'Behalf' in the Bible

Now I have applied these things, brothers, to myself and Apollos for your sake, in order that in us you may learn not [to go] beyond what is written, lest someone be inflated with pride on behalf of one [person] against the other.

Otherwise, why do they do [it], those who are being baptized on behalf of the dead? If the dead are not raised at all, why indeed are they being baptized on behalf of them?