Editing Arrow's impossibility theorem (section)

==== Preferences ====
{{Further|Preference (economics)}}In the context of Arrow's theorem, citizens are assumed to have [[ordinal preferences]], i.e. [[Total order|orderings of candidates]]. If {{math|''A''}} and {{math|''B''}} are different candidates or alternatives, then <math>A \succ B</math> means {{math|''A''}} is preferred to {{math|''B''}}. Individual preferences (or ballots) are required to satisfy intuitive properties of orderings, e.g. they must be [[Transitive relation|transitive]]—if <math>A \succeq B</math> and <math>B \succeq C</math>, then <math>A \succeq C</math>. The social choice function is then a [[Function (mathematics)|mathematical function]] that maps the individual orderings to a new ordering that represents the preferences of all of society.