The badges page for Announcer, Booster and Publicist do not mention that you cannot get both the badges for the same shared it.
The badges used to work differentlywork differently when first introduced(there were timelimit/IP limit changes since then) but I don't remember any changes which mention that the same question cannot multiple badges of the class you mention and the order in which they arewhich they are awarded were indeed changed later onindeed changed later on
