Changes

Jump to navigation Jump to search
==Preamble==
==Current Availability==I originally tried to write an [[economic definition of true love]] for Valentine's Day in 2009 on a page entitled "Dating Ed". It became one of the most popular pages on my website, receiving hundreds of thousands of views, and I maintained it across several different wikis. The version below no longer includes information about dating me, as I'm now married, but does bring back some other material that was deleted over the years.
I'm afriad that Ed is currently available for dating at this time. Exceptions to this can be made if you have a Math(s) Ph.D. ==Definition of True Love==
HoweverLet <math>H</math> denote the set of all entities (perhaps Humans, if you genuinely believe:though we might also include dogs, cats and horses, according to historical precedent).
:Let <math>p\left(You \int The\,One \ne \empty|First\,Glance\right) >> 0T</math>.denote the set of pairs of individuals who have True Love, such that:
then please stop by my office at Haas at your earliest convenience.:<math>\forall\{i,j\} \in T: \quad (i \succ_j h \quad \forall h \ne i) \wedge (j \succ_i h \quad \forall h \ne j), \quad h \in H \cup \{\emptyset\}</math>
==Future Availability==Note that:*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. Liz Lemon/Tina Fey), provided that we allow a mild abuse of notation so that <math>\{\emptyset\} \succ_{i} h</math>.
Please check back ==The Existence 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>. '''Proof:''' Recall that a preference relation is rational if it is complete and transitive:#Completeness: <math>\forall x,y \in X: \quad x \succsim y \;\lor\; y \succsim x</math>#Transitivity: <math>\forall x,y,z \in X: \quad \mbox{if}\; \; x \succsim y \;\wedge\; y \succsim z \;\mbox{then}\; x \succsim z</math> Also recall the definition of the strict preference relation::<math>x \succ y \quad \Leftrightarrow \quad x \succsim y \;\wedge\; y \not{\succsim} x</math> Then suppose: #<math>\forall j \ne i \in H \quad i \succ_j h \quad \forall h\ne i \in H\quad\mbox{(Everyone loves Brad)}</math>#<math>\{\emptyset\} \succ_i h \quad \forall h \in H\quad\mbox{(Brad would rather be alone)}</math> Then <math>T = \{\emptyset\}</math> Q.E.D. ===The Pitt-Depp Addendum=== Adding the constraint that 'everybody loves somebody', or equivalently that: :<math>\forall i \in H \quad \exists h \in H \;\mbox{s.t. }\; h \succ_i \{\emptyset\}</math> does not make rational preferences sufficient to guarantee that <math> T \ne \{\emptyset\}</math>. '''Proof''': Suppose:#<math>\forall k \ne i,j \in H \quad i \succ_j h \quad \forall h\ne i,k \in H\quad\mbox{(Everyone, except Johnny, loves Brad)}</math>#<math>j \succ_i h \quad \forall h\ne j \in H\quad\mbox{(Brad loves Johnny)}</math>#<math>\exists h' \ne i,j \; \mbox{s.t.}\; h'\succ_j h \quad \forall h\ne h',i \in H\quad\mbox{(Johnny loves his wife)}</math> Then <math>T = \{\emptyset\}</math> Q.E.D. Note: Objections to this proof on the grounds of the inclusion of Johnny Depp should be addressed to [https://scholar.harvard.edu/rabin/capital-montana Matthew Rabin]. ==The Age Rule== The defacto standard age rule is as follows: Denote two people <math>i\;</math> and <math>j\;</math> such that <math>Age_i \le Age_j</math>, then it is acceptable for updatesthem to date if and only if  :<math>Age_i \ge \max \left\{\left(\frac{Age_j}{2}\right)+7\;,\;\underline{Age}\right\}</math> where <math>\underline{Age} = 18 \;\mbox{if}\; Age_j \ge 18</math>, except in Utah. I finally found a source to attribute this to: XKCD predates my posting significantly with its [http://xkcd.com/314/ 'Standard Creepiness Rule']. ==Random Love== An amusing exploration of Random Love was recently posted as [http://what-if.xkcd.com/9/ XKCD Blog article No. 9].

Navigation menu