I kind of feel it is a cop out on the part of the person using the phrase as is conveys a quantitative value with actually specifying it. It is a lot harder to commit to writing down a concrete number as then the reader expects a reference or more information to back it up. "vast majority" just kind of slips into the brain unexamined.
few 10%
some 20%
many 30-40%
half 50%
most 60-70%
vast 80%
anyone 90%
A good way to think about this in social terms like polls etc (where %ages come up a lot) is to imagine the relative strength of two teams in a tug of war. 80% might seem low for the vast majority, but if you think about it as 4 people pulling against 1 it's easier to appreciate it viscerally.
A supermajority is usually 66% (can be 60% or 75%, etc: more than a simple majority anyway). The exact value is context-dependent, but the concept is commonly defined, and the range is broadly represented.
So I think, in my mind, a "vast" majority would be something like 90%, perhaps as low as 85%. But it's not a defined term.
I don't think it needs to be 98% or 99% (I'd describe that as "basically everyone").
Prompt: "What does vast majority mean?" Answer: "The term "vast majority" refers to a very large portion or segment of a given group or quantity, often implying much more than a simple majority or over half. It suggests an overwhelming or significantly large percentage, typically used to emphasize that the subject in question constitutes the bulk or main part of the whole. For instance, if one says "the vast majority of people support a certain policy," it means that significantly more than half of the people, possibly upwards of 70%, 80%, or even more, favor that policy."
Consensus: agreement among a vast majority of a population.