Commit 1fa3b3a0 by Markus Klinik

### 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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