It really depends on what exactly you mean by “happy” The OP says ““Roommate marriages” - wedded but no love or pleasure in each other’s company, do not qualify as happy - secretly-contemplating-divorce marriages do not count, etc.”
Someone earlier said something like “don’t conflate contentedness with happiness” . But “contentedness” is a form of “happiness”. It’s not the only form , but I suspect that if the question in a poll was whether people were “content” with their marriage rather than “happy” , you’d get different answers. Similarly " a roommate marriage" where the parties don’t take pleasure in each other’s company certainly isn’t happy, but what about one where the bedroom is dead because neither is interested in sex anymore ? I don’t think that one is automatically “unhappy”.
I don’t think “happy” and “good” marriages are necessarily the same thing.
I’m not even sure “happiness” is a good metric for judging a marriage. It’s like raising kids. No one has kids because years changing diapers and attending a bunch of birthday parties for toddlers makes them “happy”. By the same token, no one says at 29 “thank God I never have to have sex with another woman after this.”
Last anniversary was the 60th. And no, not all of these were deliriously happy all the time - but divorce was never contemplated.
I remember years ago reading that some well known female was asked if she had ever contemplated divorce. Her reply, “Never divorce. Occasionally murder.”
Ninja’d. But I recall it as: She looked up with fire in her eyes and replied, “Divorce, never. Murder, often.” I’m on better terms with the current MrsRico of 40+ years. I saw a question on another site asking, “How would you spend a night with your ex?” The common answer (mine too) was, “There are REASONS they’re the ex!” And still alive.
OP: How many marriages are “happy”? Hard to tell. But well-educated couples are much less likely to divorce than the less educated. (cite) This doesn’t count the “poor man’s divorce” aka abandonment. But educated folk seem happier or at least more satisfied.
‘What is happiness?’ is in general a rat hole to go down, not just for marriage. Once you pull on that thread, there’s no end to it. Maybe the answer actually should be based on surveys, and take them at face value, or at least what we estimate people would say, if the question is ‘reasonably happy’.
Snapshot: Around 2% of marriages end in divorce in a given year in the US. So right now there’s a couple of % in the process, a couple of % who will next year, couple more slated for 2022, etc. Most times the problem that ends things doesn’t pop up out of nowhere (might pop up from perspective of one party but other knew it was there etc) so I think it’s reasonable estimate on average a number of years worth of upcoming divorces reflect unhappy marriages now. But 10 yrs worth seems like a lot and I doubt there are nowadays large %'s of people who are unhappy but will never divorce. So I think in snapshot ‘happy’ is more than 1/2, maybe 3/4’s.
OTOH longitudinally over life, and condemning all of maybe 40%+ of marriages which eventually end in divorce as having been just ‘unhappy’ all along, then add in some people who stick out consistently unhappy marriages for life, happy might be more like 1/2, or perhaps a bit less.
I feel I should point out that you could have murdered your partner 20 years ago and you would probably be getting out of jail about now…except you would be free!