Non-self-mapping seat allocation procedures

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Common properties of all non-self-mapping seat allocation procedures in majority voting are described in the article Seat allocation procedure . This digression from the article deals with modifications of the divisor procedure with the aim of arbitrarily giving preference to large - or small - parties (similar to the actual provision that the strongest parliamentary group gets 50 seats). They do not play a role in practice.

As an example, 1000 votes were cast, for party A 500, for party B 300 and for party C 200 votes, with 100 seats to be allocated.

Not self-mapping procedures with constant rounding limit

  • The Imperiali method has the rounding rule “rounding down minus 1”. It favors larger parties more than the D'Hondt process . Divisor series when using the maximum number method: 2; 3; 4; 5; 6 etc. The distribution of seats is 51 - 30 - 19 (suitable divisor: 9.6).
  • According to the rounding rule “rounding down minus 5”, the divisor series is 6; 7; 8th; 9; 10 etc. In the example the distribution of seats is 53 - 29 - 18 (suitable divisor: 8.6).
  • According to the rounding rule “rounding down minus 145”, the distribution of seats is 99 - 1 - 0 (suitable divisor: 2.045). With the rounding rule "rounding down minus 148 (or more)", party A receives all 100 seats (suitable divisor: 2.015).

Conclusion: For any election result, a seat allocation procedure can be created which allocates the total number of seats to be allocated to the strongest party, even if it is only one vote ahead.

  • The counterpart to the Imperiali procedure is the procedure with the rounding rule "rounding up plus 1". It massively favors smaller parties. Divisor series when using the maximum number method: 0; 0; 1; 2; 3; 4 etc. The example shows the distribution of seats 49 - 30 - 21 (suitable divisor: 10.5).
  • According to the rounding rule “rounding up plus 5”, the divisor series is 0; 0; 0; 0; 0; 0; 1; 2; 3; 4 etc. The example gives the distribution of seats 47 - 31 - 22 (suitable divisor: 11.95).
  • According to the rounding rule “rounding up plus 32”, the distribution of seats is 34 - 33 - 33 (suitable divisors: all from 301 to 499).

Conclusion: For any election result, a seat allocation process can be created which distributes the total number of seats to be allocated to the parties with maximum uniformity, no matter how great the differences in party strengths. The only requirement is that each party has at least one vote.

Other non-self-mapping procedures with constant rounding limits

  • Procedure with the rounding rule "commercial rounding minus 1": preference for larger parties, divisor series when using the maximum number procedure: 1.5; 2.5; 3.5; 4.5; 5.5 etc.
  • Procedure with the rounding rule "commercial rounding minus 2": Even greater preference for larger parties, divisor series when using the maximum number procedure: 2.5; 3.5; 4.5; 5.5; 6.5 etc.
  • Procedure with the rounding rule "commercial rounding plus 1": preference for smaller parties, divisor series when using the maximum number procedure: 0; 0.5; 1.5; 2.5; 3.5 etc.
  • Procedure with the rounding rule “commercial rounding plus 2”: Even greater preference for smaller parties, divisor series when using the maximum number procedure: 0; 0; 0.5; 1.5; 2.5 etc.
  • Procedure with the rounding rule "rounding limit for the decimal value 4 with subtraction of 1": preference for larger parties, divisor series when using the maximum number procedure: 1.4; 2.4; 3.4; 4.4; 5.4 etc.
  • Procedure with the rounding rule "Rounding limit for the decimal value 4 with addition of 1": preference for smaller parties, divisor series when using the maximum number procedure: 0; 0.4 1.4; 2.4; 3.4 etc.

Non-self-mapping procedures with variable rounding limits

  • Procedure with the rounding rule "harmonic rounding minus 1": preference for larger parties, divisor series when using the maximum number procedure: 1 1/3; 2 2/5; 3 3/7; 4 4/9; 5 5/11 etc.
  • Procedure with the rounding rule "harmonic rounding minus 2": Even greater preference for larger parties, divisor series when using the maximum number procedure: 2 2/5; 3 3/7; 4 4/9; 5 5/11; 6 6/13 etc.
  • Procedure with the rounding rule “harmonic rounding plus 1”: preference for smaller parties, divisor series when using the maximum number procedure: 0; 0; 1 1/3; 2 2/5; 3 3/7 etc.
  • Procedure with the rounding rule harmonic rounding plus 2: Even greater preference for smaller parties, divisor series when using the maximum number procedure: 0; 0; 0; 1 1/3; 2 2/5 etc.
  • Procedure with the rounding rule "geometric rounding minus 1": preference for larger parties, divisor series when using the maximum number procedure: root 2; Root 6; Root 12; Root 20; Root 30 etc.
  • Procedure with the rounding rule “geometric rounding minus 2”: Even stronger preference for larger parties, divisor series when using the maximum number procedure: Root 6; Root 12; Root 20; Root 30; Root 42 etc.
  • Procedure with the rounding rule "geometric rounding plus 1": preference for smaller parties, divisor series when using the maximum number procedure: 0; 0; Root 2; Root 6; Root 12 etc.
  • Procedure with the rounding rule "geometric rounding plus 2": Even greater preference for smaller parties, divisor series when using the maximum number procedure: 0; 0; 0; Root 2; Root 6 etc.