If you think the best basis for "non-axiomatic morality" (whatever that means) is "maximized average happiness", I have to ask this question: how do you define happiness?
"Non-axiomatic" just means there's something measurable the morality is built upon. Religions, at least generally speaking, build on
at most axiom-level trust in the words of some prophetic figure, as the divinity itself is immeasurable. With what I'm mentioning, the central tenants are "what allows humans, as a species, to thrive best,
while also having as many non-necessary desires met as possible?", something that is an unsolved problem to my own knowledge, and to my knowledge of the general body of scientific knowledge. It is, however, a solvable problem, at least to my knowledge of scientific theory regarding psychology and various forms of biology.
At a certain point, social engineering to bias desires towards constructive behavior becomes a requirement, which is where the data on things like the dissatisfaction with marriage of those who've had a large number of romantic partners
alongside the extreme negative effects of single parenthood and abusive households becomes relevant to the nuclear family being our best starting point for such a data-derived morality. Which logically follows historic trends, as the nuclear family is nearly universal among humans, indicating it a behavior to arise very directly from instincts to emerge before and be preserved since the initial expansion of modern humans, or to have reliably emerged separately in almost every environment.
As for defining happiness? There's a
lot of life satisfaction metrics and metrics used to construct them, and a sizable amount of data on the relation of these with eachother and various lifestyle factors (single career women are
utterly miserable in almost every way, for example), in psychology. Thing is, we haven't pinned down a universal tendency of human preferences, or even just half-decent measures of what a good environment to grow up in is, so it's still firmly in philosophy's park to be the ethics committee. So long as they're not
ignoring what data
does exist.
Generally, happiness can also be trusted to be self-observed in controlled conditions, and indirect questions can measure at least
accepting one's lot in life, if they can't measure outright
happiness with social position. Placing societal stability
above individual happiness acts as a very direct safety valve on hedonism and social atomization, as desires that lead to societally-destructive behavior patterns can be excluded without violating the moral principals.
One of the oddities is that the
ideal state (take care of the Utopia fallacies) is a leadership of no
principals, nothing they take for granted as morally "right". The ideal leader of such a system is one who looks at the management of people as an utterly dispassionate breeding project, more or less, in such a fashion as to care
only for the metrics of sustainability and population satisfaction.
Which is something that is actually approaching reasonable to automate vital elements of, to allow for AI governance to strip the inherent limits of bias and data intake in humans in high-value positions (keeping humans in a lot of inputs, but the machines handling output details necessary to make the inputs
work and have them standing in the way of the major internal affair power structures being abused) to essentially nullify a lot of standard corruption. Lot easier to have checks against corruption in an AI than for humans. Turns it into a technological problem, instead of a societal one, once you resolve the societal problems in the way of implementing the AI properly.
Of course, many utopian systems can be said to solve a social problem to replace it with a technological one, and not a single one in history has achieved such a goal. Except maybe some subsets of capitalism that focused heavily on the "Bread and Circuses" stuff succeeding in turning a lot of scarcity into technical problems instead of social ones, locally, and it's still mostly social problems in the way of solving those issues globally. I don't have any meaningful hope for the successful establishment of an AI bureaucracy to solve corruption.
Way too out there for current
kinds of technology, way too many things have to go right, way too much along the way able to go
spectacularly wrong. Because once established, all biases of the creators are immortalized, as anti-corruption measures require an extremely high quality initial state to make it work as a lot of it comes down to tampering protections.
