I'm a lawyer. Here's a summary from Perplexity.ai, which comports well with my general understanding:
The U.S. Supreme Court defines "arbitrary and capricious" in the context of administrative-agency action primarily through the standards set forth in the Administrative Procedure Act (APA). According to the APA, a court must invalidate agency actions that are found to be "arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law" 1 3 4.
The arbitrary and capricious standard is applied when reviewing an agency's decision-making process and involves several key considerations:
Consideration of Relevant Factors: An agency action is deemed arbitrary and capricious if the agency has relied on factors that Congress did not intend it to consider, failed to consider an important aspect of the problem, or offered an explanation for its decision that runs counter to the evidence before the agency 2 3.
Rational Connection: The agency must demonstrate a rational connection between the facts found and the choices made. This requires a satisfactory explanation for its action based on consideration of relevant data 6.
Consistency and Reasoning: The decision should not be based on seriously flawed reasoning or be inconsistent with prior actions unless adequately explained. The agency must also respond to relevant arguments or comments during the decision-making process 6.
Zone of Reasonableness: Recent interpretations by the Supreme Court have introduced the concept of a "zone of reasonableness," where agency actions are upheld if they fall within a reasonable range of decisions based on the agency's expertise 4.