Something that's arbitrary seems like it's chosen at random instead of following a consistent rule. Team members would dislike their coach using a totally arbitrary method to pick starting players.

Even though arbitrary comes from a word meaning "judge" (arbiter), that doesn't mean judges are always fair. Calling a decision-maker arbitrary is usually a negative thing, suggesting the person is making rules based on whim rather than justice. A coach who selects starting players arbitrarily isn't strictly applying a rule; he could just be picking names out of a hat.

Definitions of arbitrary

adj based on or subject to individual discretion or preference or sometimes impulse or caprice

“an arbitrary decision”
“the arbitrary rule of a dictator”
“an arbitrary penalty”
“of arbitrary size and shape”
“an arbitrary choice”
arbitrary division of the group into halves”
not limited by law
capricious, impulsive, whimsical
determined by chance or impulse or whim rather than by necessity or reason
discretional, discretionary
having or using the ability to act or decide according to your own discretion or judgment
nonarbitrary, unarbitrary
not subject to individual determination
set down as a rule or guide
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