I once said in a grad school paper that 80 percent was a majority but not an overwhelming one--here substitute "vast" for overwhelming--and my professor took issue with me and said it certainly was overwhelming. So perhaps it has to be something like 80 percent?
To me, "overwhelming majority" certainly would be something like 85 percent or more.
Once you've worked this out, can y'all get on to the more gnarly problem of how many measures constitute a raft of measures. The government announced a raft of measures the other day and I don't know what we're in for.