Your assessment that an account getting double the points loses one third of the time seems to ignore the fact that there is an account that is getting 1000x the rate
I completely agree with you on that. My point was simply that it is somewhat proportional, not that you can compete with someone getting 1000x more points. You can't, but that is true under any proportional system. Perhaps under another system you have an easier time realizing your 1/1000 share, but it would still be negligible.
(replying to your reply below, which is at max comment depth)
if it is a balance based system instead of unspent outputs, it makes it a lot trickier...
what we need is some metric that consumes a finite resource and it doesnt have to be specifically coinage. Maybe something like (account balances / total activity) can be used. In the case of two accounts trading back and forth, the account balances stays constant while total activity goes way up, so the value of this shrinks to nothing at the abit level. The problem is that there also needs to be a way to pull in all the other accounts so an honest liquidity provider that is doing a lot of trading is able to get proper credits. If a snapshot of all the account balances involved in the market maker's trades can be made, then it could be used as a limiting factor.
anyway, there is a solution, just not sure the right details yet