[EM] What are some simple methods that accomplish the following conditions?

Forest Simmons fsimmons at pcc.edu
Thu May 30 15:33:14 PDT 2019

In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.  One
consequence of these constraints is that in all three profiles below the
cycle A>B>C>A will obtain.

I am interested in simple methods that always ...

(1) elect candidate A given the following profile:

P: A
Q: B>>C
R: C,
(2) elect candidate C given
P: A
Q: B>C>>
R: C,
(3) elect candidate B given
P: A
Q: B>>C  (or B>C)
R: C>>B. (or C>B)

I have two such methods in mind, and I'll tell you one of them below, but I
don't want to prejudice your creative efforts with too many ideas.

Here's the rationale for the requirements:

Condition (1) is needed so that when the sincere preferences are
P: A
Q: B>C
R: C>B,
the B faction (by merely disapproving C without truncation) can defend
itself against a "chicken" attack (truncation of B) from the C faction.

Condition (3) is needed so that when the C faction realizes that the game
of Chicken is not going to work for them, the sincere CW is elected.

Condition (2) is needed so that when  sincere preferences are
P: A>C
Q: B>C
R: C>A,
then the C faction (by proactively truncating A) can defend the CW against
the A faction's potential truncation attack.

Like I said, I have a couple of fairly simple methods in mind. The most
obvious one is Smith\\Approval where the voters have control over their own
approval cutoffs (as opposed to implicit approval) with default approval as
top rank only.The other method I have in mind is not quite as simple, but
it has the added advantage of satisfying the FBC, while almost always
electing from Smith.
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