[Election-Methods] [english 95%] Re: D(n)MAC

[Jobst Heitzig]

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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