[EM] ER-Bucklin fails monotonicity
Abd ul-Rahman Lomax
abd at lomaxdesign.com
Wed Jun 29 09:20:18 PDT 2005
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.)
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