# Language and Statistics Poll: Define “Vast”

Prompted by a number of people using the phrase “vast majority” recently, I wonder where the line between “majority” and “vast majority” is. Thus, a poll:

Assume for the sake of argument that the issue in question is a simple yes-or-no question, with only a small “no response/ don’t know” fraction.

If there are other classes of “majority” that you recognize, feel free to define them in the comments. The poll is just about the term “vast,” though.

1. #1 cisko
February 10, 2012

Has to depend on the sample size, I should think. It’d be fair to say that a national candidate who had, say, 65% of the vote would count as having the support of the “vast majority” of the electorate — that’s a plurality of maybe 40 million voters.* But if you’re talking about a group of 20 people, 65% means only six extra votes. Tough to call that “vast”.

*2008 US presidential election turnout = 131m voters

2. #2 cisko
February 10, 2012

Also, I apparently don’t know what ‘plurality’ means. A ___ of 40 million voters — margin, I guess? 40 million more votes than the next guy, out of 131 million votes cast, would surely count as a ‘vast majority’.

3. #3 KevinQ
February 10, 2012

I said 66% or higher. At the point that one side has twice the support of the other, I think you can start to talk about “vast support.” I’ll also agree with cisko’s general point that it depends on population size. Part of “vast” also means, simply, large in scope. You may have 9 out of the 10 city council members supporting you, but saying that that you had the “vast support of the council” just sounds odd.

K

4. #4 rpenner
February 10, 2012

How about 75% + (25%) (n)^(-1/4) ?

For
n < 10, 1 disagreement means you don't have a vast majority n >= 10 90% would be a vast majority.
n < 16, 2 disagreements means you don't have a vast majority n < 23, 3 disagreements means you don't have a vast majority n >= 40 85% would be a vast majority.
n >= 625 80% would be a vast majority.

5. #5 Eric Lund
February 10, 2012

@cisko: “Plurality” refers to whoever has the most votes when nobody has a majority. For example, if you have a three-way contest where Alice got 35%, Bob got 34%, and Charlie got 31%, then Alice won a plurality of votes.

I’ll third cisko’s motion that it depends somewhat on population size. More than 75% seems right for a typical local election in my area, but it could be as little as 2/3 for a nation-sized population, or as much as 90% for a typical board of directors (low double digits). I agree that for single-digit populations (city council or school board type situations) the term makes no sense.

6. #6 Lurker #753
February 10, 2012

First, let us assume that a monkeysphere (a.k.a Dunbar’s number) is ~150 people.

Second, all scaling should be logarithmic, because all of our senses work that way.

Third, why should “vast” be a binary quality? What’s wrong with “how vast?”. So we need a function that returns ‘vastness’ as a number, with 0 meaning “not vast at all”, 1 meaning “yes, okay, that’s pretty vast”, and negative values meaning “you work in PR, right?”

So, a simple ln(pro) – ln(anti to put a 50:50 split at 0. This gives: 50:50 = 0.0; 60:40 = 0.4; 70:30 = 0.85; 80:20 = 1.39; 90:10 = 2.20

However, this ignores Dunbar, and we need to get a sphere in here somehow. Unfortunately, simply scaling by (population/Dunbar) means negative vastness for all populations below 150, which seems a bit harsh, so let’s scale the former by ln(pop)/ln(50).

Now we get:

65% of 100 is not vast (0.728), but 70% is (0.997), and 80% is comfortably so (1.6)
For a population of 1000, 65% -> 1.09, 70% -> 1.5, and 80% -> 2.45.
For a population of 10000, 65% -> 1.46, 70% > 2.0, and 80% -> 3.26.

Oh, and a 57:43 split is the lower limit of a “vast” majority for a population of a million.

(I can’t believe I’ve just spent 30 minutes on this….)

Regards to all….

7. #7 Rick
February 10, 2012

I did a quick Google search on “vast majority percent” (without the quotes). the percentages that were so characterized on the first few pages were: 90%, 65%, 77%, 63%, about 90%, 72%, 72%, 59.7%, 81%, approximately 3/4, and 70.3%. (feel free to spend your time clicking of Google pages to expand this list…)

These are not, of course, minimum percentages that can be so characterized, but rather percentages that fall within the range “vast majority’, but at least it is data of some sort. It looks like the term tends to be used for those values equal to or greater than about 60%; only one used the term for a value much 60%, and that was 59.7%, which would round to 60%.

Now, how large can a percentage be and still be “a slim majority?” :)

8. #8 Sili
February 10, 2012

“vast majority” = the number of people who agree with me.

Hence “vast majority of Catholics opposing birthcontrol” = 2%

9. #9 Neil Bates
February 10, 2012

There is no true rigorous definition of such phrases, however: the Delphi poll method applied to this survey says the proper floor is about 80%. That’s about what I would say, I picked 76-80% minimum because I would say, 76% (anything over 3/4.) Maybe you could say instead, at least the next integer ratio above 1:1, which would be 2:1 or 67%. (Go ahead and laugh at all this nitpicking.) Next project: define how proportionately close you must be to justify saying “almost.”

10. #10 thomasb
February 11, 2012

I believe the word `vast` in `vast majority` is used to impart an understood overwhelming account. When used with statistics the writer understands that the statistic is merely a tiny representation of the full population and that there may be no feasible method of finding the actual accurate statistic. A vast majority means that there is enough of a diversion from the mean that even accounting for statistical errors it’s likely the majority would still hold true.

http://www.care2.com/causes/vast-majority-of-latino-voters-are-pro-conservationist-poll-finds.html

The poll only questions 337 people of what is probably hundreds of thousands, if not millions, but the numbers are so overwhelming in one direction that the writer takes liberty to believe that even as an outlying case the majority would still hold true if the poll were expanded to the entire population.

11. #11 hibob
February 11, 2012

majority: 50% +1
supermajority: typically 60% or 2/3.
Vast wouldn’t be very vasty if it wasn’t notably bigger (~10%) than “super”, so
76% min.

12. #12 T. Hunt
February 11, 2012

A ‘vast’ majority is exactly twice as big as a ‘half-vast’ majority.

Hope this helps clear things up.

Tom

13. #13 Kaleberg
February 12, 2012

Other majorities might include:

slight majority – maybe 51-55%
significant majority – over 60%
substantial majority – maybe 2/3
serious majority – 70-80%
sucker’s majority – < 50% strange majority - 51i% (i = sqrt(-1)) secure majority - 100% stalin's majority - 110% I'm sure there are also majorities that don't begin with "s", but that's how I started playing the game.