Binary Relations
Provement: R asymmetric and negative transitive => R transitive
Suppose R is not transitive
There exit x, y and z such that xRy, yRz and not (xRz)
If asymmetric:
xRy => not yRx
yRz => not zRy
If negative transitive:
Not yRx and not zRy => not zRx
Provement: R complete and transitive => R negative transitive
Voting Rules
Plurality 多数制选举
变种: Plurality with run-off
- first round finished if more than 50% voted to same candidate else keep two candidates
- second round compare between two candidates
Condorcet voting rule 双序制选举（孔多塞制）
- Do pairwise comparision
- Generate Condorcet winner
Borda voting rule
Arrow’s Theorem
No method respect 5 principle
MAUT Approach
MAUT(Multi Attribute Utility Theory)