Although every mining pool can do things differently, I wanted to get a handle on how a logical pool would behave. If a miner joins the pool and solves a hash at a low difficult, submits the result back to the pool, which then accepts it, would the next logical thing for the pool to be to assign that miner a slightly harder bit of work to do? In other words, would the "set\_difficulty" level be higher the next time around (assuming the difficulty solved by the miner is less than the network difficulty)?

If the pool does not assign harder work and lets the miner continue to solve problems at the same difficulty (which is less than the network difficulty), how does the overall pool benefit?