[EM] A new Smith-efficient, monotone and cloneproof method (significantly different than Schulze/Ranked Pairs)

[Joshua Boehme]

On 3/11/25 5:49 AM, Grzegorz Pierczyński wrote:

> I've just invented a new voting rule. It seems to me that it has very good
> axiomatic properties (it satisfies e.g., Smith, ISDA, cloneproofness,
> monotonicity, reversal symmetry) but I haven't found anything similar in
> the voting literature. I'm curious about your thoughts.

Interesting.

However, if I'm understanding the algorithm correctly, it's not monotonic.

In the step-throughs below, an uppercase pair XY means that X qualifies 
based on that pairwise matchup; a lowercase pair xy means that at least one 
of X and Y was already qualified at that step so nothing happens.


First election:
0 ABCD
2 ADBC
3 ADCB
2 BACD
7 BADC
5 CADB
8 DCBA

Margin of row over column:
     A  B  C   D
A   0 -7  1  11
B   7  0 -5  -9
C  -1  5  0 -13
D -11  9 13   0

Algorithm step-through:
D B A (DC ad db BA cb AC)
A D (AD DB)
A (AD)


Second election (same as before except the BACD voters switch to ABCD):
2 ABCD
2 ADBC
3 ADCB
0 BACD
7 BADC
5 CADB
8 DCBA

Margin of row over column:
     A  B  C   D
A   0 -3  1  11
B   3  0 -5  -9
C  -1  5  0 -13
D -11  9 13   0

Algorithm step-through:
D C B (DC ad db CB BA)
D C (DC db CB)
D (DC)



A goes from the winner to the first candidate eliminated!