36 SANDFORD FLEMING ON 



usage regarded by them as a means of obtaining the divine mind. They determined by 

 lot who should be the twelfth apostle, and thus they made a selection to which a 

 cheerful acquiescence was unanimously given. 



I have assumed a case of two electors, and pointed out the course which might be 

 followed — indeed, the only rational course which could be followed. If the principle laid 

 down be sound, could it not be applied in other cases ? Let us assume that the elec- 

 torate consists of twenty voters, what could be done in this case? If individual voters in 

 the electorate were ecj^ual in all respects, as in the first case referred to, the question would 

 be a very simple one, as it might be settled by casting lots for one of the twenty equally 

 eligible persons. It may be taken for granted that under the circumstances no one would 

 object to make the selection in this way, as being the simplest and best mode of 

 making a choice. It would remove antagonism and promote unanimity ; and, by the very 

 act of casting lots, each one of the twenty taking ])art therein would be an assenting 

 party to the choice made. Men as we ordinarily find them are, howcA^er, not alike ; they 

 differ much in their qualifications, and their opinions are not the same ; we must therefore 

 consider cases in which equal eligibility and uniformity of mind in the whole electorate 

 is not the rule. 



First, let us suppose that among the twenty electors, five voters favor the choice of 

 A, another five B, another C, and the remainder D. We should thus have A, B, C. D, 

 each eqitally desired and preferred as the representative of the twenty. 



(A+B-\-C-\-D)' 4 would therefore be the representative unit of the whole. We 

 cannot, however, take one quarter of A, B, C, and D, and combine these quarters so as to 

 form one indiAadual, but we can reduce the four to one by the principle of casting lots. 

 One of the four can be selected by what may be termed the " Apostolic" method, and 

 the person so selected would be recognized as chosen by the twenty electors as the 

 common representative of the whole. 



Secondly, let us suppose a case in which there is less diversity of opinion ; two groups 

 of five electors each favor A, one group of five prefer B, another C. The selected men 

 would thus stand A, A, B and C, and the representative itnit of the W'hole would be 

 (2 A+B-\-C)^A. As in the previous case, this complex unit would be reducible to a 

 single individual by casting lots, and it is obvious that the probability of the lot falling 

 upon A, would be as two to one. 



Tliirdly, suppose three groups of five electors desire to be represented by A and one 

 group by B. In this case we should have (3 ^l+i?) h-4, as the representative unit: in 

 selecting one of them by lot, there is undoubtedly a possibility of the lot falling upon B, 

 but the probability of A' a being chosen would be three times greater than the probability 

 in B's case. True it may be said that there should be no possibility of B's being chosen 

 in a constituency where three-fourths of the electors desire A. We must however bear 

 in mind that the primary object is not so much to have particular sections of the country, 

 as to have the whole nation, fairly represented in Parliament. If we look a little further, 

 if we take four constituencies precisely similar to the one under consideration, according 

 to the mathematical theory of probabilities, there would be retitrned out of the four, 

 three members in sympath}^ with A and one member in sympathy with B. Again, if we 

 carry the matter still further if we take into consideration every one of the constituencies 

 into which for convenience the whole nation may be diAÙded, it w^ould be found as a 



