Friends of the court need to remind the public that courts are already accountable and proud of it—accountable to the law and the Constitution, not to politicians, special interests, and rage campaigns.
-- Slate article defending judicial independence
They also have to tell their daughters about cute purple unicorns in fairyland.
This is not convincing to many people, in part because it is not true. It is hard for some to understand how a document can hold someone "accountable." The President and Congress also swear/affirm to obey the law and Constitution. So do members of state legislatures. [Art. II, VI]. The people want more than their oaths/affirmations though. They know more is needed.
Judges are also obviously somewhat accountable to politicians, special interests, and rage campaigns. Such is the case when judges are elected and have to face re-election. Some is the case when lower judges are hoping for better positions farther up the food chain. And, when judges have their positions thanks to such things, they knew who buttered their bread, don't they?
["The law and the Constitution" are also slippery things ... thus deluded souls like I can believe it means totally crazy things like securing rights to privacy and so forth]
It is true a large part of "accountability" for members of the federal judiciary must come from an ethics and professional view that stays loyal to the law. But, even there, there are other checks. Lower court judges have to answer to appeals. Judges openly make decisions, including via written opinions, which is why many are concerned when they are made sans opinions or by rulings not considered binding law for further cases. Statutory interpretation can often be overturned via new statutes. Such opinions help address where this might be necessary.
Judges are open for investigation and even impeachment. Lower federal judges can be temporarily removed from active service if judicial oversight commissions determine it is necessary. They also are influenced by public opinion and the realization that others [with power of the purse and sword] carry out their edicts.
Such is reality. 2+2 does not equal 5, even if we want to pretend that "2" really means 2.3 rounded down and 5 is 4.6 rounded up.