Commit 1fa3b3a0 authored by Markus Klinik's avatar Markus Klinik
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diminishing returns

parent a3185edd
......@@ -143,8 +143,17 @@ The main reason for choosing the weighted-product method is that the units and m
No conversion or normalization is required, the numbers can be multiplied as-is.
One objective can be a distance in meters, another one a cost in euros, yet another one a time in seconds.
\paragraph{Weights allow for diminishing returns}
\paragraph{Weights allow modelling diminishing returns}
If an objective with weight 1 doubles, the score doubles as well.
The influence of an objective on the score can be amplified by giving it a weight greater than 1.
Weights smaller than 1 can be used to model diminishing returns, which is the effect that people tend to give less value to further increases in an objective.
A person might be very happy about the first million they earn, but more money does not make them equally more happy. As a famous quote by Arnold Schwarzenegger goes: ``I now have 50 million but I'm just as happy when I had 48 million.''
For example, when an objective with weight 0.5 doubles, the score increases by a factor of about 1.4, but if it quadruples, the score only doubles.
The effect of a weight $q^w$ on the overall score can be estimated as follows.
If the objective $q$ changes by $1\%$, the score approximately changes by $w\%$.
For a derivation of this estimation, see \citet{Tofallis2014}.
\paragraph{Measurement theory}
All objectives must be units of ratio scale.
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