Spread spectrum analysis: IR vs Condorcet

[Steve Eppley]

Months ago before Rob Ritchie unsubscribed from EM, he wrote that
it's unlikely the flaw in IR will make much of a difference in the 
results.  He apparently thinks it's unlikely a noncenter candidate
can be the first choice of more voters than a center candidate, or
that even if that happens the center candidate will be protected by
vote transfers from the other wing.

Ignoring the "self-fulfilling" aspect of that prediction caused by 
the spoiler and LOE dilemmas, perhaps we could attempt some sort of 
comparison of IR and Condorcet with varying voter distributions and 
some rough approximations?  The following is a crude first attempt.  
(Undoubtedly this has already been covered in the academic literature.
References, anyone?)

Candidate distribution:
   L4  L3  L2  L1  M  R1  R2  R3  R4

Voter distribution:
  vL4 vL3 vL2 vL1 vM vR1 vR2 vR3 vR4

"Dominant" ballots for each voter cluster:
  vL4:  L4 > L3 > L2 > L1 > M > R1 > R2 > R3 > R4
  vL3:  L3 > L4=L2   > L1 > M > R1 > R2 > R3 > R4
  vL2:  L2 > L3=L1   > L4=M   > R1 > R2 > R3 > R4
  vL1:  L1 > L2=M    > L3=R1  > L4=R2   > R3 > R4
  vM:   M  > L1=R1   > L2=R2  > L3=R3   > L4=R4
  vR1:  R1 > R2=M    > R3=L1  > R4=L2   > L3 > L4
  vR2:  R2 > R3=R1   > R4=M   > L1 > L2 > L3 > L4
  vR3:  R3 > R4=R2   > R1 > M > L1 > L2 > L3 > L4
  vR4:  R4 > R3 > R2 > R1 > M > L1 > L2 > L3 > L4

Voter distribution #1:  big center
                            X
                         X     X
                       X         X
Both IR and Condorcet tend to elect M.  IR does this by eliminating
the fringes, hopefully before the middle.  In IR this is somewhat
chancy unless the voter distribution is extremely concentrated 
around the middle. 

Voter distribution #2:  two humps
                          X   X
                        X   X   X
                      X           X
Condorcet tends to elect M.  IR is likely to eliminate M.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)