Currently Uncommitted Powers
There remain persons and groups in the Courts of Chaos that have yet to ally themselves with any of the three factions contending for the throne. They are as follows...
House Darios is locked in a civil war between Darios Minor, eldest son of Lord Ahab and his wife Igdi of Helgram, and Halder, a younger son of Ahab but the eldest by his last wife Lady Mina. Darios' claim is the legal one; Halder's reasons for trying to usurp his position remain unknown. Barring intervention, whichever one of them wins seems likely to throw their backing to their traditional ally, House Formorian, though the possibility of them going to Suroth does exist if they think it will give them a greater chance to put the screws to Jesby. Darios has somewhat greater value to any of the factions than most other uncommitted houses because of their vast strength at sea.
It appears likely that this civil war is at an end thanks to the efforts of Lord Shanks; it is unclear who Lord Darios will decide to support.
House Tremere is not locked in a civil war; they seem to be handling their succession issues without violence or bloodshed. However, their succession is a horrible mess, as all of their leaders are dead, and all of the people who would normally succeed them are dead, and those who could appoint replacements are dead, which is a situation the Tremere bylaws never envisioned and so do not speak on, and nobody still living has the power to change the laws... and on and on. It will work itself out eventually; whether in time to make any sort of difference in the greater succession differences remains to be seen. House Tremere does not like Amber or most of the Houses comprising the Loyalist faction at all, and are traditional allies of Formorian, but things are so up-in-the-air that the right negotiator offering the right incentives could probably induce them to fall for any of the three factions.
Of course, it was just recently discovered that House Tremere had become infiltrated by a major Outsider's artifact, in an attempt to take over the House. While that plot was successfully quelled by a combined Amber and Helgram strike force, it is unknown as to how much effect this will have on the election proceedings. Perhaps this will cause Tremere to look more favorably on them, but whether it will is anybody's guess.
Having driven off the Squid and slowly rebuilding with the aid of Kong Interstellar, Zeta Cygni is still reluctant to involve themselves in politics if they don't have to. Which, so far, they don't. Princess Naru has recently been seen in Zeta Cygni, and a rise in pro-Alars sentiment has been noticed as well... coincidence, surely.
Persons of Importance
Anno, Keeper of the Logrus
Anno's word would probably have great weight in this debacle. Unfortunately for any party that would seek his favor, Anno does not play politics and seems unlikely to start now, especially considering how busy he is going to be in the near future. He is likely to remain firmly uncommitted for the duration to anything other than fixing the Logrus.
Princess Motoko, the Bride of the Dragon
The arbiters of the succession laws to the throne of Chaos are the priests of the College of Heralds, still busily reconstituting themselves. As a living religious icon, the word of the Bride of the Dragon carries much weight among them. While a Princess of Amber, Motoko has very strong ties to Chaos, and seems likely to act in what she believes are its best interests; but for the time being her political stance, Loyalist, Opposition, or neutral, remains unknown.
Lord Davros, Soul of the Bride
An important undeclared religious figure in his own right, Davros is fairly likely to go where Motoko goes. However, his counsel obviously carries great weight with her, and he does hail from a House that has declared for the Loyalists.
Dios, King of New Chaos
The name and memory of Dios still resonates loudly in the collective consciousness of the Courts of Chaos. While Dios -technically- wields no power in Old Chaos, his endorsement of any of the factions would be a significant moral victory for them. GETTING him to endorse anyone (or even if he wishes to) is an entirely different matter, however.