I don't know much about the Dept. of Transportation's bump rules. Just look at the whole thing with common sense. If the passenger did not cause a threat to the security of other passengers or crews, removing him with EXCESSIVE force that caused bodily harm is outright wrong! You can offer him more compensation; or upgrade him; or rebook him on a later flight; or simply choose another more agreeable passenger. Whatever happened is totally uncalled for. United handled this situation badly and so was the Airport police. By the way, where is the captain during all this?