Impressive work. But there is problem with the proofs from Block Producers side. No honest Block Producer can offer all of their rewards to voters therefore rational actors will in fact choose the cheapest BP (those giving the most rewards) that can secure their value.
Imagine that Alice returns 90 % of rewards but she has bad internet connection and she is willing to vote for any crazy hard fork and Bob returns 50 % of rewards but has good quality connection and understands the technology. With Alice, you risk that all your tokens can quickly become worthless and that must be part of your rational calculation.
The problem is that quality of Block Producer is very hard to quantify. And I must give you that dishonest BP can offer more rewards to voters than honest one.
Great thought process, I'm happy to hear that somebody thinks about DPoS that deeply.
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Thanks for the insightful comment!
I disagree, because it's kind of already happened. A year or so ago, the witness reward was so small (as steem was something like 4-6 cents) that ALL witnesses were operating at a loss compared to the fair market value of their CPU time. So we've already seen it happen before. Further, I was actually one of these witnesses, and if you ask me if I would do it again, I'd probably say yes -- I believe in Steem as a disrupter of traditional systems, and I would be willing to support it once again for free if it came to that. But for security reasons, I also think it's quite dangerous to have that situation occur. So I have mixed feelings on my food for thought question about "what is the correct reward to give?"
What you get into the second part of your comment I kind of cover in my 'reality?' section, and I basically agree. At some point people will hopefully weigh their long term interests (of value security) greater than their short term interests (of immediate financial reward). Unfortunately, you have to believe that everyone else will also understand and evaluate intelligently and rationally all of the risks -- and they may not do that if they believe they can skirt the edges and line their pockets.