votes as no votes, then you have a two thirds vote".  No need to bring out a calculator in most cases.

And, of course, depending on the situation, particularly if the question concerns an election, it might be necessary to  also explain  that "illegal votes" (votes cast for an ineligible or unidentifiable candidate) count as a vote cast, but are not credited to any candidate.  Thank goodness that isn't usually the case when someone wants to know how you calculate a majority or two thirds vote.

Edited May 23, 2018 at 08:47 PM by Richard Brown
Added last sentence to second paragraph

[Joshua Katz]

9 minutes ago, Richard Brown said:

I agree with explaining a majority as "more in favor than against" (or "more yes votes than no votes"), but it is the term "more than not" that gives me pause.  I just don't think it adequately explains what a majority is.   When explaining a "majority vote" to laymen, I usually first say "it means more than half" or "more than half of the votes cast" and then follow that up with "more yes votes than no votes".  Or, if it's regarding an election, "more votes than all the other candidates combined". 

 

Except in an appeal...  You're probably right when it's in writing.  In a conversation, depending on the context, "more than not" often works, I think.

[Benjamin Geiger]

6 minutes ago, Joshua Katz said:

Except in an appeal... 

Tangentially related: Instead of having the "more than half need to vote in the negative" rule, why isn't the question changed to "should the decision of the chair be overturned?" with a majority in the positive being needed to overturn?

[Guest Rosie]

On 5/22/2018 at 11:52 PM, Joshua Katz said:

First answer: A majority is neither 51% nor "one more than half." It is simply "more than not." A majority of 12 is 7 since 7 in favor and 5 opposed is more in favor than opposed. A majority of 11 is 6 since 6 in favor and 5 opposed is more in favor than opposed.

Second answer: You do not round up for a 2/3 vote. To have a 2/3 vote, you must have at least 2/3 voting in favor. The easy way to calculate that is "twice as many as not." I don't know where your examples are coming from, perhaps calculator error, but 2/3 of 12 is just 8 (one third is 4), and 2/3 of 15 is just 10. Notice that, if there are 12 voting and 8 in favor, there are 4 against - twice as many in favor as against. The same is true if 15 vote and 10 are in favor. If 19 are voting and 12 are in favor, there will be 7 against - but 12 is less than twice 7, so the vote won't carry. On the other hand, if 13 are in favor, and 6 against, there are more than twice as many in favor as against, and so the vote will carry (assuming, of course, in both cases, than a 2/3 vote is necessary). 

OK, to be sure, for a board of five, two thirds would be three (for a written consent that requires a minimum of 2/3 of the directors to be in approval). 

[Atul Kapur]

If you require 2/3 of the five directors, then you need 4 votes in favour. 

2/3 of 5 is 3 & 1/3 (= 3.3333.....).

3 < 3 & 1/3   so three votes does not meet the threshold.

 

Note that you said "requires a minimum of 2/3 of the directors"

The usual requirement in RONR is that the denominator is the number of votes cast by those eligible to vote. So the total depends on how many vote (abstentions do not count as votes). Please check your rules to confirm the requirement.

[Gary Novosielski]

On 6/21/2022 at 1:41 PM, Guest Rosie said:

OK, to be sure, for a board of five, two thirds would be three (for a written consent that requires a minimum of 2/3 of the directors to be in approval). 

Please do not tail-end on a four-year-old question.  New question should be asked in new topics.

 

[Gary Novosielski]

On 5/22/2018 at 11:34 PM, Guest Betty Thompson said:

First question:  How do you calculate a majority (51%) for an odd number of members?  For example, 51% of 12 is 7 (50% is 6 and you need one more vote than 50%).  But, for 11, 50% is 5.5 members and one more is 6.5 or 7 when rounded up.  But, if you multiply 7 by .51, you get 5.61 which is 6 when rounded up.

Second question:  At what decimal point do you round up for a two-thirds vote.  For example, two-thirds of  12 is 8.0004, two-thirds of 15 is 10.005, two-thirds of 19 is 12.673, and two-thirds of 20 is 13.34.  For two-thirds of 19 and 20, I can see rounding up to 13 and to 14, respectively, but for 12 and 15, it seems that two-thirds should be 8 and 10, respectively.

Thanks, Betty.

Your calculator is well and truly munged.

Two thirds of 12 is 8

Two thirds of 15 is 10

Two thirds of 19 is 12⅔

Two thirds of 20 is 13⅓  (That one was at least close, but suffered from poor rounding.)