[Election-Methods] Elect the Compromise

[Juho]

On Aug 27, 2007, at 23:15 , Jobst Heitzig wrote:

> Think about Borda using scores 0, 1, and 2, without equal rankings  
> allowed: The A voters can give A at most a score of 55*2=110 and  
> have to give either B or C at least a score of 28. Hence whatever  
> the A voters do, they cannot be sure to have A elected since the B  
> voters could advance B or C to at least a score of 118 by giving it  
> a score of 45*2=90. From this one can see easily that there is no  
> group strategy equilibrium electing A or B. All group strategy  
> equilibria elect C, for example the one in which everbody puts C  
> first and her favourite second. The drawback is only that these  
> equilibria are not globally attractive, since there are starting  
> points (e.g. sincere rankings) from which the process of repeatedly  
> replacing the strategies by optimal respond strategies to the  
> current strategies will not eventually lead to an equilibrium but  
> may get stuck in a cycle.

How about the weighted Borda that I described earlier? Square root  
weights would give 0, 1 and 1.4 points instead of 0, 1 and 2.

In line with what Forest wrote I'm not advocating these methods,  
except as challenges on this list. The most obvious problem is  
clones, e.g. one candidate from the Democrats and two from the  
Republicans. From this point of view one could require that votes 55  
A>>C>B 45 B>C>>A and 55 A>>C>B 45 C>B>>A will not elect C.

Juho



		
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