# The d'Hondt voting system for European Parliament

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 electorate1 is split up into 'constituencies,' depending on where in the United Kingdom the voters live. Several political parties2 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:

1. Take the highest number of votes in the present table and award a seat to that party
2. 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)
4. 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 two3 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 three4 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 two5 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 67.56:

 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 cast7. 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 percentage8 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 individually9 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.

1The voting public2Including independent candidates who, for the purposes of this system, are taken to be a party with a single candidate.3The number of seats awarded to Party One so far, plus one.4The number of seats awarded to the party so far plus one.5As the party only has one seat so far.6270/4, as they now have three seats.7If 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.8For instance, all parties who received less than 5% of the votes.9For 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.

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