[EM] relationship between DMC/RAV and Approval

[Russ Paielli]

Folks,

A week or two I posted a message to EM asking about the effect of using 
the DMC/RAV rules for Approval votes. Kevin Venzke said it would be 
equivalent to Approval itself. This should have been obvious to me, as I 
will explain.

Let's look at it from the other direction. Suppose I have a DMC 
election, but I constrain all voters to rank all their approved 
candidates equally, and I also constrain them to rank all their 
unapproved candidates equally. In other words, suppose I force them to 
vote as if it were an Approval election.

The only way for one candidate to gain a pairwise vote on another 
candidate is to also gain an approval vote on that same candidate. 
Hence, the difference in approval counts for any two candidates will be 
equal to their pairwise vote difference. The result is that the approval 
counts tell the whole story: the approval winner is *the* winner.

Perhaps that observation is obvious to some, but I think it is 
significant nevertheless. Approval Voting is a special case of DMC/RAV. 
In other words, DMC is a generalization of Approval.

To my way of thinking, this suggests that, in some significant sense, 
DMC is at least as good as Approval. Any voter who prefers Approval can 
always vote in DMC as if it were Approval -- and essentially have his 
vote counted as if it were Approval. The fact that other voters may 
excercize the added freedom to rank candidates does not diminish the 
right of any voter to refrain from excercizing that freedom.

This line of reasoning is analogous to saying that Approval is at least 
as good as Plurality because any voter can still approve only one 
candidate as in Plurality and have his vote counted the same way as it 
would be counted in Plurality. But if that voter claimed that everyone 
should be so constrained, most of you here on EM would obviously disagree.

So Approval generalizes Plurality, and DMC/RAV generalizes Approval. But 
of course, generalizations are not necessarily unique. I wonder if other 
  Condorcet/Approval hybrids (e.g., AWP) also reduce to Approval if the 
votes are constrained to Approval votes.

--Russ