[EM] Fixing IRV

[Roy]

Richard Moore <rmoore4 at h...> wrote:
> All voting systems that eliminate alternatives
> prior to selecting a winner violate monotonicity [86].

I wouldn't be terribly surprised if my method violated monotonicity, 
but only when there is no Condorcet winner. Each round of elimination 
is discarding candidates who could not possibly be Condorcet winners 
(because more people are ranked above them than below).

Are there available some data I could use to see how my system 
handles various Smith set situations (preferably along with results 
from some system that we like).

With this data:

4 ABC
1 ACB
3 BCA
3 CAB
1 CBA

C has exactly half above the median point and half below. If we 
require a majority to eliminate, C continues (and wins); if we 
require a majority to continue, C is eliminated and A wins. I presume 
a similar situation arises in all Smith set results. I don't see an 
opportunity for non-monotonicity in this example; I would like to see 
an example that demonstrates it. Perhaps a situation with inner and 
outer Smith sets?

One correction to my original spec: tie ranking among N candidates 
should contribute 1/N vote for each of them to each of the ranks they 
share (e.g., if 3 candidates tie for 2nd, each gets 1/3 of a vote for 
2nd, 3rd, and 4th). Thus there are no half-rank values, but there are 
fractional votes.

Is anybody (besides me) interested in pursuing this method further? 
It's not that it's a technically better method than any other 
Condorcet method; it just offers a more pursuasive argument to IRV 
advocates, because it's better than IRV by their own standard 
(majority rule).