The last election for the POTUS had the declared winner elected by an overall loss of 3mm votes.
The UK is plowing ahead with a hard brexit with a 52% majority on a 72% turnout (38% of the electorate explicitly said they wanted to leave), with a minority government propped up by a bribe with a minor political party from Northern Ireland.
I'm sure I can find more examples (and I'm aware that I'm cherry picking examples too), but to say that that you require a "supermajority" in most western countries isn't strictly true. (excuse the phrasing)