Here's a vague idea... How about a reputation ledger? My reputation will accumulate over time, and people will trust me, simplifying some transactions. For example I could rent a short-term stay at a lower rate because I am such a nice fellow and will never mess anything up.

Because my reputation has direct monetary value I would be hesitant to mess it up by being a dick, unless for a very big gain. The counter-parties will know the value of my reputation as well as the total value of outstanding liabilities against my reputation, so they will not give me any resources worth more than my current reputation capacity.

This has nothing to do with mining or coins, just an immutable public ledger. For all I care every notary public will be given a right to sign a block in the ledger, and collectively they will establish consensus.

Yelp on steroids, basically.