Why do the other lords of the North support this character in S6?

Question

In Season 6 of Game of Thrones we see Ramsay Bolton murder his father, Roose. Then the Karstarks and the Umbers declare their support for Ramsay. Reasons why I find this hard to believe:

1. Ramsay is a psychotic sadist but not shown as particularly competent at ruling or war. More importantly (given the setting) he's a legitimized bastard. His highborn father and newborn baby brother (both of whom he kills) should command far more respect. How did the Karstarks or the Umbers not try to arrest him or seize his titles?
2. Roose is a sociopath too, but also a proven military leader and ruler who has managed to come out on top in the most destructive conflict in 15 years. The Karstarks were already pledged to him; what prompted them to throw in with Ramsay after he killed the guy who actually knew what he was doing?

Answer 1

You're making a big assumption that their support for him was genuine.

They - and the other Northern lords Jon struggled to persuade - seemed convinved the Starks were finished. Most stayed neutral, Karstark (a sinister character) tried to position himself as Ramsay's second in command; Umber seemed to respond to this by also working to be as close.

You could interpret it as loyalty. My reading of it was, that Karstark wanted to be in the right place that he could take over from Ramsay, biding his time until the increasingly reckless Ramsay finally created an opportunity that he could seize on. Meanwhile, the Umbers didn't want to have to serve Ramsay or Karstark, and recognised this as a potential threat to their status and wanted to also be in a position to challenge when Ramsay's power finally imploded. Keep your friends close and enemies closer and all that.

Ramsay then cunningly exploited this unstated rivalry by:

• Letting the Karstarks lead the cavalry charge - which they'll have been happy to do as an opportunity to show the North that they're the ones who won the battle and because the odds in their favour seemed overwhelming. He then fired arrows on both sides, ensuring that when he beat Jon's army, the Karstarks would be sufficiently weakened to pose no threat
• Letting the Umbers lead the infantry charge, and letting Umber make his "Who owns the North?" speech - for very similar reasons. Let them think they're winning glory and strengthening their status, then sit back and watch them take heavy casualties and come out of it weakened.

This is a little bit like the equivalent situation in the books, where:

...Winterfell contains an uneasy alliance of Northern lords, including at least one who is secretly working against Ramsay. The reader isn't entirely sure (certainly at first) who's genuinely loyal, who's going through the motions out of fear and who's actively planning rebellion; and there's a heavy atmosphere of mistrust and betrayal.

Answer 2

Because, at least at that point, he's winning. Look at their options:

• Stannis' army is considered to be largely dead and defeated. Even before his failed assault on Winterfell, he did not have much support from the North.
• Sansa is with Petyr Baelish, whom the Northern lords do not trust. Also, Robb lost the support of the Karstarks when he executed Rickard for murdering two Lannister boys.
• The Boltons have control of Winterfell and the military force to hold it. They also have the support of the crown, which includes the financial and military support of the Baratheons and, more importantly, the Lannisters. That also puts them in line with the Freys, who control the key lands to the south of them.

Given those options, and especially not realizing that Jon Snow is out there building an army of his own, their options are pretty limited. If they broke with Ramsay over the murder, they would have to either support one of the other two, or go rogue on their own. Any of those would probably result in the defeat and destruction of their houses. They probably consider supporting Ramsay the only safe and viable option available to them.

Answer 3

Adding to @KutuluMike's great answer, let me add a few more.

Ramsay is a psychotic sadist

Ramsey's being a psychotic sadist makes them more fearful of him as they don't know what he will do if they don't declare support for him. I don't believe his character must be a deciding factor for their support as he was legitimized by his own father and there is no heir to Roose Bolton.

but not shown as particularly competent at ruling or war.

I disagree. He is good at reign of terror and instilling fear into people as evidenced by what he has done to Theon Greyjoy. Also, he is shown as competent at archery and fighting strategy in the war. If you remember the last battle scene between Ramsey Bolton and Jon Snow, Ramsey's strategy was very brilliant and original killing his own soldiers to build a wall and surround Jon Snow's soldiers. If Sansa and Petyr had not helped Jon Snow, Jon would have been defeated miserably.

His highborn father and newborn baby brother (both of whom he kills) should command far more respect.

Of course, if only they had not been killed by Ramsey.

How did the Karstarks or the Umbers not try to arrest him or seize his titles?

As mentioned before, they feared him and there was no heir to Roose Bolton.

I think No. 2 question was well answered by @KutuluMike.