Definition:Total Preordering
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Definition
Let $S$ be a set.
Let $\precsim$ be a preordering on $S$.
Then $\precsim$ is a total preordering on $S$ if and only if $\precsim$ is connected.
That is, if and only if there is no pair of elements of $S$ which is non-comparable:
- $\forall x, y \in S: x \precsim y \lor y \precsim x$
Also known as
Some sources call this a linear preordering.
Some sources within the field of game theory call it a preference relation, in accordance with its specific application.
Sources
- 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $1.7$: Terminology and Notation