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.

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Ladattava julkaisu This is an electronic reprint of the original article. |