[EM] Arrow's theorem

[Dave Ketchum]

On May 3, 2011, at 7:55 PM, S Sosnick wrote:
>
> On May 2, commenting on the criterion of Independence from  
> Irrelevant Alternatives, Forest
> Simmons wrote, "IIAC is a totally unreasonable requirement."  On May  
> 3, Kevin Venzke added,
> "IIA isn't compatible with Condorcet.  It's not compatible with much  
> of anything.  I take that to be
> the point of Arrow:  If you want IIA you have to do some drastic  
> things."
>
> While I agree with those comments, I think that one can--generously  
> but usefully--equate
> Arrow's theorem with a broader point, namely, no election system in  
> which voters rank
> candidates can have all properties that seem democratic and  
> appropriate.  For example, no
> election system in which voters rank candidates can guarantee both  
> Condorcet compliance and
> Later-no-harm.
>
> The reason is that "democratic" embraces majority rule, and--when 3  
> or more voters rank 3 or
> more candidates--each candidate may be ranked below at least one of  
> the other candidates by a
> majority of the voters.

"Majority" clearly makes sense in Plurality elections.  If we get 49A,  
48B, and 3C, C is a clear loser, voters could not indicate their  
preference among A and B while voting for C, and we clearly need a  
Runoff between A and B.  Of course, if we get 33A, 33B, and 33C, it is  
time to wish for something different.

Given 49A, 48B, and 35C in Approval, there is less value in a Runoff.   
Most C voters could, and presumably did, indicate their choice between  
A and B.  Some unhappy voters could have noticed that they could not  
both vote for two vs one disliked and for one of the two as liked  
most.  These last could promote such as Score or Condorcet.

> Voting cycles can result, and they make trouble for any democratic  
> system.
>
But the cycles are simply information - that there are voters who  
like, most, each of A, B, or C - information that methods such as  
Plurality never know.  While properly responding is a challenge, the  
having of the information is useful if we wish to, ACTUALLY, respond  
to the voters true desires.


>
> --Stephen H. Sosnick (3-Apr-2011)

Clearly you meant May, not Apr.