[EM] RE : Majority Criterion, hidden contradictions

[Kevin Venzke]

Hi,

--- Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> I've been realizing just how defective the Majority Criterion is. 
> People tend to assume that the Majority Criterion is an important 
> characteristic of any proper democratic election system. 

I suspect that many people would insist on a majority favorite being
elected at least if the method collects enough information to 
determine who this candidate is.

> Yet the 
> Criterion itself suffers from a number of serious problems.
> 
> (1) It is clear that any method which satisfies the Majority 
> Criterion cannot maximize the expected value of the election. Range 
> is the method which directly does the latter, and this is directly 
> connected with its non-satisfaction of the Majority Criterion.

However, it is possible that there is no real method that can "maximize
the expected value of the election," unless you just mean to maximize
the value among all possible methods.

I don't think it is fair to say that Range "directly" "maximizes the
expected value of the elections." I would grant that Range is equipped
to do this better than other methods due to the ballot format, though.

> This is because the Majority Criterion neglects preference strength, 
> and thus a minor, practically inconsequential preference is given the 
> same weight as a clear, stark preference. So if Preference Strength 
> is considered in determining the winner, in the presence of expressed 
> first-preference votes of a majority, it must be true that under some 
> circumstances preference would alter the winner and thus the Majority 
> Criterion would not be satisfied.

Yes.

> (2) There is a serious semantic problem in how the Criterion is 
> expressed and applied. It is commonly stated that the Majority 
> Criterion is satisfied by Plurality and not by Approval. In order to 
> state this about Approval, one must presume that there are 
> unexpressed preferences on the part of voters.

It is most natural to make this assumption. I use Woodall's interpretation,
that Approval is equivalent to a rank-ballot method where all candidates
given any ranking receive one point from that ballot.

> Approval, just like Plurality -- Approval *is* Plurality plus an 
> additional freedom of the voter -- allows voters to express a 
> preference between two candidates. Just vote for only one of them. If 
> a majority express this preference for one candidate, then, under 
> Approval as well as under Plurality, then that candidate cannot lose 
> to the less-preferred candidate. (And if this preference is expressed 
> over all other candidates, the candidate cannot lose the election.)
> 
> Looks to me like Approval *does* satisfy the Majority Criterion. 

I can see nothing at all wrong with that interpretation, but personally
I don't like to imagine that the Approval voter is only submitting
first preferences.

> Range, generally, does not.
> 
> However, Approval allows the voter to abstain from a pairwise 
> election. The voter does so by giving both candidates the same vote. 
> By voting for both candidates, the voter has expressed a preference 
> for both of them over all other candidates not so marked, and has 
> abstained from the pairwise election between them. Only by assuming 
> that the voter has a preference between the two even though this 
> preference has not been expressed, and then by using this unexpressed 
> preference to determine if the method satisfies the Majority 
> Criterion, do we come up with the answer that Approval does not satisfy
> it.

Right.

> This is important because many writers assume that the Majority 
> Criterion is some kind of gold standard for elections, and when it is 
> asserted that Approval fails to satisfy it, this can be and is 
> considered a fatal argument, or at least a serious defect of Approval.

I don't feel that Majority needs to be satisfied under Approval, in
order to be publicly acceptable.

Kevin Venzke



	

	
		
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