Chapter 17

History 17-1

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This is one of the best all around sites that I have found. It is titled “The MacTutor History of Mathematics Archive.”
http://www-history.mcs.st-and.ac.uk/~history

This is an award-winning site that links to all sorts of mathematics information.
https://mathshistory.st-andrews.ac.uk/HistTopics/History_overview

Vilfredo Pareto:
http://www.britannica.com/EBchecked/topic/443519/Vilfredo-Pareto… See the whole entry

Section 17.4: Apportionment Paradoxes

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17.4 Outline

  1. Introduction
  2. Alabama paradox
  3. Population paradox
  4. New states paradox
  5. Balinski and Young’s impossibility theorem

 

17.4 Essential Ideas

Alabama Paradox

A reapportionment in which an increase in the total number of seats results in a loss of seats for … See the whole entry

Section 17.3: Apportionment

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17.3 Outline

  1. Definition of apportionment
  2. The apportionment process
    1. upper quota
    2. lower quota
    3. standard divisor
    4. standard quota
    5. quota rule
  3. Adams’ plan
    1. definition
    2. modified divisor
    3. modified quota
  4. Jefferson’s plan
  5. Hamilton’s plan
  6. Webster’s plan
  7. Hungtington-Hill plan
    1. arithmetic mean
    2. geometric mean
  8. Summary of apportionment
… See the whole entry

Section 17.2: Voting Dilemmas

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17.2 Outline

  1. Fair voting principles
  2. Majority criterion
  3. Condorcet criterion
    1. Condorcet candidate
    2. definition
  4. Monotonicity criterion
    1. straw vote
    2. definition
  5. Irrelevant alternative criterion
  6. Arrow’s impossibility theorem
    1. fairness criterion
    2. comparison of voting methods
    3. insincere voting
    4. transitive law
    5. Codorcet’s paradox
    6. impossibility theorem

 

17.2 Essential

… See the whole entry