Not quite sure whether this will ever be more than a dicdef. It also risks being original research.

A binary decision is a two-way choice, or equivalently, one that obeys the law of the excluded middle.

A binary decision is expressed by a two-valued variable, and conversely any two-valued variable expresses a binary decision. Examples of such variables are:

• The truth values of classical logic.
• Boolean data types.

• Principle of bivalence