My opinion is that to fix systemic unfairnesses ('the impartial referee') transfer of wealth is okay and to use those money to healthcare is just good use of resources if it goes to the target group. Bad luck is not an example of systemic unfairness. More difficult question is whether transfer of wealth is okay just to support naturally more unfortunate groups. I believe that is good, reasonable and beneficial policy but how to argue that everybody would be obliged to do this is a more difficult question. I'll return to it maybe later. Best I can now say is that currently democracy grants legitimacy for it, but this is bit shady as anything deriving legitimacy from democracy is circular as democracy is in effect legitimized by democracy...
On a side note... What amount/level/quality of information do you think the "the impartial referee" has? There seems to be room for debate in this area.
'Partial referee' (btw, I didn't mean impartial, sorry not native in English) was a sort of allusion to my previous arguments in which I defined difference of fair inequality and unfair one. If you are damn good tennis player then that isn't really unfair to anyone. If the the difference in the game, however, is due to partial referee, then that is. My argument is that wealth accumulation and deprivation is partly due to such unfairness in economics, so it is okay to even things out with transfer of wealth. In this case partial referee was reference to the de facto rules of economics. It obviously isn't a real feeling and thinking thing.
I'm not sure if I caught what your idea was, but it seems it could be something relevant, so feel free to clarify it.
Of course to determine what is the right 'correction' for each income-class is difficult question (not to mention how to enforce it), one in which the accidentally mentioned impartial referee would be good to have. I don't see how we could get one so we'll have to go with the usual 'who manages to enforce his opinions no matter how wins'.
By the way, there are two concepts that should be familiar to all before we continue on debating on equality: 'equality of outcome' and 'equality of opportunity'. Even these aren't precise science but at least they are lot better than the terribly ambiguous plain equality.