Shivering:Ritual of Accession

Quick Walkthrough
#Receive your next task from Sheogorath.
#Choose which duchy you wish to become Duke/Duchess of.

Detailed Walkthrough
Speak to Sheogorath, who will have appeared in the back row of pews in the Sacellum Arden-Sul. He wishes to promote you to Duke/Duchess, explaining that such a task entails removing the existing Duke or Duchess from power and advises you to speak to the priests. 

The Rituals of Removal
Speaking with Arctus and Dervenin about "Accession" will yield a considerable amount of information pertaining to both the Rituals of Accession, as well as the Sacellum and Arden-Sul. Return to Sheogorath when you have decided which Duchy you wish to rule. Choosing Mania requires killing Thadon, thus initiating the Ritual of Mania, while choosing Dementia means killing Syl, thus initiating the Ritual of Dementia. You can only complete one of the two quests.

Rewards and Implications
Your choice at this point has several implications, although either choice allows you to complete the Main Quest:
The Ring of Lordship you receive as duke or duchess has different enchantments for the Mania and Dementia versions.
During the course of the Main Quest you will gain the power to summon both Golden Saints and Dark Seducers. Your choice, however, will determine just when you will receive each power and the duration of the summon. You will be able to summon a Daedra aligned with your Duchy for 60 seconds when you become Duke/Duchess; after The Helpless Army you will be able to summon the other Daedra for 120 seconds.
The unique item you get to loot from your dead predecessor is different. Syl is carrying Nerveshatter, whereas Thadon is wearing the Diadem of Euphoria. However, you will subsequently be able to acquire the other item during The Roots of Madness quest.
The forces defending the Fringe during Retaking The Fringe will be different: Golden Saints for the Duke/Duchess of Mania or Dark Seducers for the Duke/Duchess of Dementia.
The Daedra under attack during The Helpless Army will be different: for the Duke/Duchess of Mania, you help the Dark Seducers at Pinnacle Rock; for the Duke/Duchess of Dementia, you help the Golden Saints at Brellach. The Daedra you help will then reward you with a suit of their armor: Golden Saint Heavy Armor or Dark Seducer Light Armor.
The final opponent during The Roots of Madness will be different: it will be whichever of Syl or Thadon you previously left alive, and you will now get to obtain their unique item.
You will receive full access to your respective House, Mania or Dementia, once you are granted Lordship.
If you choose to usurp Syl, the priest from Mania will claim that you have "forsaken the name Arden-Sul" and will refuse to speak to you for the rest of the game. The same applies to the Dementia priest if you kill Thadon.
If you choose to depose Thadon the Dark Seducers outside of Xirethard will become hostile to the player after Syl has her confrontation with Sheogorath in the Sacellum Arden-Sul. They will remain that way through the completion of the main quest line.

Notes
 If you want both achievements on the Xbox 360, save before choosing so that you can complete both. If you do not, you will need to create a new character to obtain the other achievement.
Golden Saints and Dark Seducers will refer to you as the Duchess of Mania or Dementia even if your character is male. This is caused by the respective Daedra checking her own gender and not the player's.
In addition to the Daedra calling you "Duchess" regardless of gender, the opposite applies, and you may be called "Duke", even if the player's character is female.

Journal Entries