Recusal
When a judge or someone in a similar position takes themselves off a case because they might be biased or have a conflict of interest. It's like saying, 'I can't be fair here, so I'm stepping aside'.
Examples
The judge announced his recusal because his brother worked for the defendant.
She requested the recusal of the committee member who had publicly criticized her work.
Due to his prior involvement with the company, the auditor announced his recusal from the investigation.