Understanding the D'Hondt Method: Its Use in the Northern Ireland Assembly

What is d’Hondt?

The d'Hondt method is a mathematical formula used worldwide in various electoral systems, including the Northern Ireland Assembly.

The d'Hondt method is named after Belgian lawyer and mathematician, Victor d'Hondt, who developed it in the 1880s as an attempt to better accommodate different linguistic groups and political traditions in the Belgian parliament.

The method assigns seats or positions based on the proportion of votes each party receives in an election. It does this by repeatedly calculating a quotient for each party and giving the next seat or position to the party with the highest quotient. This enables power to be distributed among parties according to their size, which is important in a diverse political landscape like Northern Ireland.

How does it work?

Originally, the d’Hondt method was used to determine the number of seats that parties were allocated in a legislature. The d’Hondt formula was calculated across a number of stages or rounds depending on how many seats were available. A quotient for each party was determined at the beginning of each round and the party with the highest quotient was allocated that seat.

The d’Hondt quotient is calculated as V / (1 + S) where V is the number of votes a party has and S is the number of seats they held at the beginning of the round.

In the first round S will be 0 for every party, effectively meaning that the quotient for every party will be the number of votes that they received in the election. Therefore, the party with most votes is allocated the first seat. This party’s quotient is then re-calculated for the next round. Their quotient will now be S / (1 + 1). This means that the only quotient that will change from one round to the next is the one for the party that came out top in the previous round.

The formula is recalculated for as many rounds as are required (in other words, the number of seats that are available) and the party with the highest quotient at the end of each round is allocated the seat.

When does the Assembly use d’Hondt?

The Northern Ireland Act 1998 requires that the Assembly uses the d’Hondt method when allocating Ministerial positions to the Executive (after the offices of First Minister, deputy First Minister and  Justice have been filled) and also when allocating the Chairpersons and deputy Chairpersons of Assembly committees.

The method allows these leadership positions to be allocated proportionately according to the number of seats that each party won in the Assembly election.

D’Hondt is also used informally to achieve party balance according to size in a range of other Assembly procedures. However, d’Hondt is not used  to determine the 90 MLA seats available in the Assembly after an election is held. This is determined by the single transferrable vote system. It is also not used to allocate the positions of First Minister and deputy First Minister nor the office of the Minister of Justice. First Minister and deputy First Minister are nominated by the largest parties within each of the two largest political designations. The office of the Minister of Justice is filled by an election process during which any Member may nominate another Member for the position which must be agreed by the Assembly with parallel consent in a cross-community vote.

Illustrative example of an Executive being formed

Let’s look at an example of how an Executive might be formed based on a fictional party make-up of the Assembly. Please note that this example is for illustrative purposes only.

Fictional Assembly make-up

The table below shows the party make-up of a fictional Assembly after an election:

This example assumes that the largest Nationalist party (and the largest party overall), Party A, has nominated the First Minister and the largest Unionist party, Party B, has nominated the deputy First Minister and both have affirmed the terms of the pledge of office.

It also assumed that, after the passing of a cross-community vote with parallel consent, an MLA from Party C has been allocated the Minister of Justice position. There are now seven remaining positions in the Executive and they will be allocated using the d’Hondt method.

The d’Hondt formula is S / (1 + M) where S is the number of seats held by the party on the day on which the Assembly first met after the election and M is the number of Ministerial positions that they have, if any. At the start of the process, M is zero for every party other than Party C who already occupies the Minister of Justice position and whose M value is therefore 1.

The d’Hondt process therefore runs as follows:

Notice that in round 3, Party D and Party E had the same quotient. In this event, the choice goes to the party that received the most first preference votes in the Assembly election. In this case, Party D received more first preference votes than Party E and was offered the next choice of Ministerial positions.

In this fictional Assembly, no party declined the opportunity to take a position in the Executive. The final make-up of this Executive is:

• Party A nominated the First Minister and had first choice and fifth choice of the remaining positions. 3 positions in total.
• Party B nominated the deputy First Minister and had second choice and sixth choice of the remaining positions. 3 positions in total.
• Party C holds the position of Minister of Justice and was offered the final choice of ministerial position. 2 positions in total.
• Party D was offered the third choice of positions. 1 position in total.
• Party E was offered the fourth choice of positions. 1 position in total.

Allocating Ministers in the Executive

Seven Ministerial positions within the Executive are determined by d’Hondt. The Minister of Justice position must be filled before these Ministers may be appointed. Even though the Justice Minister is elected rather than appointed, the party allocated the position is included in the d’Hondt formula.

When initially devolved the Justice Minister position was not subject to the d'Hondt formula for allocating ministerial positions within the Northern Ireland Executive. This changed when the Northern Ireland (Miscellaneous Provisions) Act 2014 came into force in September 2014.

The d’Hondt formula for allocating Ministers to the Executive is S / (1 + M), where S is the number of seats held by members of the party on the day on which the Assembly first met following its election and M is the number of Ministerial positions that they have, if any.

Therefore, in the first round, M will be 0 for every party other than the party from which the Minister of Justice was just appointed. In their case M will be 1, effectively halving their quotient for the first round while every other party’s quotient remains the same as the number of seats that they have.

The party with the largest quotient at this point is offered the first pick of Ministerial positions before their quotient is re-calculated for the next round. This means that the only quotient that will change from one round to the next is the one for the party that came out top in the previous round.

The Ministerial position that a party chooses with their pick is completely up to that party. However, it should be noted that there is nothing that requires parties to take a seat in the Executive — they can refuse and the seat will be offered to the next eligible party with the next highest quotient. In effect, there is no legislative barrier to parties not taking their allocated seat following an election or withdrawing from the Executive if they wish.

As seven Ministerial positions need to be filled, there will be seven rounds of d’Hondt to determine which party is next to be offered a Ministerial position from those that remain, and then nominate a Minister from within their party.

Further reading

In 2013 the Assembly’s Assembly and Executive Review Committee undertook a Review of d’Hondt, Community Designation and Provisions for Opposition.

In relation to d’Hondt, the Committee concluded that there was no consensus on ceasing to use or replace the current d’Hondt system as the mechanism for allocating Ministerial positions or Committee Chairperson/Deputy Chairperson.

• Section 18 Northern Ireland Act 1998
• Northern Ireland Assembly Standing Order 44
• View the Committee’s full report.
• Read the debate in Plenary about the Committee’s report (2 July 2013).

Watch the Assembly Education Service’s video on the Assembly and Executive which includes a clear and concise description of the d’Hondt process and how it works: