[EM] A new election method...

[Buddha Buck]

As a demonstration as to how easy it is to come up with a new election 
method, here's a technique that popped into my head in reaction to Roy's 
questions concerning elimination ballots and monotonicity.  I'm not 
claiming that this method is monotonic -- I'm not quite good enough to 
prove it -- but this method does have some features which might appeal to 
IRV supporters:

1.  It is an elimination method.
2.  It uses a ranked ballot.
2.  It utilizes first-place information, although not in the same way as IRV
3.  At any stage, it is acceptable to terminate the procedure if any one 
candidate has a majority of first-place votes.

It is also a Condorcet method, in that if a Condorcet winner exists, that 
winner will be elected.

Here it goes...

Based on a ranked ballot, list the candidates in order of descending 
first-place votes (if there is a tie, compare the number of 2nd-place 
votes, etc, to establish an order.  If two candidates (out of  N) have 
exactly the same number of 1st place, 2nd place, ... Nth place votes, list 
them in alphabetical order).

Use this listing as a seed for a single-elimination tournament, with a 
candidate advancing in the tournament if he, compared head-to-head with his 
opponent, is defeated.

Eliminate the "winner" of the single-elimination tournament, and 
relist/eliminate, etc until a single candidate remains.

Example:  Four candidates

30 ABCD
30 BACD
20 BCAD
25 CBAD
15 CBDA
30 CDBA
50 DCBA

Listed in 1st-place order:
70 C
50 B     B
50 D    D    D
30 A

More people prefer C to B (120:80), more prefer A to D (105:95), and more 
prefer B to D (120:80), so D is eliminated.

Round 2...

030 ABC
030 BAC
020 BCA
120 CBA

Listed in 1st-place order,

120 C
050 B     B
030 A    A     A

More prefer C to B (120:80), More prefer B to A (170:30), so A is eliminated

Round 3:

080 BC
120 CB

Listed in 1st place order:

120 C
080 B     B

More prefer C to B, so B is eliminated.

Round 4:

200 C

C wins.

Is that method clear?

Since no candidate is eliminated unless another candidate defeats him 
pairwise, the Condorcet Winner (if one exists) cannot be eliminated and 
therefor must win.

How would someone go about examining this method for monotonicity?

Later,
   Buddha