42 Proportional Representation. 



points in connection with the method just described. It 

 will be noticed that papers are transferred to all candidates 

 to whom it is possible to transfer any. The magnitude of 

 the numbers A P, A Q, &c., has not much influence on the 

 magnitude of the numbers ap, aq, &c. Thus, for instance, 

 if there be a large vote on a party ticket on which the 

 first name marked is A, and the second P, this ticket is 

 not permitted to overpower the electors who have also 

 voted for A, but have not followed the ticket. Nor, on the 

 other hand, can it be said that any injustice is done to the 

 electors who voted on the ticket, for at least as many papers 

 are transferred from A to P as from A to any other candi- 

 date. Thus it will be seen that the method is such that no 

 inducement is held out to the electors to vote on a ticket. 



It is now to be noticed that, if the papers transferred 

 from A to P have not subsequently to be transferred from 

 P to some other candidate, it is quite immaterial what par- 

 ticular ap papers we transfer from the parcel A P to P. If, 

 however, by means of this transference and other trans- 

 ferences from B, C, &c, to P, P's votes be raised above the 

 quota, P will have a surplus to distribute. But, as already 

 pointed out, the names indicated after P on the papers in 

 P's heap have not very much influence on the numbers 

 to be passed on from P to the remaining unelected candi- 

 dates. Hence we see that we can, without influencing to 

 any great extent the subsequent course of the election, 

 adopt a simple but somewhat empirical rule for selecting 

 the papers from the A P parcel to be passed on to P. The 

 rule proposed is as follows : 



Break up the parcel A P into smaller parcels, according 

 to the names next indicated, ignoring the names of elected 

 candidates. Let the parcels be denoted and arranged as 

 follows : 



APQ, APR, APS, . . . API. 



Here A P Q denotes the parcel in which are placed all 

 the papers on which Q is the unelected candidate indicated 

 next after P, and so on for the rest ; whilst A PI denotes 

 the parcel in which are placed the papers on which no un- 

 elected candidates are indicated after P. 



We now transfer to P as many of the above parcels as we 

 can without surpassing the number ap of papers which are 

 to be transferred, taking the parcels in the order above 

 indicated. It may happen, of course, that we thus get a 



