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d’Hondt election calculations


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Friday 29 August 2014  •   4 Vine Moon 2014

 Quotients for each round:
 
  30768   15384   10256   10256   10256   7692   7692   6153.6   6153.6   5128   5128   5128   4395.4   4395.4   4395.4  
  15345   15345   15345   7672.5   7672.5   7672.5   7672.5   7672.5   5115   5115   5115   5115   5115   3836.3   3836.3  
  12098   12098   12098   12098   6049   6049   6049   6049   6049   6049   4032.7   4032.7   4032.7   4032.7   4032.7  
  10008   10008   10008   10008   10008   10008   5004   5004   5004   5004   5004   5004   5004   5004   3336  
  5460   5460   5460   5460   5460   5460   5460   5460   5460   5460   5460   2730   2730   2730   2730  
  802   802   802   802   802   802   802   802   802   802   802   802   802   802   802  
  298   298   298   298   298   298   298   298   298   298   298   298   298   298   298  
  150   150   150   150   150   150   150   150   150   150   150   150   150   150   150  
  62   62   62   62   62   62   62   62   62   62   62   62   62   62   62  
  28   28   28   28   28   28   28   28   28   28   28   28   28   28   28  
 
Cumulative seats won:
 
Party A 1   2   2   2   3   3   4   4   5   5   5   6   6   6   7  
Party B 0   0   1   1   1   1   1   2   2   2   2   2   3   3   3  
Party C 0   0   0   1   1   1   1   1   1   2   2   2   2   2   2  
Party D 0   0   0   0   0   1   1   1   1   1   1   1   1   2   2  
Party E 0   0   0   0   0   0   0   0   0   0   1   1   1   1   1  
Party F 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  
Party G 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  
Party H 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  
Party I 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  
Party J 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  
 
Total seats won 1   2   3   4   5   6   7   8   9   10   11   12   13   14   15  

D’Hondt elections, such as the English, Scottish and Welsh regional elections for the European Parliament, work by allocating the available seats in a number of rounds.
In each round, a “quotient” is calculated for each party. This is the number of votes divided by one plus the number of seats already allocated to the party.
The party with the highest quotient is allocated a seat, and the process continues until all available seats are allocated.

You can use this page to review old results, follow results as they come in, or experiment to see how many votes your party needs to get that extra seat!

Fill out the names of the parties, and put in the votes. You can use percentages instead, if you wish. Press the button to submit changes.
The result you are looking for will be in the column with the total available seats shown at the bottom.
A tie means that more than one seat gets allocated in a round, and if there is no result column with the total available seats at the bottom, the result is invalid.

In case you are interested, here is the important part of the code:
for ($round = 0; $round <= $total_rounds; $round++) {
for ($party = 0; $party < $total_parties; $party++) {
if ($round == 0) { $quotient[$round][$party] = $partyvote[$party]; } else { $quotient[$round][$party] = $partyvote[$party] / ($seat[$round - 1][$party] +1); }
}
$max[] = max($quotient[$round]);
for ($party = 0; $party < $total_parties; $party++) {
if ($round == 0) { $seat[$round][$party] = 0; } elseif ($quotient[$round][$party] == $max[$round]) { $seat[$round][$party] = $seat[$round - 1][$party] + 1; } else { $seat[$round][$party] = $seat[$round - 1][$party]; }
}
}

William Morris

updated June 2009
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