Five years ago I'd agree with you, but in the current climate "minority" has negative connotations associated with it. E.g. a deminished value of opinion and lack of representation. Thus "small majority" has become more palatable and socially acceptable.
That's your attempt at a neologism, I had no idea what you meant until you tried explaining it and honestly it feels a bit unnecessary...
Say what you mean.
I'd say the same with you using the term neologism. Seems pretentious. First time I've ever heard the term or yet had anyone ever use it during a conversation. We all learn new things everyday and travel in different social circles. The fact is everything is hip and new at one time or not, but "small majority", has been around for at least 5+ years.
Neologism is a somewhat common word in my native language (neologismo), it's a term I learnt in middle school during language classes, sorry if it sounds "pretentious" to you but it's a perfectly apt word to describe what I wanted.
"Small majority" is of a different kind, much more akin to weasel words. Hence: say what you mean, don't hide behind a neologism that tries to masquerade as something else.
I have no clue what "weasel words" mean. None of this is common in my native language or socio economic up bringing. One of things I've learned in life is to know your audience. Speak words that anyone can understand. I have very clearly articulated the definition of what "small majority" means to the point that anyone can comprehend it. Instead of circling the drink why don't you psychoanalyze "what i really mean". Or more like what think the deep rooted issue is here? What am i not saying?