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We have the rule:

We compare parties A and B in two different elections. If it happens that A wins votes and B loses votes, it cannot happen that A loses a seat and B wins a seat.

Concretely, I have to prove that Hamilton's method does not meet this rule by giving an example in which happens that A wins 2000 votes and B loses 2000 votes, A loses a seat, B wins a seat and the others stay the same.

I supose that the number of votes of A and B are big enough so that 2000 is a small amount and there is an extra party that increases the votes without changing the number of seats. But I am not able to find this example.

  • What could be a suitable example?
  • What would be the intuition to find such an example?
EvaMGG
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  • What is Huntington's method? The usual paradoxes of this sort come down to rounding issues, as in the famous Alabama Paradox – lulu Apr 21 '20 at 14:44
  • Just to say, I thought Huntington-Hill avoided the Alabama and Population paradoxes and that therefore it must violate the quota rule. this appears to confirm that. But, it's been a while since I looked at these things and I am hazy on the details. – lulu Apr 21 '20 at 14:53
  • @lulu I edited and explained how the Huntington's method works. – EvaMGG Apr 21 '20 at 15:16
  • @lulu there was a mistake, it wasn't Huntington, it must be Hamilton's method. – EvaMGG Apr 22 '20 at 08:34
  • The Hamilton method is the mechanism for apportioning seats to a state based on a per capita quotient; it has nothing to do with voting. –  Apr 22 '20 at 08:57
  • @higgs Could this quotient per capita be the vector of the percentages of votes (between 0 and 1) of each party multiplied by the number of seats? – EvaMGG Apr 22 '20 at 09:09

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