Arbitrary and Capricious means doing something according to one’s will or caprice and therefore conveying a notion of a tendency to abuse the possession of power.
In U.S this is one of the basic standards for review of appeals. Under the "arbitrary and capricious" standard, the finding of a lower court will not be disturbed unless it has no reasonable basis. When a judge makes a decision without reasonable grounds or adequate consideration of the circumstances, it is said to be arbitrary and capricious and can be invalidated by an appellate court on that ground. In other words there should be absence of a rational connection between the facts found and the choice made. There should be a clear error of judgment; an action not based upon consideration of relevant factors and so is arbitrary, capricious, an abuse of discretion or otherwise not in accordance with law or if it was taken without observance of procedure required by law. [Natural Resources Defense Council, Inc. v. United States EPA, 966 F.2d 1292, 1297 (9th Cir. 1992)] There is, however, no set standard for what constitutes an arbitrary and capricious decision.
Example of a state statute defining arbitrary and capricious
Fla. Stat. § 120.57 (2009)
§ 120.57. Additional procedures for particular cases
(1) ADDITIONAL PROCEDURES APPLICABLE TO HEARINGS INVOLVING DISPUTED ISSUES OF MATERIAL FACT.
d. Is not arbitrary or capricious. A rule is arbitrary if it is not supported by logic or the necessary facts; a rule is capricious if it is adopted without thought or reason or is irrational;