Agreeing on moral axioms also might be non-trivial. I for example do not agree with the one you list above, but instead go withz Peter Singer on preventing suffering and not protecting life per se. So abortions for example and even euthanasia of severely sick people including newborns are fair game. Also leads to the question if animal suffering should count and if so, how much? I think trying to take our moral debates down to principals like this might be a super valuable exercise for society though. Regardless if we program Watson to be president or not.

Edit: of course this in practice would devolve to 50+% of the country in essence saying "Whatever I think the bible says should be our acxiom". Completely ruining the discussion.