Intransitivity#Intransitivity

An intransitive relation is in mathematics, a binary relation on a set, which has the property that there are, are at least three elements from this set, apply for and, but not. A relation is thus intransitive, if it is not transitive. Originally intransitive relations by the Marquis de Condorcet in the context of elections were examined ( see also Condorcet paradox).

Formal definition

Is a set and a binary relation on, then called intransitive if:

Examples

An illustrative example of an intransitive preference relation is the game rock, paper, scissors. This wins the election of stone scissors, scissors for paper and paper to stone. If the relation is transitive, so would have made ​​" stone wins against scissors " and " scissors wins against paper " follow " Stone wins against paper ", which is against the rules. For this reason, the relation can not be transitive, it is intransitive.

Another example of an intransitive relation is intransitive dice.