Changes

:<math>\forall\{i,j\} \in T: \quad (i \succ_j h \quad \forall h \ne i) \And wedge (j \succ_i h \quad \forall h \ne j), \quad h \in H \cup \{\emptyset\}</math>

#Completeness: <math>\forall x,y \in X: \quad x \succsim y \;\Orlor\; y \succsim x</math>#Transitivity: <math>\forall x,y,z \in X: \quad \mbox{if}\; \; x \succsim y \;\Andwedge\; y \succsim z \;\mbox{then}\; x \succsim z</math>

:<math>x \succ y \quad \Leftrightarrow \quad x \succsim y \;\andwedge\; y \not{\succsim} x</math>

Note: Objections to this proof on the grounds of the inclusion of Johnny Depp should be addressed to [httphttps://elsascholar.berkeleyharvard.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 them 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].