By the way, if you're interested in delegated voting, I wrote a paper on using it in a democracy some time ago:

  https://docs.google.com/document/pub?id=1jidmNJHWAtsPLCUD7EPPm8jOEV93kSXbZOMycqCWOyA

I think delegating voting is a great idea. I'm less convinced that it would work for replacing hashing in the block chain, but it might.

Some more problems for you to consider:

• If I control a key with 10 delegators, then I spend that key to 10 new keys, what happens to the delegations? Does it make sense for a key to have fan-out (ie 1 key to delegate to 10 other keys)? Do you split the value evenly or not?
• How do you efficiently detect and resolve delegation loops? ie, key A delegates to B, B delegates to C and C then delegates to A? You have to do this efficiently because otherwise setting up new delegations is a way to DoS the system. Note that detecting cycles in a large graph is slow, Tarjans algorithm is O(number of edges). If each key in the system takes part then every new address in the system potentially makes setting up new delegations harder. As the number of keys in the system grows without bound over time, that could be an issue
• Keys are owned by end users who may or may not know/care about the inner workings of their currency. How do you get new users to delegate appropriately?

It should be possible to run a parallel block chain based on proof-by-stake, but using the same transactions. It could be done with an adapted Bitcoin software. Once such a chain was up and running you could compare the results vs the existing chain.

I don't have the time/energy to do this myself.