If you could ensure every wallet belongs to only one person by requiring something like a credit card verification or identity number during creation, could you then limit the amount of coin that any one wallet could mine(they may own more by buying or selling something for coin), thereby giving the whole community an equal chance?

Or you could give the coin away to everyone part of the community xxxcoin per wallet, and make it an requirement to keep your cpu/card available for mining a certain number of hours per month to stay part of the coin community? So the solving of the blocks are done not for reward, but as a responsibility/requirement to be part of the coin community. Once again you would need to make sure that only one wallet per person is possible, so that becomes the difficult problem if government is not involved.

Maybe a solution would be to require a fingerprint/voiceprint/retinascan per wallet? Software would then be required to tell fake fingerprints/voiceprints/scans from real ones???

Someone cleverer than me would have to do that bit...