[EM] Trying to have CD, protect strong top-set, and protect middle candidates too

[Forest Simmons]

Does optional approval cutoff wreck burial protection?

Suppose we have a sincere scenario

40 C>B
35 A>B
25 B>C

and the C faction decides to bury the CWs B.  The B faction anticipates
this and responds by truncating C.  It is in the interest of the A faction
to leave the default implicit approval cutoff in place.  The C faction
doesn't want to give A too much support so they use the explicit cutoff
option:

40 C>>A
35 A>B
25 B

The approval winner is B the CWs.

If they left the implicit cutoff in place it would be worse for them; their
last choice would be elected.

So I think MDDA with optional explicit cutoff is fine with respect to
truncation and burial.

How about the CD?

In this case the sincere profile is

40 C
35 A>B
25 B>A

The B>A faction threatens to defect from the AB coalition.
The A faction responds by using the explicit cutoff:

40 C
35 A>>B
25 B

The approval winner is C, so the threatened defection back-fires.

It seems to me like that is plenty of chicken defection insurance.

The obvious equilibrium position (for the chicken scenario) is

40 C
35 A>>B
25 B>>A

Under MDDA(pt/2) the only uneliminated candidate is A.

But if the B faction defects, all candidates are eliminated, and the
approval winner C is elected.

This is why I like MDDA(pt/2).

An interesting fact is that MDDA(pt/2) is just another formulation of my
version of ICA.  They are precisely equivalent.  Here's why:

In my version of ICA, X beats Y iff

[X>Y] > [Y>X] + [X=Y=T] + [X=Y=between] , in other words,

[X>Y] > [Y:>=X] - [X=Y=Bottom],

which in turn equals

100% - [X>Y] - [X=Y=Bottom], since  100%= [X>Y] + [Y>=X].

So X beats Y iff

[X>Y] > 100% - [X>Y] - [X=Y=Bottom].

If you add [X.Y] to both sides and divide by 2, you get

[X>Y] +[X=Y=Bottom]/2 > 50%,

precisely the "majority-with- half-power-truncation" rule.

So (my version of) ICA is precisely equivalent to MDDA(pt/2).

I believe it to be completely adequate for defending against burial,
truncation, and Chicken Defection.


Now suppose that p<q<r, and p+q+r=100%, and we have three factions of
respective sizes p, q, and r:, with r + q > 50%.

p: C
q: A>>B
r: B>>A

Then under the pt/2 rule both C and B are eliminated, but not A, so A is
elected.

Suppose that the B factions defects.

Then A is also eliminated, and the approval winner C is elected.

Etc.

So which of the two equivalent formulations is easier to sell?  ICA or
MDDA(pt/2) ?

Forest
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