LXXIV EOYAL SOCIETY OF CANADA. 



" That at the next meeting of the Eoyal Society, the undersigned will move: 

 " That in any contest for the election of Fellows should no candidate receive the requisite number 

 of votes, the Council shall elect such members as it may deem most suitable, at any meeting of the 

 Council held before the date tixed for the annual meeting, provided a quorum of members of Council 

 be present." 



Henry T. Bovet. 



Halifax, May 19th, lS9i. 

 The Hon . Secretary of the Royal Society of Canada. 



Dear Sir, — Being unable to be present at the approaching meeting of the E. S. C, I take the 

 liberty of addr-essing to you a few remai-ks to serve as a contribution to the discussion of the amend- 

 ment of Rule 6 on the mode of election of members. I assume yo\i are familiar with the modes of 

 election proposed by Dr. Fleming and myself respectively and referred to in the Proceedings of the 

 last two years. These so far as I know are the only methods under discussion. I wish to institute a 

 comparison of their respective merits or defects. 



Dr. Fleming's method may fail to effect an election even when the voting papers contain sufficient 

 information for the purpose. Thus let there be five candidates A, B, C, D, £, and let us suppose 

 eleven voters attach the numbers 5, 4, 3, 2, 1 to their names respectively ; three voters the numbers 

 1, 3, 4, 5, 2; other three voters the numbers 1, 2, 4, 5, 3 ; one voter, the numbers I, 2, 3, 5, 4; one 

 voter, the numbers 1, 3, 2, 4, 5, and one voter, the numbers 2, 1, 3, 4, 5. Their totals are thus 65, 65, 

 65, 65, 40 respectively. If therefore there be only one or two or three vacancies, Dr. Fleming's 

 method fails to elect, although obviously a majority of the voters wish A to fill the first vacancy, B 

 to fill the second and C the third. 



If, as would appear from Dr. Fleming's statement of his method in the Proceedings, he proposes 

 to require a candidate, in order to election, to obtain a total equal to two-thirds of the highest possible 

 total, his method will frequently fail to elect. In the above example no candidate has so large a total ; 

 and thus in this case even if there were four vacancies his method would f:xil to elect. But this 

 restriction is not essential to his system and may therefore be left out of account. 



My method also may fail to elect ; but only in the case in which the voters are equally divided 

 between candidates (in which case an election can be effected only by some species of fictitious com- 

 promise under any good system), and in the case in which the voting papers do not supply sufficient 

 information to show that at least one candidate is preferred to all others (in which case also com- 

 promise is the only resort, as e. g. in the ordinary method of balloting at public meetings). So far 

 as I can see no method of voting by letter can meet these cases. In my 'proposed amendment of rule 

 6 (Proceedings of 1892, p. V.^ the first case was provided for; the second case, which would probably 

 be of very rare occurrence, might be provided for by referring the election in any such case to the 

 ne.xt meeting of the section, to be conducted by the ordinarj' method of ballot. 



That Dr. Fleming's method may effect an election in both these cases is so obvious that I need 

 not give an example. At first sight this might seem to be an advantage; but the election of a 

 candidate whom the majority of the voters do not wish to elect, cannot be advantageous. 



The possibility of electing the wrong man, ze., of electing one candidate when the majority of 

 the voters wish another to be elected, is the most serious defect of Dr. F.'s method. That this is 

 possible was shown by me in the Proceedings of '92, p. VI., in the case of a single vacancy, and was 

 tacitly admitted by the committee appointed to report on these methods (Proc. of '93, p. XLV.) ; for 

 they reported that in the case given, Dr. F.'s method elected "the best all-round candidate," not the 

 candidate whom the majority of the voters wished to elect. 



That even when there are two vacancies the wrong candidates may be elected is obvious from 

 the following example : — Let there be five candidates, A, B, C, D and E. Let eleven voters attach to 

 their names the numbers 5, 4, 3, 2, 1, respectively, and nine voters the numbers 1, 2, 4, 5, 3. The 



