Doesn't this scheme compromise the security of the bitcoin network. I mean, the security aspect of it is based on the total hashrate at every moment in time. if at any moment it decreases...then there's a potential weakness.
Yes it does. It makes half PoW and half of luck. If this is good, then make it 100% luck. does it work? No. Its not secure.
This propose just lower security for name of "economical".
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It's not even necessarily economical. People will just ramp up their hashing power for round 1 to try and get into round 2 so the energy expenditure over those 2 minutes would rise way above normal.
And then for the other 8 minutes, they got the bitcoin network by the balls so to speak. Relying on a small subset of miner hashing power. Sounds like a recipe for disaster. But I do admire the OP for defending his proposal and taking the time and effort to discuss it here.