[EM] [Fwd: Re: approval voting and majority criterion]

[Ken Johnson]

James Green-Armytage wrote:

>I wrote:
>  
>
>>>majority criterion: If a majority of the voters prefers all of the members of a given set of candidates over all candidates outside that set, and they vote sincerely, then the winning candidate should come from that set.
>>>      
>>>
>
>Ken Johnson wrote:
>  
>
>>James - Can you elucidate why this should be a required criterion?
>>    
>>
>
>	Sure. Look at it this way. Let's say that 55% of an electorate are to the
>left of the center, and 45% are to the right of center. If a method goes
>ahead and elects a right of center candidate anyway, then we know
>something has gone wrong. Plurality is problematic for this reason, and so
>is approval. 
>
What has gone wrong? Consider, for example, a specific CR profile:
55%: A=99, B=100
45%: A=99, B=0
If people vote sincerely, the election goes to candidate A. Of course, 
the voters who have a slight preference for B may insincerely give A a 
zero rating, so that B wins. This isn't necessarily a good outcome, it 
is just an unavoidable consequence of insincerity. But with more 
candidates, this result may not be unavoidable. For example, suppose the 
CR profile with a third candidate C is as follows,
55%: A=99, B=100, C=0
45%: A=99, B=0, C=100
Now, unless the B supporters know for sure that they are a majority, 
they will vote sincerely and the election will go to candidate A, who 
has the strong, unanimous approval of all voters. This is arguably not a 
bad outcome.

>	The goal of single winner voting is majority rule. While majority rule is
>fraught with dangers and paradoxes, it is axiomatically preferable to
>minority rule. Given two groups of different size with irreconcilable
>opinions on a given issue, any value-neutral decision-making rule must
>logically chose to execute the wishes of the larger group.
>
>James
>
>  
>
It may be that majority rule is preferable, but as illustrated above it 
is clearly not self-evident that majority rule is always preferable. 
Therefore majority rule should not be posited axiomatically; it needs to 
be justified on the basis of a more fundamental statement of "the goal 
of single-winner voting".

Ken Johnson

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