PROCEEDINGS OF SECTION G. 493 



The system then is inequitable as between different candidates. 

 It is equally unjust in its incidence between electors, as may be 

 shown as follows : — 



Suppose there are a large number of candidates for n seats. 

 Suppose, further, in the first place, that none of the candidates 

 receive a quota until the last count, so that there are no surplus 

 votes to transfer, but only the votes from eliminated candidates. 

 Suppose that the transfer goes on until there are only ?? + 1 can- 

 didates left. Tiie lowest on the list — say X — is then rejected and 

 the remaining n candidates elected. 



Take the candidate X first. The voters who gave him first 

 preference are virtually disfranchised. Their first votes failed 

 to elect X, and they get no chance of utilizing their higher pre- 

 ferences which might have been sufiicient to return an eliminated 

 candidate. Consequently their votes have what might be called 

 an " effective weight " of zero. This will always happen in the case 

 of candidates rejected in the final count, but not in the case of 

 those previously eliminated. 



Take now the voters who gave first preference votes to G, an 

 eliminated candidate. Let us make the assumption (the only 

 reasonable one in the absence of positive knowledge) that at every 

 subsequent transfer the votes are equally divided among the re- 

 maining candidates. At the final count X will have secured 



— - of the votes, the remaining fi-actiori of -^^ being equallj^ 

 divided among the successful candidates. This shows that T^rrp 

 of the votes are effective in securing the return of a candidate and 



-j^ are wasted in the sense that the higher preferences have no 

 chance of being counted. In other words, the " effective weight " 

 of the votes which go to all the eliminated candidates has an 

 average value of ^,- . 



In just the same way the " effective weight " of the votes cast 

 for the successful candidates is unity. This is the simplest case 

 that can arise. If, however, some of the candidates receive quotas 

 before the final count, the results are a little more complicated. 

 The "effective weights" of the last two groups then beco'iie a 

 little less than -—^ and unity respectively, because, when a trans- 

 fer of surplus votes takes place, some will find their way to A' and 

 consequently be wasted. 



We have, so far, only considered the simplest case that can 

 arise. However, some of the candidates may gst quotas before 



