## Explanation of the (not recommended) "BTR-IRV" 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). After collecting the votes, the N-candidate election proceeds in a sequence of N-1 "rounds." In each round one candidate is eliminated and he is erased from all votes. For example, if "Bush" were eliminated, then the above vote would become "Nader>Gore>Buchanan."

The one to eliminate is found as follows. Find the two candidates A and B whom the fewest voters top-rank. Now, ignoring all candidates except A and B in all the votes, i.e. based solely on the A>B and B>A relations in those votes, perform a 2-candidate majority election among A and B only. The loser of that "election" is the one we eliminate.

After N-1 rounds only one candidate remains standing. He is the one that BTR-IRV elects.

Warning. Like a lot of voting system proposals, this sounds on its face like a pretty good method. (Heck, every voting system ever seriously proposed sounds at first like it is a pretty good method.) Two properties that sound good are that BTR-IRV always elects a Condorcet winner if one exists (and indeed always elects a "Smith set" member; IRV cannot claim either); and BTR-IRV, like IRV, is immune to the DH3 pathology. Nevertheless, a lot of good-sounding methods have bad properties. And indeed, BTR-IRV has some bad properties:

1. It quite likely will lead to self-reinforcing 2-party domination just like the plurality and IRV systems it was intended to "improve." If so, third-parties would be suicidal idiots to want it.
2. Like IRV, it suffers from "add-top failure." (On the other hand: like IRV, if you add new votes that rank the current winner W top and all others co-equal bottom, then W still wins; and if you alter votes that used to rank W co-equal bottom, so that they now rank W one rung above bottom but below all others, then W still wins.)
3. It abandons a known alleged-advantage of IRV called "later no harm." That is, in IRV, by casting a vote "later" in your top-to-bottom candidate ordering, you cannot hurt the election chances of somebody you ranked "earlier." This advantage is supposed to be important because it encourages voters to rank, i.e. give their opinion of, every candidate, as opposed to just "truncating" their ballot and say voting for only one ("plurality style"). This was a clear "selling point" for IRV over plurality voting. Supposedly the main reason the "Bucklin system" (which was used in the early 1900s to elect Governors in several US states) was jettisoned, was that it failed later-no-harm in a major way so that most voters just voted plurality-style, defeating the whole purpose of the Bucklin system. [Actually, I am skeptical of these alleged and supposed claims; and in IRV it can be strategic to "truncate" your ballot in spite of IRV's later-no-harm property.] BTR-IRV abandons that selling point.
4. While IRV is immune to candidate-cloning, BTR-IRV is not:
Chris Benham's BTR-IRV cloning-failure example (before cloning D). Winner is A after B,C,D eliminated in that order.
#voters their vote
2 B>A>D>C
3 D>C>B>A
4 A>C>B>D
Benham's BTR-IRV cloning-failure example (after cloning D). Winner is B after C,D1,D2,A eliminated in that order.
#voters their vote
2 B>A>D1>D2>C
2 D1>D2>C>B>A
1 D2>D1>C>B>A
4 A>C>B>D2>D1