[heptathorp]

1. How does the entire network just agree to switch to a new algorithm? How do they decide what the new algorithm is?

2. When everybody forks off of the compromised chain, haven't we effectively created an altcoin? What is the value of this nascent altcoin?

3. I'm thinking the value can't be very much, otherwise it would be way out of proportion to the difficulty considering there are not yet any ASICs for the new algorithm. Wouldn't it then be very much worth it for someone to attack it again using, say, a botnet?

[Frogolocalypse]

I don't think you're actually interested in the answers. Any pow change would simply be a hard fork with no or opt-in replay protection. I say none, because there's no need to provide protection to the compromised chain. The patch will have already been developed. The core developers will already have vetted many pow algorithms, and a decision would be made at the time.

It's actually not very complex.