Editing Cardinal utility (section)

=== Order of preference ===
{{Details|Preference (economics)}}

In 1955 [[Patrick Suppes]] and Muriel Winet solved the issue of the representability of preferences by a cardinal utility function and derived the set of axioms and primitive characteristics required for this utility index to work.<ref>{{cite journal |last1=Suppes |first1=Patrick |first2=Muriel |last2=Winet |date=April 1955 |url=http://suppes-corpus.stanford.edu/article.html?id=11 |title=An Axiomatization of Utility Based on the Notion of Utility Differences |journal=Management Science |volume=1 |issue=3/4 |pages=259–270 |jstor=2627164 |doi=10.1287/mnsc.1.3-4.259 |access-date=2010-06-10 |archive-url=https://web.archive.org/web/20100721014253/http://suppes-corpus.stanford.edu/article.html?id=11 |archive-date=2010-07-21 |url-status=dead |url-access=subscription }}</ref>

Suppose an agent is asked to rank his preferences of {{math|''A''}} relative to {{math|''B''}} and his preferences of {{math|''B''}} relative to {{math|''C''}}. If he finds that he can state, for example, that his degree of preference of {{math|''A''}} to {{math|''B''}} exceeds his degree of preference of {{math|''B''}} to {{math|''C''}}, we could summarize this information by any triplet of numbers satisfying the two inequalities: {{math|''U<sub>A</sub>'' > ''U<sub>B</sub>'' > ''U<sub>C</sub>''}} and {{math|''U<sub>A</sub>'' − ''U<sub>B</sub>'' > ''U<sub>B</sub>'' − ''U<sub>C</sub>''}}.

If {{mvar|A}} and {{mvar|B}} were sums of money, the agent could vary the sum of money represented by {{mvar|B}} until he could tell us that he found his degree of preference of {{mvar|A}} over the revised amount {{math|''B''′}} equal to his degree of preference of {{math|''B''′}} over {{mvar|C}}. If he finds such a {{math|''B''′}}, then the results of this last operation would be expressed by any triplet of numbers satisfying the relationships {{math|''U<sub>A</sub>'' > ''U''<sub>''B''′</sub> > ''U<sub>C</sub>'' }} and {{math|''U<sub>A</sub>'' − ''U''<sub>''B''′</sub> {{=}} ''U''<sub>''B''′</sub> − ''U<sub>C</sub>''}}. Any two triplets obeying these relationships must be related by a linear transformation; they represent utility indices differing only by scale and origin. In this case, "cardinality" means nothing more being able to give consistent answers to these particular questions. This experiment does not require measurability of utility. [[Itzhak Gilboa]] gives a sound explanation of why measurability can never be attained solely by [[introspection]]:
{{quote
|text=It might have happened to you that you were carrying a pile of papers, or clothes, and didn't notice that you dropped a few. The decrease in the total weight you were carrying was probably not large enough for you to notice. Two objects may be too close in terms of weight for us to notice the difference between them. This problem is common to perception in all our senses. If I ask whether two rods are of the same length or not, there are differences that will be too small for you to notice. The same would apply to your perception of sound (volume, pitch), light, temperature, and so forth...
|author=Itzhak Gilboa
|source=Theory of decision under uncertainty<ref>{{cite book |last=Gilboa |first=Itzhak |date=2009 |url=http://www.econ.hit-u.ac.jp/~kmkj/uncertainty/Gilboa_Lecture_Notes.pdf |title=Theory of Decision under Uncertainty |publisher=Cambridge University Press |isbn=978-1-1077-8251-8 |access-date=2010-03-30 |archive-url=https://web.archive.org/web/20180219002606/http://www.econ.hit-u.ac.jp/~kmkj/uncertainty/Gilboa_Lecture_Notes.pdf |archive-date=2018-02-19 |url-status=dead }}</ref>}}

According to this view, those situations where a person just cannot tell the difference between {{mvar|A}} and {{mvar|B}} will lead to indifference not because of a consistency of preferences, but because of a misperception of the senses. Moreover, human senses adapt to a given level of stimulation and then register changes from that baseline.<ref>{{cite book |last=Poundstone |first=William |date=2010 |title=Priceless: The Myth of Fair Value (and How to Take Advantage of It) |location=New York |publisher=Hill and Wang |page=39 |isbn=978-1-4299-4393-2 |url=https://books.google.com/books?id=xWjTZhw1MiUC&pg=PA39}}</ref>