Consider 2 miners. One hopper and one non-hopper. Imagine that both of them have 1GH/s. It takes both of them 4s to generate a share. Now one goes gives that share to a pool which offers a lot for it, but the other gives that share to a pool which offers less. What is immoral in that?
As I explained, pool hopping breaches the implied covenant of good faith and fair dealing between miners.
And really, the pool does not offer less for a share because of hoppers. It there were no hoppers that pool would still offer less for that share.
That is incorrect. The pool really does offer less for a share because of hoppers.
The expected payout per share is based on how many shares have already been accumulated towards the current block. The lower that number, the higher the payout per share. Now, consider a pool's hash rate. The more pool hoppers the pool has, the more the pool's hash rate will go up when there are fewer shares accumulated and will go down when there are more shares. The share count resets to zero when the pool finds a block, which is determined only by the average hashing power. So more pool hoppers means more of that average hashing power comes out at low share counts and less at high counts. This means the pool spends more time at high share counts than it does at low share counts.
For a non-hopping miner, the average payout per block is solely depending on the average share count. This goes up with more pool hoppers because the hash rate goes down when the share count is high, leading to more time spent at the higher count.
I do see a lot of defense of pool hoppers based on misunderstandings of the mathematics. The analogy to coal miners sharing a vein is apt. The more mine hoppers in this case, the less time the miners spend mining a vein (because there are more people mining then, so it goes faster) and the more time the miners spend trying to expose a new vein (because there are fewer people mining then).
Well you are right, that in a pool with pool hoppers miners will be paid less if there won't be pool hoppers. But this is only because the pool hoppers will compete with miners over the hot deals, while they will leave "bad deals" intact.
Since you mentioned math lets agree first on some facts, ok?
1) When the block is still being solved, share submitted with sequence number 100 has higher expected payout value than share submitted with sequence number 100000. (Proof draft: When submitting share number 100 or 100000, there is still the same expected number of shares needed to solve the block, that means the total number of shares will be higher in the latter case)
2) When there are no hoppers, miners submit shares, where some of them have expected value > 50 / difficulty and some of them have expected value < 50 / difficulty. In the long run, the expected value of all shares together will average to 50 / difficulty.
3) With hoppers: hoppers do not submit shares with expected value < 50 / difficulty. However they submit shares with expected value > 50 / difficulty. That means 24/7 miners will receive less shares with expected value > 50 / difficulty. That way, those shares submitted with EV < 50 / difficulty by 24/7 miners will no longer be offset by the highly paid shares and in the long run such miner will receive less than 50 / difficulty per share.
However it is not hoppers fault, that there are miners who submit shares with low EV. Seriously, if you found ounce of gold and sold it for 1/3 of it's market price and later you tried to sell other ounce of gold for higher price than market price without success, would you really blame other people for your loss?
Hoppers are not forcing you to sell your shares to the pool for cheap. If you sell it for cheap, than it is purely your own responsibility and don't talk about covenant. We don't run a charity here and we will not skip hot deals just because you are doing bad deals with your shares.