Editing Ordinal utility (section)

==Constructing additive and quadratic utility functions from ordinal data==

The mathematical foundations of most common types of utility functions — quadratic and additive — laid down by [[Gérard Debreu]]<ref name="Debreu1952">{{Cite journal
|last=Debreu |first=Gérard|year=1952
|title= Definite and semidefinite quadratic forms |journal= Econometrica |volume=20|issue=2|pages=295–300
|doi =10.2307/1907852
|jstor=1907852}}</ref><ref name="Debreu1960">{{Cite book
|last=Debreu |first=Gérard|year=1960
|chapter= Topological methods in cardinal utility theory 
|editor-last= Arrow|editor-first=Kenneth
|title= Mathematical Methods in the Social Sciences,1959
|publisher= Stanford University Press
|location= Stanford|pages=16–26
|doi = 10.1017/CCOL052123736X.010|isbn=9781139052092|url=https://cowles.yale.edu/sites/default/files/files/pub/d00/d0076.pdf}}</ref>
enabled [[Andranik Tangian]] to develop methods for their construction from purely ordinal data.
In particular, additive and quadratic utility functions in <math>n</math> variables can be constructed from interviews of decision makers, where questions are aimed at tracing totally <math>n</math> 2D-indifference curves in <math>n - 1</math> coordinate planes without referring to cardinal utility estimates.<ref name="Tangian2002">{{Cite journal
|last=Tangian |first=Andranik|year=2002
|title= Constructing a quasi-concave quadratic objective function from interviewing a decision maker
|journal= European Journal of Operational Research |volume=141|issue=3|pages=608–640
| doi=10.1016/S0377-2217(01)00185-0}}</ref><ref name="Tangian2004">{{Cite journal
|last=Tangian |first=Andranik|year=2004
|title= A model for ordinally constructing additive objective functions
|journal= European Journal of Operational Research |volume=159|issue=2|pages=476–512
|doi= 10.1016/S0377-2217(03)00413-2
}}</ref>