Council Seat

 refers to an unmarked quest in Fallout 3.

This mini-quest can be started by speaking with Bannon inside the Rivet City Market District. He will inform you that he believes Seagrave Holmes is planning to steal his seat in the city council. He then tasks you to find incriminating evidence on Seagrave Holmes that will put a rest to his stealing of the chair.

Retrieve the evidence
You can wander into Seagrave's Room (easy lock) in the Mid-Ship Deck right by the door to the Market District. Once inside find the Holodisk near the footlocker at the end of his bed (there are two holodisks in his room, one is called "holotape" while the other has a defined name.) After retrieving the tape you can read it and learn that Seagrave is communicating with the slaver boss Eulogy Jones. Now you can talk with Bannon and Seagrave Holmes.

Choose a side
Seagrave claims that the message makes it clear that he is not going to cooperate with the slavers and that you should inform Lana Danvers that Bannon is trying to blackmail him. Bannon will tell you to report this evidence to Lana Danvers but must not tell her that it is he who sent you on the task to find evidence of Seagrave.

You can find Lana Danvers at the 3rd level of the tower. Just go up the stair well to the top, and enter the door that says bridge tower. Choose the person to side with and denounce the other to Lana Danvers.

Rewards
This mini-quest awards no immediate Bottle caps (though the 10% discount is a win situation) or Karma.

Bannon's reward

 * A permanent 10% discount at the Potomac Attire
 * One Schematics - Deathclaw Gauntlet.

Seagrave Holmes's reward

 * A permanent 10% discount at Rivet City Supply.

Whichever party you turn in will also penalize you with a 10% price increase at their store. Choosing which party to support is a tactical choice, since Bannon rewards the player with a Deathclaw Gauntlet Schematic and sells the player apparel at a discount whereas Holmes gives no instant reward, yet has more material at a better discount. Additionally, Holmes is a constant source of rare .44 ammunition and will pay the highest prices for any kind of loot.(not known to work for PC on some occassions)

With both DLC's Broken Steel and The Pitt, you can use the ammo press to obtain .44 ammo and choose the Warmonger perk to learn how to build all custom weapons in perfect condition without finding the actual diagrams.