# The d'Hondt voting system for European Parliament

Created | Updated Jan 19, 2011

The United Kingdom must elect several politicians for seats (or positions of power) in the European Parliament, a body responsible for making decisions in the European Union (EU). To do this, the electorate^{1} is split up into 'constituencies,' depending on where in the United Kingdom the voters live. Several political parties^{2} will then enter lists of candidates to stand for each constituency.

Each voter may then vote for one of the parties, and the total number of votes for each party in a constituency is calculated. The votes won by each party must be translated into numbers of seats won, and this is where the d'Hondt method is used. The d'Hondt method was invented by Belgian mathematician and lawyer Victor d'Hondt (1841 - 1901) in 1878.

### The mechanism of the d'Hondt method

In the d'Hondt method, the seats are awarded one at a time, using a revised set of figures each time. The following method is used:

- Take the highest number of votes in the present table and award a seat to that party
- Calculate the new number of votes the party just awarded a seat has: (New number) = (Actual number of votes cast) / (Number of seats awarded to this party so far plus one)
- Return to the start using the new number of votes for that party
- Repeat until all seats have been awarded

**Example:**

The following table shows the original results of an election:

Party: | One | Two | Three | Four | Five |

Votes: | 270 | 100 | 80 | 70 | 10 |

The first seat would go to Party One as it has the most votes in the table. According to the instructions, the actual number of votes is now divided by two^{3} to give 135:

Party: | One | Two | Three | Four | Five |

Votes: | 135 | 100 | 80 | 70 | 10 |

Seats: | 1 | 0 | 0 | 0 | 0 |

As you can see, Party One still has more votes than anyone else. This means that another seat is awarded to Party One, and its actual number of votes, 270, is divided by three^{4} to give 90

Party: | One | Two | Three | Four | Five |

Votes: | 90 | 100 | 80 | 70 | 10 |

Seats: | 2 | 0 | 0 | 0 | 0 |

Now that this has happened, Party Two is awarded the next seat as it now has the most votes. The number of votes for Party Two is now divided by two^{5} to give 50:

Party: | One | Two | Three | Four | Five |

Votes: | 90 | 50 | 80 | 70 | 10 |

Seats: | 2 | 1 | 0 | 0 | 0 |

Party One is awarded another seat as they now have the most votes again, and then its number of votes is recalculated as 67.5^{6}:

Party: | One | Two | Three | Four | Five |

Votes: | 67.5 | 50 | 80 | 70 | 10 |

Seats: | 3 | 1 | 0 | 0 | 0 |

Party Three is awarded a seat and has its total votes reduced to 40, then Party Four is awarded a seat and has its total votes reduced to 35. Assuming that all the seats are now awarded, the resulting situation is:

Party: | One | Two | Three | Four | Five |

Votes: | 270 | 100 | 80 | 70 | 10 |

Seats: | 3 | 1 | 1 | 1 | 0 |

### The easier way...

The easier way to calculate numbers of seats is to create a table with the actual number of votes divided by 1, 2, 3, 4 and so on:

Party: | One | Two | Three | Four | Five |

Votes divided by 1: | 270 | 100 | 80 | 70 | 10 |

Votes divided by 2: | 135 | 50 | 40 | 35 | 5 |

Votes divided by 3: | 90 | 33.3 | 26.67 | 23.33 | 3.33 |

Votes divided by 4: | 67.5 | 25 | 20 | 17.5 | 2.5 |

All that is necessary now to award 'x' seats is to pick the 'x' highest numbers from the table. One caveat - if a party is awarded four seats, for example, a 'votes divided by five' row is added so that no number is picked from the bottom row without adding another row. In this example, six seats will be awarded, so the six highest numbers will be selected.

Party: | One | Two | Three | Four | Five |

Votes divided by 1: | 270 | 100 | 80 | 70 | 10 |

Votes divided by 2: | 135 | 50 | 40 | 35 | 5 |

Votes divided by 3: | 90 | 33.33 | 26.67 | 23.33 | 3.33 |

Votes divided by 4: | 67.5 | 25 | 20 | 17.5 | 2.5 |

Seats awarded: | 3 | 1 | 1 | 1 | 0 |

#### Why use the d'Hondt method?

- As the number of seats awarded increases, the resulting number of votes given by (original votes/{seats + 1}) becomes nearly equal, as the number of seats awarded to each party plus one is roughly proportional to the number of votes. If Party A had won a small number of seats, then its resulting number of votes would be large compared to the other parties' resulting numbers. Thus, a seat would be awarded to the Party A in order to counter the imbalance. This means that minority parties can win fair representation.
- A threshold limit, or
*barrage*, can be set so that no party may hold more than a certain number of seats regardless of the number of votes it receives. - The method is simple enough to be checked by anyone.
- The method is tried and tested - Austria, Finland, Israel, the Netherlands, Poland and Spain are among the countries that use the system.

### Modifications to the d'Hondt system

#### Open lists and closed lists

The method shown above is shown using political parties and shows a closed list system. The voter is given a choice as to which party he votes for. Once the seats have been allocated to the parties, the voter has no control over who receives the seat - it can be *any* one of a list of members of that party, as chosen by the party. In the United Kingdom, these lists are determined beforehand and shown on the voting form. After the vote, it is *completely at the discretion of the party* as to which candidates receive the seats.

The alternative is an open list. In this system, the voter is presented with a choice of candidates and a certain number of votes to cast^{7}. The votes for each party are calculated by adding up the votes for each member, and the most-voted-for members take the seats won by their party.

#### Exclusions

There are a few ways in which some votes can be ignored:

- All votes for candidates or parties who failed to receive more than a certain percentage
^{8}of the votes could be ignored. This avoids the possible election of an unpopular party or candidate. - In an open list system, all votes for a party in which none of the candidates have received a certain percentage of the votes individually
^{9}could be ignored. This avoids the possible election of an unpopular candidate.

In the European elections, the number of seats available is small enough for the system to work without any exclusions being necessary.

### More information...

For more information, see the Electoral Reform Society website.

^{1}The voting public

^{2}Including independent candidates who, for the purposes of this system, are taken to be a party with a single candidate.

^{3}The number of seats awarded to Party One so far, plus one.

^{4}The number of seats awarded to the party so far plus one.

^{5}As the party only has one seat so far.

^{6}270/4, as they now have three seats.

^{7}If this number is more than one, the voter must vote for several different candidates. These candidates do not have to be from the same party.

^{8}For instance, all parties who received less than 5% of the votes.

^{9}For instance, a party may have enough votes to avoid the above rule, but its candidates could each have less than, say, 1% of the votes each.