Hogben. — Preferential Voting in Single-member Constituencies. 307 



In the case of equality, when at the last stage two or more candidates 

 are equal, and it is necessary to exercise a casting-vote, it is probably the 

 best rule to give this to the candidate of the two or more equal candidates 

 at the last count who stood highest at the first count ; or, if this does not 

 determine it, to the one who stood highest at the second count ; or, if the 

 candidates in question be equal at all counts, to determine the result by 

 drawing lots. 



In the " inconsistent case " there are, say, three candidates — A, B, C — 

 of whom A beats B, B beats C, and C beats A. For instance, if the votes 

 are distributed as in Table I, except that the last two lines are 



CBADE .. .. .. ..26 



BCADE .. .. .. ..24 



then Table VI becomes 



Table VIII (First Trial Table). 



and Table VII becomes 



Table IX (Second Trial Table). 



B. 



C. 



, rule, we reject A and B, and C is elected. 



Is this result 



Following the 

 correct ? 



Now, Table IX shows that the majority that affirms that B is better 

 than C (i.e., 204) is less than the majority that affirms that C is better than 

 A (namely, 210), and less than the majority that affirms that A is better 

 than B (also 210) ; hence B should go out. 



Again, C is better than A ; therefore C is elected. (This proof is general 

 in character.) It is evident that the candidate with the biggest net majority 

 will get a greater trial total than the average of the trial totals, and there- 

 fore all those with trial totals not greater than the average must be rejected, 

 which is the same rule as before. (Cases of equality may occur here also, 

 and should be treated as before.) 



