A foundational-axiomatic view implies a philosopher king because the vast majority of citizens lack the intellectual ability, much less motivation, to understand it and apply it to political decisions.
Anti-foundationalists, in contrast, think that reality is far too complicated for a single person to figure out, and so we need extended democratic discussion. They also tend to believe that average citizens have a considerable degree of rationality and good motivation, and so can be trusted to be responsible voters. This is, of course, imperfect, but as Churchill famously said, it is better than all the alternatives.
As far as analytic philosophy goes, the classic version is foundationalist-axiomatic, but later versions, such as Strawson, are anti-foundationalist. Later Wittgenstein I think is a mixed case.
Anti-foundationalists, in contrast, think that reality is far too complicated for a single person to figure out, and so we need extended democratic discussion. They also tend to believe that average citizens have a considerable degree of rationality and good motivation, and so can be trusted to be responsible voters. This is, of course, imperfect, but as Churchill famously said, it is better than all the alternatives.
As far as analytic philosophy goes, the classic version is foundationalist-axiomatic, but later versions, such as Strawson, are anti-foundationalist. Later Wittgenstein I think is a mixed case.