Basically, instead of an economic currency unit being mined, the value being protected is instead some form of reputational trust-token; 30 seconds of Googling leads to articles like this: https://www.forbes.com/sites/shermanlee/2018/08/13/a-decentr...
Thinking about things this way essentially boils the fundamental problem into what IMO is a pretty "general elegant theory", which is simply to construct a properly balanced incentive structure, which asymmetrically disincentivizes "bad" behavior while encouraging "good" behavior, in much the same way that Bitcoin's core ledger-validation/mining abstraction rewards miners for securing the network while also discouraging prohibitively expensive attack scenarios.
I'm not saying it's easy or obvious, but I think this is exactly the sort of decentralized trust problem that blockchains are well-suited for.