Completeness is the first axiom of preferences necessary to use expected utility theory.
- A set of preferences is complete if, for all pairs of outcomes A and B, the individual prefers A to B, prefers B to A, or is indifferent between A and B.
- Such preferences need not be sensible. Someone who prefers dying a painful death to winning $1 million could still have a complete preference ordering.
- In essence, the only thing completeness rules out is a “decline to state” option.
- Completeness is a reasonable axiom for situations with important stakes. Someone may not be able to provide stable answers to trivial outcomes.