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Private blockchains are interesting, but only based on where they fit on that spectrum. Some people consider DPoS systems "permissioned blockchains" because only the elected block producers can produce. With PoW, anyone can spend money on a mining rig, turn it on, and produce blocks (in theory). Some private blockchains may make sense within, for example, a corporate structure or within a group of companies working together where data interoperability is a major cost and having a shared protocol use very useful for solving the coordination problem. It's similar, I guess, to a private database with decentralized nodes that has very clear specifications for how things work. Getting everyone to agree on that protocol can be tricky and having a governance mechanism to remove those who are not performing is also valuable, which a private blockchain could give, but it's still not unique to "blockchain technology" in a meaningful way, IMO.

I like what Ari Paul said about permissioned blockchains last year:

Yes - I think that banking, medical, and supply chain industries will be "transformed" by permissioned blockchains, but not because permissioned blockchains are new or interesting.

Rather - these industries simply never implemented other types of permissioned distributed ledgers that have been around for 50+ years. So now all of the focus on blockchain is pressuring them to finally upgrade their databases that are comically obsolete.

https://twitter.com/AriDavidPaul/status/983104467762536448

When you look at markets and supply chains, some are obviously better organized than others. When blockchain proposals are popular, that suggests a market failure - which could be solved by a centralized solution if there's an organization trusted by all participants.