RE: Non-lineair rewards: convergent linear vs fish-size bonus
No oranges, all apples! Comparing reward scaling functions to reward scaling functions, that is what my blog post is about. Maybe read @trafalgar's post for some background on the orange line. @trafalgar talks in terms of n^2/(1+n) that as scaling function translate to n/(1+cn)
In this plot the X axis is in VEST on a log scale (added the fish type graphics to make it understandable to people who don't think in terms of MVEST)and the Y axis represents . The Y axis can ve seen as $ vote value "per MVEST".
You could multiply each of the equation by some c x V, but doing so will just show slightly curved almost linear lines that truly don't communicate what the "per MVEST" graph communicates. That's the whole problem I am trying to address here. If you use a lineair X axis or plot $ against MVEST or both, you end up obfiscating that whatever S you choose for the orange curve, you either allow orcas and whales to not be incentified to good behaviour, or you end up screwing over new accounts so badly that you basically end up stating that we are full and new accounts are no longer welcome.
But in case you want to play with the scaling equations a bit, here is the code I used to make this graph: