[EM] ER-Bucklin fails monotonicity

[Abd ul-Rahman Lomax]

At 05:28 AM 6/29/2005, James Green-Armytage wrote:
>Yes, this is interesting. However, I suggest that ER-Bucklin(whole) should
>perhaps be tallied in a different way. In the second example, you assume
>for tally purposes that D is in 2nd place on the A=B>D ballots. However, I
>suggest that we should still consider D to be in 3rd place, because there
>are still two candidates who are ranked strictly ahead of D. If we do
>this, I think that B still wins.

This is a good example of how less than full consideration of the 
implications of an action can lead to faulty results. Truly, James' 
analysis is obviously correct. D is indeed ranked third on those ballots, 
even though the form might seem to indicate differently. The reality is 
that the voter was unable or unwilling to choose between A and B for first 
place and second place, and so marked them both in first place. 
Conceivably, actual ballot design might make this moot, but even better 
would be simple analysis of the ballots prior to tabulation that corrects 
the apparent advanced placement of D.

Theoretically, the voter could have as well left first place blank and 
marked A and B in second place. This should be exactly equivalent; again, 
ballot analysis might move those two votes up to first place so that all 
ballots can be compared.

I think of an argument against allowing overvoting, that it gives the voter 
more than one vote. Yes, it might appear that way. (I think this argument 
was actually made in a court decision about a form of Approval voting, but 
I haven't actually read the decision, which may have hinged on details of 
the voting method under consideration.) But only one vote is effective, or 
none. Never are the two votes simultaneously active. The real meaning of 
one voter, one vote should be that one voter may not cast two votes for one 
candidate, or, better, that all voters have equal rights.

(The limitation of the effect of overvoting to one vote is clearly seen by 
considering all pairwise contests. Overvotes are either moot to a pairwise 
contest, they are a vote for only one in the contest, or they are a vote 
for both, in which case they are equivalent to abstention.)