>[!abstract] >Transitivity is a fundamental property of relations in logic and mathematics whereby if A is related to B and B is related to C, then A must also be related to C. In preference theory, this means that if a decision-maker prefers A over B and B over C, they should also prefer A over C, ensuring consistency in choice. Transitivity underpins rational decision-making, ranking systems, and formal proofs, since it allows local pairwise comparisons to extend into coherent global orderings. Its violation ([[intransitivity]]) reveals important limitations in models of rationality and exposes complexities in human behavior, voting systems, and competitive dynamics. >[!related] >- **North** (upstream): — >- **West** (similar): — >- **East** (different): [[Intransitivity]] >- **South** (downstream): —