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Politicians and Polytopes: notes on mathematics of preferential voting.

This mailing list receives notes from its owner, on the topic of designing optimal and fair preferential voting methods.

New subscribers with on-topic not vexatious communications can ask for the moderating to be removed, e.g. before the posting of their first message.

The method used in deriving good preferential voting methods, is roughly as follows: (1) An embedded solution is defined. So far it is just First Past the Post (FPTP) (or SNTV). (2) Axioms defining fairness are iteratively used; i.e. "if wins then wins" shadows from touching cones. (3) Thirdly, proportionality is dropped in.

The 1/3 quota is part of preferential voting. It seems that in the USA, cities are not properly told about the importance of the 1/3 quota and how the recommendation of the IRV promoting lobbyist (in USA) should be discarded under the ideal of elections being fair.

By 2005, voting methods will be accurately ranked.


  1. Derivation of the IFPP 3 candidate method: http://www.ijs.co.nz/quota-13.htm
  2. The Single Transferable Vote mailing list: http://groups.yahoo.com/group/single-transferable-vote
  3. REDLOG Quantifier Elimination system: http://www.fmi.uni-passau.de/~redlog/
  4. June 2002: A webpage showing how the Alternative Vote (AV) lets hundreds of thousands of voters be outvoted and defeated by 2 opposing FPTP votes, is here: http://www.ijs.co.nz/irv-wrong-winners.htm

Some keywords: hyperspace shadows, inequalities, wrong winners, hypergeometry, electoral reform, fairness, symbolic algebra, constraints, Boolean barriers, logic, IRV, RCV).

Craig Carey, UTC 20-Dec-2004, 9-Nov-2002

Auckland, New Zealand

List started on 4-April-2000

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  • 51
  • Mathematics
  • Apr 4, 2000
  • English

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