Could αὐθένται just refer to the fact that the members of a deliberative assembly are all active in the discussion - all author speeches of their own, one might say - rather than to their being possessors of decision-making authority?
Alexander is discussing “symbouleutic” rhetoric here. That was a conventional category of rhetoric involving speeches addressing policy issues delivered before deliberative bodies, not dialogues among the members. He’s discussing the audience of the rhetor–he observes that in the context of deliberative assemblies the members of the audience have decision-making authority, just as judges in the courtroom have authority to render judgments–but the audience for praise/blame speeches, he notes, aren’t engaged in a decision-making process at all. Here, I think, Alexander uses αὐθένται in the sense of “having decision-making authority,” rather than in the sense that they have the ability to speak on their own. I don’t think he’s necessarily envisioning a scenario where the members of the assembly have a turn at speaking themselves–the essential point is that they are the ones with authority for the decision. The focus is on the rhetor, and It’s the rhetor who does the speaking–presumably Alexander is going to address how the rhetor should construct his speech when targeting each of the three different types of audiences that he distinguishes.
This is of course the 2d century CE, not 5th or 4th century Athenian democracy, but even in that era in which he was writing there would have been many opportunities for politicians/rhetores to address deliberative bodies, whether assembled masses of citizens or councils of one sort or another or other groups responsible for making decisions. These types of institutions, particularly at the local level, continued to coexist with an autocratic central power.
There is a slight difference in this respect from αὐθεντῶν in Aristonicus, which in context means something like “speaking his own mind,” as opposed to reporting the words of someone else.
With regard to concordance interpolations, we’ve had a discussion about these right here:
http://discourse.textkit.com/t/concordance-interpolations/12654/1
I tend to prefer a more conservative approach than my arch-enemy Paul Derouda, who wants to slash the Iliad and the Odyssey to pieces.