The ideal proof of work algorithm should serve no other useful purpose besides enabling disparate actors to provably sacrifice resources foreign-to-the-system.

The ideal proof of work algorithm should serve no other useful purpose besides enabling disparate actors to provably sacrifice resources foreign-to-the-system. Anything the PoW algo does which is useful above and beyond provable sacrifice increases the incentive for PoW miners to attack the network. For example, if you could either use your GPU to mine $COIN for $10/day or to mine $ANTICOIN for $1/day, you could attack $COIN in full knowledge that your GPUs would still earn $1/day of $ANTICOIN afterwards.