Economic definition of true love - Revision history

Ed: /* The Pitt-Depp Addendum */

2024-10-04T14:59:49Z

The Pitt-Depp Addendum

Ed: /* The Pitt-Depp Addendum */

2024-10-04T14:47:24Z

The Pitt-Depp Addendum

Ed: /* The Pitt-Depp Addendum */

2020-12-19T00:00:25Z

The Pitt-Depp Addendum

Ed: Ed moved page Dating Ed to Economic definition of true love without leaving a redirect

2020-10-06T17:02:53Z

Ed moved page Dating Ed to Economic definition of true love without leaving a redirect

Ed at 17:02, 6 October 2020

2020-10-06T17:02:27Z

Ed: /* The Brad Pitt Problem */

2020-10-06T17:00:23Z

The Brad Pitt Problem

Ed at 17:00, 6 October 2020

2020-10-06T17:00:10Z

Ed at 16:55, 6 October 2020

2020-10-06T16:55:13Z

imported>Harsh: /* Definition */

2016-03-03T00:13:16Z

Definition

imported>Lauren: /* The Brad Pitt Problem */

2015-11-10T06:10:41Z

The Brad Pitt Problem

@@ Line 57: / Line 57: @@
 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].
-Additional Note: The claim that [https://en.wikipedia.org/wiki/Depp_v._Heard Johnny loves his wife hasn't aged well]. This should be changed to Johnny loves himself, or some such.
 ==The Age Rule==

← Older revision		Revision as of 14:47, 4 October 2024
Line 57:		Line 57:

	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].		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].
		+	Additional Note: The claim that [https://en.wikipedia.org/wiki/Depp_v._Heard Johnny loves his wife hasn't aged well]. This should be changed to Johnny loves himself, or some such.

	==The Age Rule==		==The Age Rule==

@@ Line 56: / Line 56: @@
 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 [http://elsa.berkeley.edu/~rabin/ Matthew Rabin].
+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==

← Older revision		Revision as of 17:02, 6 October 2020
Line 57:		Line 57:

	Note: Objections to this proof on the grounds of the inclusion of Johnny Depp should be addressed to [http://elsa.berkeley.edu/~rabin/ Matthew Rabin].		Note: Objections to this proof on the grounds of the inclusion of Johnny Depp should be addressed to [http://elsa.berkeley.edu/~rabin/ 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].

@@ Line 30: / Line 30: @@
 Also recall the definition of the strict preference relation:
-:<math>x \succ y \quad \Leftrightarrow \quad x \succsim y \;\and\; y \not{\succsim} x</math>
+:<math>x \succ y \quad \Leftrightarrow \quad x \succsim y \;\wedge\; y \not{\succsim} x</math>
 Then suppose:

← Older revision	Revision as of 17:02, 6 October 2020
(No difference)

@@ Line 9: / Line 9: @@
 Let <math>T</math> denote the set of pairs of individuals who have True Love, such that:
-:<math>\forall\{i,j\} \in T: \quad (i \succ_j h \quad \forall h \ne i) \And (j \succ_i h \quad \forall h \ne j), \quad h \in H \cup \{\emptyset\}</math>
+:<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>
 Note that:
@@ Line 26: / Line 26: @@
 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</math>
+#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 \;\And\; y \succsim z \;\mbox{then}\; x \succsim z</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:

@@ Line 1: / Line 1: @@
-==Current Availability==
+==Preamble==
-Denoting Ed's availability <math>A</math> at time <math>t</math> as <math>A_t</math>,and defining <math>T</math> as below, it appears that:
+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.
-:<math>\forall t \in \{now, \ldots, \infty\}  \;\;A_t=0</math>
+==Definition of True Love==
 Let <math>H</math> denote the set of all entities (perhaps Humans, though we might also include dogs, cats and horses, according to historical precedent).
@@ Line 17: / Line 9: @@
 Let <math>T</math> denote the set of pairs of individuals who have True Love, such that:
-:<math>\forall\{i,j\} \in T: \quad (i \succ_j h \quad \forall h \ne i) \and (j \succ_i h \quad \forall h \ne j), \quad h \in H \cup \{\emptyset\}</math>
+:<math>\forall\{i,j\} \in T: \quad (i \succ_j h \quad \forall h \ne i) \And (j \succ_i h \quad \forall h \ne j), \quad h \in H \cup \{\emptyset\}</math>
 Note that:
@@ Line 23: / Line 15: @@
 *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>.
-===The Existence of True Love===
+==The Existence of True Love==
 Can we prove that <math> T \ne \{\emptyset\}</math> ?
-====The Brad Pitt Problem====
+===The Brad Pitt Problem===
 Rational preferences aren't sufficient to guarantee that <math> T \ne \{\emptyset\}</math>.
@@ Line 34: / Line 26: @@
 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</math>
+#Completeness: <math>\forall x,y \in X: \quad x \succsim y \;\Or\; y \succsim x</math>
-#Transitivity: <math>\forall x,y,z \in X: \quad \mbox{if}\; \; x \succsim y \;\and\; y \succsim z \;\mbox{then}\; x \succsim z</math>
+#Transitivity: <math>\forall x,y,z \in X: \quad \mbox{if}\; \; x \succsim y \;\And\; y \succsim z \;\mbox{then}\; x \succsim z</math>
 Also recall the definition of the strict preference relation:
@@ Line 47: / Line 39: @@
 Then <math>T = \{\emptyset\}</math>  Q.E.D.
-====The Pitt-Depp Addendum====
+===The Pitt-Depp Addendum===
 Adding the constraint that 'everybody loves somebody', or equivalently that: