In fair division, a topic in economics, a preference relation is weakly additive if the following condition is met:[1] Every additive utility function is weakly-additive.
However, additivity is applicable only to cardinal utility functions, while weak additivity is applicable to ordinal utility functions.
Weak additivity is often a realistic assumption when dividing up goods between claimants, and simplifies the mathematics of certain fair division problems considerably.
In particular the adjusted winner procedure only requires weak additivity.
Case where the assumptions might fail would be either The use of money as compensation can often turn real cases like these into situations where the weak additivity condition is satisfied even if the values are not exactly additive.