Weakly additive

In <a href="/facts/Fair_division/v4PN6nfD">fair division</a>, a topic in <a href="/facts/Economics/HYctA2Dn">economics</a>, a <a href="/facts/Preference_(economics)/4h4tND8S">preference relation</a> is weakly additive
if the following condition is met:

If A is preferred to B, and C is preferred to D (and the contents of A and C do not overlap) then A together with C is preferable to B together with D.
Every <a href="/facts/Additive_utility/xWMFGEeN">additive utility</a> function is weakly-additive. However, additivity is applicable only to <a href="/facts/Cardinal_utility/5jeuW4Iw">cardinal utility</a> functions, while weak additivity is applicable to <a href="/facts/Ordinal_utility/pFbpa2dg">ordinal utility</a> functions.
Weak additivity is often a realistic assumption when dividing up <a href="/facts/Good_(economics)/AtK6gQh2">goods</a> between claimants, and simplifies the mathematics of certain fair division problems considerably. Some procedures in fair division do not need the value of goods to be additive and only require weak additivity. In particular the <a href="/facts/Adjusted_winner_procedure/8R0qtuYB">adjusted winner procedure</a> only requires weak additivity.

Weakly additive open-in-new

Weakly additive