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Economic definition of true love (view source)
Revision as of 17:27, 25 February 2012
, 17:27, 25 February 2012→True Love
*The definition employs strict preferences. A polyamorous definition might allow weak preferences instead.
*The union with the empty set allows for people who would rather be alone (e.g. Tiny Fey), provided that we allow a mild abuse of notation so that <math>i \succ_{\{\emptyset\}} h</math>. The inclusion of the empty set is not necessary with weak preferences as then we can allow <math> i \succsim_i i</math> without violating the definition of the preference relation.
===The Existance of True Love===
Can we prove that <math> T \ne \{\emptyset\}<math> ?
====The Brad Pitt Problem====
Rational preferences aren't sufficient to guarantee that <math> T \ne \{\emptyset\}<math>.
Recall that a preference relation is rational if it is complete and transitive:
#Completeness: <math>\forall x,y \in X: \quad x \succsim y \;\or\; y \succsim x
#Transitivity: <math>\forall x,y,z \in X: \quad \mbox{if}\; \quad x \succsim y \;\and\; y \succsim x \;\mbox{then}\; x \succsim z
Also recall the definition of the strict preference relation:
:<math>x \succ y \quad \Leftrightarrow \quad \quad x \succsim y \;\and\; y \nsuccsim x</math>
