This is just an idea which I would like to get feedback on.
I am thinking the fundamental flaw in any consensus algorithm that relies on some asset, is that the economic game theory is such that the asset will concentrate towards a winner take all over time.
For example in proof-of-stake or proof-of-importance (reputation+stake) the miner with sufficient stake and/or reputation can keep the minority chain sufficiently paced but more often behind the other chain such that most vote on the other chain, but ultimately he uses his power to vote the minority chain to the permanent lead thus orphaning all the rewards of the lesser stakes who were fooled into voting for what they thought was statistically the more likely longer chain. There are other variants of this strategy.
In proof-of-work selfish mining works in general when the adversary has at least 33% of the hashrate, and 25% under some network configurations.
One potential solution I see to this problem is to make mining an unprofitable asset burning operation.
But if this is accomplished by burning coins, eventually end up with 0 money supply.
Or
I did I think show it might be possible to eliminate the selfish mining strategy in proof-of-work but at the cost of penalizing the honest party to a double-spend, by paying all chains proportionally. I am not clear how this could work for non-proof-of-work.