It really depends on what you’re talking about a majority of. If you’re talking about election votes or a political position, for example, then I would say that 2/3 or 3/4 is the vast majority, because you’re essentially never going to get 9/10 or 19/20 on anything that you’re discussing. OTOH if you’re talking about winning a bet, losing one time in three doesn’t seem like you’re winning the vast majority of the time, and eating 2/3 of a cake doesn’t seem like a ‘vast majority’.
I ask because a military assessment of the likelihood of success of the Bay of Pigs operation put it as a “fair chance.” Evidently, JFK understood that to mean something like 60%, whereas the planners thought it more like 15%.
You totally win the thread with this one. 
The guy that thought 15% then wrote “fair chance” should’ve been shot. That was spectacularly innumerate of him.
For me, it’s not context dependent. 67% would still not be a vast majority of voters to me. It may be an unusually large or even unprecedented majority (if the context allows), but it’s not “vast majority.”
An actual numerical minority constitutes a “vast majority” if it serves your needs and you don’t care about (A) objective truth and (B) what people think of you. A person of sufficient sociopathy would be able to create the alternate reality necessary to make such a contrafactual statement true (at least, in their own head and in the minds of their true believers).
A person of slightly less sociopathic mindset can get around “A” by (silently) provisoing the statement “a vast majority of everyone who matters”.
I’d say that a “vast majority” is around 90% (90.91%, if I want to be precise), because that’s the point at which one side exceeds the other by an order of magnitude.
A “fair chance” is around 15%, but could be even lower depending on the context: I’d consider that to mean a chance high enough that you’d be negligent to not consider it in planning. For high enough stakes, even a 1% chance or less could be a “fair chance”. If Kennedy interpreted it as meaning “definitely over 50%”, then the miscommunication was his, not his analysts’.
But this is less compelling when you consider that this notion of order of magnitude is related to our arbitrary use of base 10. Outnumbering by powers of 2 (“orders of magnitude in binary”) seems like a more natural concept.
Yes, the idea that the percentage depends heavily on context is the most compelling insight from this thread.
*A vast majority of people voted for President X.
With this poker hand, I’d expect to win the vast majority of the time.
The vast majority of infections are not fatal.
*
I think in different contexts, I’d infer substantially different percentages.
Interesting! Both those numbers are within what I would consider the arguable range, although near opposite ends.
As a professional writer, I have never encountered any such standards. The AP Stylebook (which I have) has no such appendix, nor does the Chicago Manual of Style. This is not the kind of issue that stylebooks typically address.
88.6% or more
Definitely a good amount more than just a majority.
I don’t think so. As has been pointed out, some of these phrases are highly context-dependent.
In many contexts, in my mind, “fair chance” means something like “it might happen, wouldn’t rule it out.” Here, “fair” means something like “less than good,” rather than “equally weighted.”
At the very least, 70%. And preferably, clear a threshold of 80-85%.
What…?? Surely it borders on criminal negligence to order a military operation forward with the knowledge that it has a 85% chance of failure.
The word “fair” can be used in in a lot of ways. Not quite as many as the infamous “is”, but still quite a few.
In the classic grades of condition, there’s “poor, fair, good” with maybe a couple of others at one or both ends. In that taxonomy “fair” means near the middle.
Likewise compare “The food at that restaurant was good”, “The food at that restaurant was fairly good”, “The food at that restaurant was bad”, and “The food at that restaurant was fairly bad.” At least as I parse those, the term fairly is a de-intensifier. IOW, “fairly” moderates the other adjective towards meh.
If somebody actually thought the chance of success was 15% and the chance of failure was 85%, then representing those 6:1 odds as “fair” was an invitation to miscommunication.
Another (contrary) thought: Compare these two sentences: “The plan has a fair chance of success.” vs. “The plan has a fair chance of failure.”
Strictly speaking the sentences are perfectly complementary. Spock would get that immediately. More human decision-makers would parse one of those as a much more favorable assessment than the other.
If somebody actually thought the chance of success was 15% and the chance of failure was 85%, then representing those 6:1 odds as “fair chance of success” was an invitation to miscommunication. They should more logically have chosen “fair chance of failure.”
The fact I think this tells me that in this case I read the word “fair” as significantly different from 50%; maybe around 66% = 2/3rds. Although up above I argued it means something close to 50%.
The meta-point being I think “fair” has lots of fuzzy connotations, and can be vague bordering on contradictory in the right (=wrong) circumstances. That make it a very fraught (fairly fraught? :)) word to use when accurate communication is important.
IANA linquist or trained expert in English writing. I may be all wet here from end to end. But the original cite to JFK shows at least one other person read it other than as intended.
Wow, you guys are tough. I’d be good with 75% for “vast majority”. I would put 90% in the range of: hard for there to be anything of consequence that 90% of the electorate agrees with. And I assume we are talking about something like “the electorate”.
Not even remotely. It depends on what’s at stake.
For something like Bay of Pigs, then yes, to have launched that with clear understanding of a 15% chance of success would have been criminal.
At other desperate times in other desperate places, those odds are fully acceptable. What do you suppose the odds of success or survival are for US infantry on the NK DMZ today or on the inter-German border facing the Warsaw Pact in the 1970s and early 1980s? Obviously I’m talking post-attack, as their odds in peacetime are/were quite good. 
Way I see it, “vast majority” implies something higher than “supermajority”. Common “supermajority” levels in various contexts are 75%, 66% and 60%.
So based on that, something over 75% is arguably a “vast majority”, meaning “more than the usual supermajority levels, but not necessarily unanimous or overwhelming”.
So it would go like this:
-
Majority (50% plus 1 - 60%)
-
Supermajority (range of 60%-75%)
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Vast majority (75% plus 1 - 95%)
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Overwhelming majority (95% plus 1 - 100% minus 1)
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Unanimous (100%)
As for “fair chance”, my immediate suspicion would be something like 50%, though it would be highly context-specific.
I like all of this. For fair chance, coming from someone else I might take it as anywhere from 10% to 70% as I said upthread. But for me I would say the following:
Ten or twenty percent: fighting chance
Thirty or forty percent: fair chance
Fifty percent: even chance