Editing Expected utility hypothesis (section)

=== Ramsey-theoretic approach to subjective probability ===
In 1926, [[Frank Ramsey (mathematician)|Frank Ramsey]] introduced Ramsey's Representation Theorem. This representation theorem for expected utility assumes that [[preference]]s are defined over a set of bets where each option has a different yield. Ramsey believed that we should always make decisions to receive the best-expected outcome according to our personal preferences. This implies that if we can understand an individual's priorities and preferences, we can anticipate their choices.<ref>{{cite journal| vauthors = Bradley R |date=2004|title=Ramsey's Representation Theorem|url=http://personal.lse.ac.uk/bradleyr/pdf/Ramsey.dialectica.pdf|journal=Dialectica|volume=58|issue=4|pages = 483–498 |doi=10.1111/j.1746-8361.2004.tb00320.x}}</ref> In this model, he defined numerical utilities for each option to exploit the richness of the space of prices. The outcome of each preference is exclusive of each other. For example, if you study, you can not see your friends. However, you will get a good grade in your course. In this scenario, we analyze personal preferences and beliefs and will be able to predict which option a person might choose (e.g., if someone prioritizes their social life over academic results, they will go out with their friends). Assuming that the decisions of a person are [[Rationalism|rational]], according to this theorem, we should be able to know the beliefs and utilities of a person just by looking at the choices they make (which is wrong). Ramsey defines a proposition as "[[neutrality (philosophy)|ethically neutral]]" when two possible outcomes have an equal value. In other words, if the probability can be defined as a preference, each proposition should have {{sfrac|1|2}} to be indifferent between both options.<ref>{{cite web | vauthors = Elliott E | title = Ramsey and the Ethically Neutral Proposition | url = http://www.edwardjrelliott.com/uploads/7/4/4/7/74475147/[natrep]_ramsey_and_the_ethically_neutral_proposition.pdf | work = Australian National University }}</ref>
Ramsey shows that

: <math> P(E) = (1-U(m))(U(b)-U(w)) </math><ref>{{cite journal| vauthors = Briggs RA |date=2014-08-08|title=Normative Theories of Rational Choice: Expected Utility|url=https://plato.stanford.edu/archives/fall2019/entries/rationality-normative-utility/}}</ref>