In English, there is a phenomenon known as the "royal we" where a speaker used first person plural as a stand-in for first person singular. Generally, this phenomenon associates itself with arrogant and schizophrenic-type personalities. In Greek or Latin, poets often employ the first person plural so it is essentially the "poetic we" rather than the "royal we."
Herodotus II and I have recently doubled our number of lines per week in order for us to finish before summer vacation. Although this certainly requires more time, it also provides me with a greater sample size in which to notice patterns. One of the things that stood out to me as I read our most recent section was the use of the "poetic we." Μήδεια employs this tactic quite frequently, although she also uses the first person singular within 2-3 lines of her first person plural. I did not notice, although I might have missed it, Kreon using the poetic plural, nor any of the other characters (I am happy to be corrected if someone notices an instance). So, I wondered why Medea, specifically, might use this rhetorical device.
Euripides, as I remember reading in my Bacchae class freshman year, likes to use "halved" characters, i.e. two main characters who each represent one set opposing characteristics usually housed in a single person. Unlike his half characters, Medea seems to be a duel (or possibly more) character. She switches from courageous and fearsome at one moment, to helpless and despairing the next, to conniving and persuasive, sometimes within a single speech. Like Hekate (Μήδεια line 397), the goddess she worships, to whom each of the three main Gods (Zeus, Poseidon, and Hades) gave a small segment of their domain, she functions as a polymorphic character. Each of the characters around her serve a single function. Even the chorus of women acts essentially as a single entity; they represent a moderate buffer to the extreme arguments put forward by any side. But Medea demonstrates so many different personality traits and skills that she becomes awesome and terrifying.
Update 03/24/11: Jason also uses the "poetic we" at least once. I ran across this in line 451 where he refers to himself as κἀμοὶ which is a crasis of και + αμοι (from αμος, "our"). However, this is the first time it is mentioned by another character. Also, interestingly enough, Jason is being deceptive here and saying things he only half means in a typical Μήδεια style. I will have to investigate further.