## Explanation of Tideman "Ranked Pairs" Condorcet voting system

Each "vote" is a rank-ordering of all the N candidates, for example "Nader>Gore>Bush>Buchanan" would be a possible vote (with N=4). We then find the candidate pair AB with the largest pairwise margin of victory A>B (this is the pairwise victory we are "most sure is valid") and "lock it in" by drawing an arrow from A to B. We proceed through all victories in decreasing-magnitude order, "locking them in" if so doing does not create a directed cycle in the directed graph we are drawing. The root of the resulting directed-graph (the only candidate with no arrows pointing to him) then is the winner.

Tideman Ranked Pairs (TRP) has some enjoyable properties:

1. TRP is monotonic; raising your vote's ranking of some candidate cannot hurt his election chances (and similarly, lowering it cannot help his chances).
2. Smith set and Condorcet properties: TRP always elects "Condorcet winner" (who beats all opponents pairwise) whenever one exists; and it always elects a member of the "Smith set" (each of whose members beats every nonmember pairwise).
3. Winner ≠ Loser: The TRP winner (candidate with no arrows pointing to him at the end of the procedure) is never the same candidate as the TRP loser (candidate with no arrows pointing away from him).
4. TRP is fairly simple to describe and program, although not nearly as simple as range voting.

Unfortunately, TRP also has some not-so-enjoyable properties:

1. Add-top failure: An honest voter's vote can cause his favorite candidate to be defeated, whereas, if that voter had stayed home, his favorite would have been elected.
2. Add-bottom failure: An honest voter's vote can cause his most-hated candidate to be elected, whereas, if that voter had stayed home, he would have been defeated.
3. Favorite betrayal: It can be best strategy for a voter to dishonestly rank his true favorite below top ("betraying" him in order to cause the election of a "lesser evil").