THE THEORY OF THE QUOTA IN PROPOR- 

 TIONAL REPRESENTATION— I. 



By E. L. Piesse, B.Sc, LL.B. 



(Read July 8, 1912.) 



1-5. — Introductory . 



1. Ulsyroportionate representation from single-member 



districts. Statistics. 



2. Multi-member districts. 



3. The systems considered in this paper. 



4. Statistics of close contests. Influence of quota on 



size of majority. Odd-member districts. 



5. Quota defined. 



•6-21.' — Single Transferable-Vote Systems. 



6. Hare quota. 



7. Droop quota. 



8. Comparison of these quotas in a contest between 



candidates. 

 9-21. Comparison in contest between parties. 



9. Quotation from Beport on Ta^manian General 



Election, 1909. 



10. Assumptions made in argument. 



11. Graphical representation of cases of dispro- 



portionate representation (Fig. 1). 

 12-13. Illustrations. 



14. Causes of disproportionate representation. 

 15-18. Algebraical analysis. 



19. Besults for six- and seven-member districts. 



20. liesults in a close contest. 



21. Statistics as to Droop quota. Conclusion. 



22-52. -List Systems. 

 22. Introductory. 

 23,24. The problem stated. 



25. Symbols used in the analysis. 



26. The ideal solutiori. 



27-29. Graphical representation (Figs. 2, 3). 

 30-43. The three solutions proposed. 



30-35. First, the rule-of-three method. 

 36-42. Second, proportion of votes to a member 

 as nearly as possible the same for all 

 parties (Fig. 4). 

 43. Third, fraction of a member returned by 

 each vote as nearly as possible the same 

 for all votes (Fig. 5). 

 44-46. The methods used in Europe. 

 44:. Historical. 



45, 46. The D'Hondt mMod. 

 47-50. Comparison of the various methods. 

 47, 48. Comparison in close contests. 



49. Criticisms of the D'Hondt method. 



50. The rule-of-three method sufficient in three- 



party contest. 

 51-52. Rules for a three-party contest. 



h53. — Conclusion. 



