Thanks for your reply!
I only mentioned spline interpolation because of my 'ugly' curve with that 'knee'. :)
However, anyway my curve only served as an example to show my idea: to start flat to make self-upvoting less attractive and to end also flatter than n^2 to avoid huge rewards for single posts.
There are much better curves (for example sigmoid function like curves could be interesting) to serve the same purpose ... but ... I was just too lazy to seek a suitable curve. :)
Yes, unfortunately, concerning 'diminishing returns' you are probably right: with enough accounts one can circumvent their effect ... but at least the 'traditional' circle voting would be somewhat more dificult.
I have nothing against building a following (I also like to upvote my friends and receive their upvotes), therefore I had suggested that the 'diminishing returns' only should have an effect for a certain time span (there could be a similar reloading mechanism like voting power anyway has).
Anyway, just consider my thoughts as 'food for (further) thoughts' - it's well possible that there are better ideas and solutions.
Don't think there is actually anything wrong with 'ugly and ugly could be of use if it aligns with the users mindframe (such as the redfish/minnow threshold). I would propose ugly in such a way is a desireable trade for user experience purposes.
Something like:
'My curve' is 'ugly' because I just mixed two curves together into one single graph to demonstrate my idea. I mean, if one used one single curve (maybe a sigmoid one?) instead, which also starts flat and ends not so steep, then it would have the same effect, but just looked much better. :)
You are right, in general there is no problem with looking 'ugly' of course.
Your example curve looks more or less linear ... :)
The example curve would give an 'ugly jump' 2.5% bonus at each of the fish-size thresholds used by Steemitboard because of the use of the floor function. Basically switching to a slightly steeper linear line at every power of ten thresholds for the vesting shares. Not sure if its the best function to use, but I do think that fish-size thresholds make a lot of sense for incentivizing the use of few large over many small accounts in a way everyone can understand. Give minnows a slightly better deal than redfish. Dolphins a slightly better deal than minnows, etc.
What may be ugly algebraically may well be quite simple as the interaction of two algorithms - just look at the curation rewards during the reverse auction to see what I mean.
Just an idea.
Now that type of reward function makes sense, tie it to something tangible that almost every Steemit user can grasp. I'm not sure that I agree with the chosen "bonus" (I think keeping it to something smaller like 1% is a bit fairer), but that's a whole other topic.
I imagine that type of function would add more of a gamification element into the Steem ecosystem, the real sense of "powering-up" each time that we move from one level to the next, which could drive more engagement within the community. It's also intuitive that the users who put up the most risk (power up the most Steem) get some extra perks for doing so.
It's certainly not as easy to power up 100K Steem as it is to do it for 100 (from the risk/reward perspective), having this type of bonus would certainly incentivize taking on a bit more risk and perhaps cause some who'd decide against it within the current linear function to reconsider their position.
Just did this post on the subject for those that are interested.
For clarity, here is an example of what the account size correction factor for both types of function could basically end up looking like.
The steps in the blue line show the different fish sizes. I hope these two together in one graph show the difference in impact on the handicap for new accounts.