Actually, as I see it, Bromo, the popular mandate argument falls squarely on both sides. On one side, the popular mandate has given the Xigalias seats in the Chancellorship and in the RA. On the other side, however (and it seems to be forgotten by the Xigalias' supporters), the popular mandate has also given the opposing faction a mandate: three of the five RA seats (a majority!) are occupied by members of the same unofficial faction. In fact, you recognise this when you say, "the Majority in the RA isn't particularly sympathetic to CLEO."
The STV voting system, Bromo, also makes it so that political systems may have candidates which are more representative of the diverse body of citizens' political beliefs. I don't think that it gives any elected candidate the power to say, "I received the most primary votes, therefore my mandate is of greater power or strength than yours" or any other similarly childish and immature rhetoric. All those elected did so with an equal mandate of the people, because of the way in which the system is constituted to provide for preferential voting of candidates and the sharing of other preferential votes if a candidate is disqualified.
Also, I would also note that popularity is an animate thing, often dependent on the perceptions of whomever is doing the statistics. Sure, the election is a popularity contest in a way, but it doesn't guage today's popularity. However, it's two months since the election and I think that, in my opinion, the Xigalias are becoming less popular — however, I may be saying this because the people who I have been speaking to most recently happen to oppose CLEO (i.e., my perception). I think CLEO knows this though and it can explain why, some month and a half after the election, she's going back to the mandate we all received from the referendum, reinvigorating support for it, in an order to garner more political support for her. Though maybe I see it this way because I have been reading The Prince again recently. 
It's a well-known trick by people who see themselves in the minority of parliamentarian politics. I've done it myself multiple times with my elections in Sandus and with my former political position in the Grand Unified Micronational, an intermicronational organisation comprising a multitude of RL micronations. "The result of such and such said this and I am willing to get such and such done during my tenure, and I request it be done as soon as possible."
