<p>How would you show that whenever  additively represents an agent’s preferences, then so does any function ′ that differs from  only by the choice of zero and unit.</p>
<p>If we assume that  additively represents an agent’s preferences, so that for some subvalue functions 1, 2, ... , ,
(⟨1, 2, ... ,  ⟩) = 1(1) + 2(2) + ... + ().</p>
<p>and assume ′ differs from  only by a different choice of unit and zero, which means that there are numbers  &gt; 0 and  such that ′(⟨1, 2, ... ,  ⟩) =  ⋅ (⟨1, 2, ... ,  ⟩)+.</p>
<p>How do we show that that there are subvalue functions1′,2′,...,′ such that
′(⟨1, 2, ... ,  ⟩) = 1′(1) + 2′(2) + ... + ′().</p>

<self-study>
subvalue additivity
jayil
# subvalue additivity

(Asked by: username_0 on 2022-10-27)

How would you show that whenever additively represents an agent’s preferences, then so does any function ′ that differs from only by the choice of zero and unit.

If we assume that additively represents an agent’s preferences, so that for some subvalue functions 1, 2, ... , ,
(⟨1, 2, ... , ⟩) = 1(1) + 2(2) + ... + ().

and assume ′ differs from only by a different choice of unit and zero, which means that there are numbers > 0 and such that ′(⟨1, 2, ... , ⟩) = ⋅ (⟨1, 2, ... , ⟩)+.

How do we show that that there are subvalue functions1′,2′,...,′ such that
′(⟨1, 2, ... , ⟩) = 1′(1) + 2′(2) + ... + ′().

**Tags:** self-study

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