The Borda count and agenda manipulation

A standard objection to the Borda count, as an actual voting procedure, is that it is subject to agenda manipulation. The classical example is the introduction, in order to favour a candidate or option y, of a new option z ranked on every voter's preference scale immediately below y; y may as a result obtain the highest Borda count, although, if z had not been introduced, a different option would have done so. Strategic use of this device is not greatly to be feared, but it does point to a defect in the system: equating the distance on each voter's preference scale between any option and the next imposes a penalty for dissimilarity. The corrective is to vary the distances by introducing a measure of dissimilarity, as perceived by the voters and revealed by their preference scales. Two possible ways of doing this are described, yielding revised and adjusted Borda scores. It is shown by examples that these will often, but not always, undo the `agenda manipulation' effect, and questioned whether it is desirable to undo it altogether.