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.
Many ways.

Btw, does you model offer objective consensus or does it rely on weak subjectivity in the sense of V. Buterin?
I argue in my white paper that TaPoS is as objective as proof-of-work. I think
Vitalik's idea of how TaPoS could be attacked is as implausible as doing a long-con attack on Bitcoin.
One class of approaches at solving the problem is to combine the Slasher mechanism described above for short-range forks with a backup, transactions-as-proof-of-stake, for long range forks. TaPoS essentially works by counting transaction fees as part of a blocks score (and requiring every transaction to include some bytes of a recent block hash to make transactions not trivially transferable), the theory being that a successful attack fork must spend a large quantity of fees catching up. However, this hybrid approach has a fundamental flaw: if we assume that the probability of an attack succeeding is near-zero, then every signer has an incentive to offer a service of re-signing all of their transactions onto a new blockchain in exchange for a small fee; hence, a zero probability of attacks succeeding is not game-theoretically stable. Does every user setting up their own node.js webapp to accept bribes sound unrealistic? Well, if so, theres a much easier way of doing it: sell old, no-longer-used, private keys on the black market. Even without black markets, a proof of stake system would forever be under the threat of the individuals that originally participated in the pre-sale and had a share of genesis block issuance eventually finding each other and coming together to launch a fork.
In my white paper I refute the above logic:
6.5 DecidableUnlike how
PoW is pragmatically decidable only for the the one chain that rules them all (meaning effectively that all other PoW blockchains are undecidable except Bitcoin), the Transactions as Proof-of-Stake (aka TaPoS)¹ employed in DPoS makes implausible the nothing-at-stake long range retroactive chain forks (aka long-con attack) without requiring that any DPoS blockchain is predominant over all others.
TaPoS provides this security because although not selling the discarded private keys for the stake is in theory an altruistic-prime incentive for an undersupplied good[Vitalik], it is not plausible for an attacker to obtain the private keys for every historic transaction, so as to not create resistance by the current stake holders to the attackers fork (because otherwise the attackers fork would double-spend the current stake holders stake back to the historical owner of the stake).
Note that I helped Dan Larimer invent TaPoS.¹
¹ Daniel Larimer,
Transactions as Proof-of-Stake. Invictus Innovations, Nov 28, 2013.
Key design decision prompted by Shelby Moore III.
Summary in BitFury whitepaper.
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.
The hashrate value is only going to be some % of the market cap daily. So to attack this coin and double-spend, you just rent that level of hashrate. Otherwise the coin needs to become the "one chain that rules over all the rest" and is dominated by entrenched mining farms which refuse to rent out 51% of the hashrate.
So what happens in that later optimistic case is that if those who transact end up paying a transaction fee for this PoW to be done on some mining farm. Thus the mining farms are not paying for the hashrate, yet they have the hashrate available to attack the coin when they are ready to flip the switch and take control.
But the mining farms have this huge investment which they don't want to destroy, thus they will not attack in any overt way which undermines their investment.
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#msg15972492One of the other problems is that you are disincentivizing buy & hold investors/speculators.
You are basically emulating Freicoin's market failure and its demurrage concept.
I don't see penalizing those who don't transact as a viable model for a store-of-value which is one of the attributes of money.
Power vacuums are disequilibria. That is the fundamental point of my white paper and my attempt at a technical solution.
So in your proposed negative interest rate design, if the loss of stake is
greater than the cost of the proof-of-work, then all savers will transact to themselves,
thus this is just proof-of-stake so the majority stake must collude to do the 51% attack I explained as quoted above. If the loss of stake is
less than the cost of the proof-of-work, then there is a gradual transfer of the ownership of the coin to the mining farms and thus the stake eventually becomes winner-take-all concentrated.
I hope readers are starting to understand how very difficult it is to design a money system which is not a winner-take-all power vacuum.