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The Pamphlet Collection of Sir Robert Stout: Volume 53

Laplace's Objection

Laplace's Objection.

It may be said that the proposed method is open to the objection raised by Laplace to the method of Borda. To this I think it a sufficient answer to say, that if we have a method which will truly interpret the wishes of the electors, as expressed by their voting papers, we need not trouble ourselves whether they vote honestly or not; that is their own concern. If we provide a method which will bring out a correct result for honest electors we need not try to go further, and endeavour to construct a method which will force dishonest electors to vote honestly. Nevertheless, it may be pointed out that Laplace's objection is not of so much force in this case as in the case of Borda's method. For if an elector vote otherwise than according to his real views it will be at the risk of having his vote at the final scrutiny counted against the candidate whom he considers most fit for the office to be filled. This risk would be sufficient to deter most electors from voting otherwise than according to their real opinions. If, in spite of this risk, an elector persists in voting otherwise than according to his real views we must take him at his word. To illustrate this objection, let us suppose that B and C are two formidable page 21 candidates, and that A is in reality inferior to each of them, but that the voting is as follows, BA = 5, CA = 4, AB = 1, AC = 1; so that B's supporters, in their anxiety to defeat C, put A second, and C's supporters, in their anxiety to defeat B, put A second. The result at the first scrutiny is A 13 votes, B 11 votes, C 9 votes. Thus C is rejected and A wins in the final scrutiny. A wins because the whole of C's supporters put him second. Had one of C's supporters voted according to his real views, and put B second, the result would have been different.

If the preferential mode of voting were not employed, this objection would be of great force; for then the supporters of each candidate would put his most formidable opponent at the bottom of their list at the first scrutiny, knowing that they would have at the second scrutiny an opportunity of reviewing their vote.