[EM] Yet Another Lottery Method

[Simmons, Forest]

Ralph suggested that in the example
 
45 B>A>>C
40 C>>A>B
15 A>C>B
 
the smallest faction might prefer a 100% C lottery to a 55%A+45%B, and in that case approving only C would be better than approving only A.
 
But if  100%C is better than 55%A+45%B, for the A>B>C faction, then  60%A+40%C would be better still for that faction.  So their best bet is to vote sincerely  A>C>>B .
 
Forest
 

Ralph's example & commentary:

Assuming the votes are:

45:  A, B approved  ( B>A>>C )
40:  C approved ( C>>A>B )

The remaining 15 voters are of the opinion
A>C>B

if they approve A only:
C is eliminated ( 45+15 = 60 votes approve A and not C )

result is:
A: 40+15 = 55%
B: 45 = 45%
C: elim = 0%

OTOH, if they approve C (tactical voting)
A,B are eliminated ( 55% approve C and none other)

results is
A: elim= 0%
B: elim= 0%
C: 100% ( only remaining )

It is not clear to me that a 55% chance of your favorite and 45% chance
of your lowest choice is superior to a 100% chance of your middle
choice.

This means that depending on the 15 voters relative preference
strengths,
it might be in their interests to tactical vote and just approve C,
even though
they prefer A to C.

If the ranked choice must be consistant with the approval choice, they
could
just vote C approved and C first choice as a pure tactical vote.


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