This paper compares the vulnerability of Borda Elimination Rule (BER)
and of Nanson Elimination Rule (NER) to monotonicity paradoxes under both fixed and
variable electorates. It is shown that while NER is totally immune to
monotonicity failure in 3-candidate elections, neither of these two rules
dominates the other in n-candidate elections (n>3) when no
Condorcet Winner exists. When the number of competing alternatives is larger
than three and no Condorcet Winner exists, we find profiles where NER violates
monotonicity while BER does not, profiles where BER violates monotonicity while
NER does not, as well as profiles where both NER and BER violate monotonicity.
These findings extend to both fixed and variable electorates, as well as to
situations where the initial winners under both rules are the same, as well as
to situations where the initial winners under both rules are different. So,
which of the two rules should be preferred in terms of monotonicity in n-candidate
elections (n>3) where no Condorcet Winner exists, depends on the kind
of profiles one can expect to encounter in practice most often. Nevertheless,
in view of the results of 3-candidate elections under other scoring elimination
rules, we conjecture that inasmuch as BER and NER exhibit monotonicity
failures, it is more likely to occur in closely contested elections.