Monotonicity, the 1/3 quota (of IFPP method)
The page derives a 3 candidate 1 winner method. Firstly P2 or truncation resistance eliminates papers having exactly three preferences. Then truncation resistance and the rule on getting the number of winners right, allows the method to be factorised into two 5 paper examples, e.g. with one having these papers: (A),(AB),(AC),(B),(C). Then P2 can eliminate 2 more papers leaving (AB),(B),(C). Then another dimension can be removed by dividing the counts by the total weight. The 2 winner 3 candidate solution can be found by a similar argument (appeared at the PaP mailing list in late 2002) or alternatively by negating the votes and swapping winners with losers.
Introduction: A method that results in preferential voting methods that have desirable principles that are not rejected by a very critcal skeptical public audience the inevitable idea that the winners can be found by extending ties between candidates as if the ties were just like shock waves or shadows. The idealism is as simple to grasp as the algebraic consequences of it are difficult to make progress with.
Most of the argument is in the 3 pictures so the . The pictures themselves are not so good in that a dimension was reduced using a x/y division, and to derive a 4 candidate solution, it would seem better with the extra dimension than with the division. A problem is that an “its obvious” argument is used done at the same time. Anyway the results are OK. [The division projects 3-space onto a 1=a+b+c triangle.]
Here a method for selecting a winner in a 3 candidate election is derived. electing A method for electing winners where the ballot papers specify a rank for 1 or more candidates, i.e. the numbers 1, 2, 3,…, can be derived from principles, at least where there are 3 candidates.