488 PROCEEDINGS OF SECTION G. 



3. A STUDY IN PROPORTIONAL REPRESENTATION, 



By F. W. Bar ford, M.A., A. I. A. 

 (Commonwealth Bureau of Census and Statistics, Melbourne.) 



Synopsis. 

 Introductory. 

 Scope of the inquiry. 

 Inequities of present electoral system. 

 Hare system : Modifications introduced by Clark and Gregory : 



The quota : Mathematical analysis of quota. 

 Party-list voting: Rule of three method: D'Hondt method: 



Mathematical analysis of D'Hondt method. 

 Cumulative voting : Block voting : Limited voting : Preferential 



voting. 

 Statement of problem : Conditions for satisfactory electoral system 



laid down: Practical scheme submitted. 

 Proposal for action by Association. 

 Conclusion. 



INTRODUCTORY. 



It seems as if a word of apology is due to the Association from 

 a writer who brings to it for consideration such a subject as elec- 

 toral reform, which might appear to be somewhat outside the 

 scope of its activities. Several facts in extenuation may, however, 

 be urged. Firstly, the subject is one of enormous importance in a 

 country which sees an election, either for Federal or State Parlia- 

 ments, every year. Secondly, the am.ount of practical achieve- 

 ment is disappointingly small corapai-ed with the amount of study 

 which has been devoted to the subject, and the volume of literature 

 which has grown up around it. And thirdly, the coincidence of a 

 meeting of this Association with the approach of another Common- 

 wealth election has led me to hope that this choice of subject 

 might lead to a valuable discussion, which would once more fasten 

 the attention of the public upon a matter, which of late years 

 has been allowed to fall into an undeserved neglect. 



This neglect is the more unfortunate since the subject has 

 been handled in Australia with conspicuous ability. Although, 

 for more than a century past, discontent has been expressed in 

 England with its electoral machinery, it was not until 1857 that 

 a constructive scheme at all adequate to the importance and com- 

 plexity of the subject made its appearance. This was the famous 

 system elaborated by Hare, and subsequently advocated so ably by 

 John Stuart Mill. The high level of argument maintained in their 

 writings attracted universal attention, and in Australia the new 

 Bystem was warmly taken up by many adherents, foremost among 



