This is a straw man argument. Such a person would certainly choose a lesser pain as a means of avoiding a greater one.
Thanks for your comments. I don't think that is a straw man argument at all. It is exactly this part of what Epicurus says - that we DO sometimes choose pain to maximize pleasure - that is in issue.
I wouldn't normally think it necessary to point this out (that we sometimes choose pain) but it is being ignored by the "painfree" chorus, and even if mentioned at all only in an exceptional way, never clearly stated to be something we can and should do on a routine basis to maximize pleasure.
