[EM] IRV's "majority winner". What if we let the people choose?

[Brian Olson]

The controversial example:

49  A>C>B
48  B>C>A
  3  C>B>A

Two ways of putting voter's internal preferences behind that (Both sets 
of ratings exhibit the above rankings):

*{number of voters} {A's rating}, {B's rating}, {C's rating}:

*49 .03,.01,.02
*48 .01,.03,.02
*3 .01,.02,.03

IRV = B; all others = C

The above example presents a population with very weak differences in 
degree of preference between the choices. I believe that a situation 
like this is implicitly part of the social assumptions that Condorcet 
backers make. Voters would be happy to get their second choice because 
there isn't that much of a difference between that and their first 
choice. The compromise choice is obviously the right way to go.


*49 1,.01,.1
*48 .01,1,.1
*3 .01,.1,1

IRNR, IRV = B; Condorcet, Borda = C; Raw Cardinal Ratings = A

This example electorate has very strong preferences for a primary 
choice over a secondary, and for the secondary over the tertiary. I 
believe this is the model assumed by IRV backers.

Under this set of ratings, IRNR emulates IRV, while under the first 
ratings it had the same solution as Condorcet. The IRV process 
disqualifies C in the first round, those votes then go to B which wins 
in the second round.

Raw CR given ratings like this chose the plurality winner. Whodathunkit?


So, under the first set of ratings, IRV is clearly an aberration. The 
compromise choice found by every other method is the right thing to do. 
Under the second set of ratings, it's not so clear. Depending on the 
system, all three results are possible. Which one is the most just? The 
straight utilitarian answer goes with Raw CR and Plurality! Condorcet 
and Borda disregard the strength of people's desires. IRV is vulnerable 
to nasty singularities, is this one of them? IRNR is my pet, why should 
any of you like it?

Breakfast for thought, good day. :-)

(results calculated with http://bolson.org/voting/vote_form.html )

Brian Olson
http://bolson.org/