Dear Raphfrk,
you wrote:
I wonder if it would be worth repeating the draw if no compromise appears.
The chances of each side winning outright would be
P-win = P^n/(P^n+Q^n)
Q-win = Q^n/(P^n+Q^n)
That is an obvious idea, you're right. But with strategic voters, this
will never lead to full cooperation since then it is always "safe" for a
small number of voters to switch from cooperation (approving the
compromise) to defection (bullet voting): They will get a slight chance
that all n ballots are amoung theirs, but won't risk that the other
faction's favourite wins.
The essential point why D2MAC and D(n)MAC produce an equilibrium at full
cooperation is because when a small group of voters defect, the other
faction's favourite gets a positive winning probability!
Yours, Jobst
If both are 50/50, then that is the same as a random lottery.
This system favours the larger side. If n=4 and P was 0.6 and Q was
0.4, then
A would win in 83% of cases. This would mean that P voters would need
to rate
C > 8.3 out of 10 before they will compromise.
The advantage is that it allows recovery if one of the ballots drawn is
from a
small hold out group, so compromise fails.
Another option is to have a limited/finite number of redraws. Maybe this
has basically the same effect as modifing n as it sets the 'chances of
no compromise needed probability'. Also, in practice, it might be needed
as you could be drawing forever, but that would require no candidate to
be approved by n voters.
If there was 1 re-draw, then that doubles the odds of an A or B outright
win.
This means the compromise must be more popular to ensure a win.
There are ofc some issues if there is more than 3 candidates and
deciding who to
approve.
A feature of this system is that it reverts to random ballot for the 2
candidate case.
This may result in candidates who would be discouraged from running due
to spoiler
effects in plurality being encouraged to run due to 'civic duty'.
Raphfrk
--------------------
Interesting site
"what if anyone could modify the laws"
www.wikocracy.com
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