Proof-of-importance is an obfuscation of proof-of-stake, because it doesn't burn transaction fees, so a cartel majority of stake holders (who thus can control which chain wins) could do as many transactions as they want, paying any transaction fees to themselves:
I am doing my best to share why I abandoned unprofitable PoW within the limited time I have to share.
I am not going to share the scheme because a facet of the scheme is employed in my ongoing (current) solution, even though my current design no longer employs unprofitable PoW. I am instead burning transaction fees and using TaPoS to prevent long-con nothing-at-stake attacks. But the "longest chain rule" is not the default consensus mechanism in my design. I can't give more details than that right now. My design has multiple facets which are (afaik) novel.
W.r.t to consensus ordering algorithm, I have I think a design which removes the power of control from those who have the most wealth resources and puts the control in the hands of those who transact the most. The capitalists transact very little and thus are not consumers and are wealthy. The rest of us transact a lot and our power is that we are the consumers!
Thank you for providing these interesting details! I think I got your basic idea. I'm curious to know in what ways your concept can improve the idea of TaPoS.
Btw, does you model offer objective consensus or does it rely on weak subjectivity in the sense of V. Buterin?
I explained to you that your negative interest idea could be attacked by a 51% attack which enables only the majority to retain stake by orphaning the minority's blocks. So it is just an obfuscated minted block reward. That is not unprofitable PoW.
Of course, this scenario would be possible. But would it make sense economically? I have my doubts. In case of profitable PoW, such an attack indeed makes sense since you only hurt the minority miners, whereas the owners of the currency remain unaffected. With a negative interest on your stake (that gets inevitable due to the attack), the owners would quickly get discouraged from using/keeping the currency, which will eventually lead to depreciation.
It's not sufficient to look at the nominal value of your stake, you also have to take its real value into account.
Additionally I explained to you that if you did indeed have unprofitable PoW then it would have insufficient hashrate and it could be attacked very cheaply by renting hashrate.
I'm not sure how big the hashrate would be if it's used to avoid negative interest on your stake. For sure the total hashrate would depend on the market capitalization of the coin and its popularity. It would also depend on the interest rate itself and how it can be decreased by PoW blocks.
Even if the hashrate alone was insufficient to protect the coin, an attacker would still have to buy/rent 51% of the stake if we put an upper limit on block creation for each account, in proportion to its stake.
Without acquiring the necessary stake, you would have to create a whole new alternative chain (fork) by doing PoW, which would be very costly even if the hashrate is lower than in Satoshi's PoW. This would amount to surpassing the cumulative hash power (or energy) as I explained here:
https://bitcointalk.org/index.php?topic=1570198.msg15972492#msg15972492