Answers.Body: <p>I'd describe this as a <a href="https://en.wikipedia.org/wiki/Ranking" rel="nofollow noreferrer">Ranking</a>.</p>
  
  <p>However, it's not always possible to distil a set of outcome preferences to a transitive metric, this is one of the central axioms of game theory. <a href="http://gametheory101.com/courses/game-theory-101/the-transitivity-axiom/" rel="nofollow noreferrer">The Transitivity Axiom</a> so the problem is relatively well understood (that is, at least, if I've understood your problem)</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-09-04T17:54:34.410Z
Answers.LastActivityDate: 2017-09-04T17:54:34.410Z
Answers.UserDisplayName: Thomas Kimber
Body: <p>I have an idea for a transformative decision rule (TDR), but I want to know if there's already a name for it.     </p>
  
  <blockquote>
    <p>Any ordinal scale should be converted to a scale such that all  the outcomes are assigned consecutive values.          </p>
  </blockquote>
  
  <p>Let <em>v</em> be the function that assigns values to outcomes (defined as ordered pairs of acts and states).     </p>
  
  <p>Let <em>x</em> and <em>y</em> denote any particular such ordered pairs.<br>
  Let <em>P</em> be the preference.<br>
  Let <em>X+</em> be the set of all outcomes that are more preferred than <em>x</em> (similarly also for <em>y</em>) <em>X+</em> in <em>P</em>.
  &nbsp;     </p>
  
  <blockquote>
    <p>If <em>x</em> in <em>Y+</em>, and <em>x</em> is the closest outcome to <em>y</em> in <em>Y+</em>, then <em>v(x) = v(y) + 1</em> for all <em>x,y</em> in P.       </p>
  </blockquote>
  
  <p>I could have explained it more formally mathematically, but Latex doesn't seem to render here. If there's no name for it, I'm thinking of "The Law of Consecutive Ordinals (LCO)". As for why I support the rule, it's because it's a rule that needs to be applied to an ordinal scale before I apply an effective decision rule (EDR) that I thought of for ordinal scales. I want to know if there's a name for that principle.</p>
  
Tags: <decision-theory>
Title: Is there a name for this principle?
UserDisplayName: Tobi Alafin
ThreadText: # Is there a name for this principle?
  
  (Asked by: username_0 on 2017-09-01)
  
  I have an idea for a transformative decision rule (TDR), but I want to know if there's already a name for it.
  
  > Any ordinal scale should be converted to a scale such that all the outcomes are assigned consecutive values.
  
  Let *v* be the function that assigns values to outcomes (defined as ordered pairs of acts and states).
  
  Let *x* and *y* denote any particular such ordered pairs.  
  Let *P* be the preference.  
  Let *X+* be the set of all outcomes that are more preferred than *x* (similarly also for *y*) *X+* in *P*.
  
  > If *x* in *Y+*, and *x* is the closest outcome to *y* in *Y+*, then *v(x) = v(y) + 1* for all *x,y* in P.
  
  I could have explained it more formally mathematically, but Latex doesn't seem to render here. If there's no name for it, I'm thinking of "The Law of Consecutive Ordinals (LCO)". As for why I support the rule, it's because it's a rule that needs to be applied to an ordinal scale before I apply an effective decision rule (EDR) that I thought of for ordinal scales. I want to know if there's a name for that principle.
  
  **Tags:** decision-theory
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2017-09-04. Score: 1
  
  I'd describe this as a [Ranking](https://en.wikipedia.org/wiki/Ranking).
  
  However, it's not always possible to distil a set of outcome preferences to a transitive metric, this is one of the central axioms of game theory. [The Transitivity Axiom](http://gametheory101.com/courses/game-theory-101/the-transitivity-axiom/) so the problem is relatively well understood (that is, at least, if I've understood your problem)
  
  
  ---
  
  