Posts in the Northern Ireland executive are allocated according to the
, a type of proportional representation.
The total number of votes a party receives from the electorate is divided by a figure which increases as the party wins more ministerial positions.
The first divisor in the first round is one, allowing the party with the most votes to take the first ministry of their choice.
After that, the divisor will be one - plus the number of posts allocated.
So the next choice of ministry is likely to go to the second party, because the votes received by the first party will be divided by two (one - plus one representing the number of posts allocated) while the second party has not yet had the number of its votes divided.
As the divisor gets bigger, the party total gets smaller, thus allowing parties with fewer votes to win ministerial positions.
The D'Hondt system is also used to allocate 56 seats in the Scottish Parliament.
As well as voting for a constituent MSP, who is elected by the first-past-the-post method, voters in Scotland have a second vote which they can use to choose candidates from a party list.
Scotland is divided into eight regions. The second votes in each of these regions are distributed among the list candidates according to the D'Hondt system until seven MSPs have been elected per region.
The system is named after its creator, Victor D'Hondt (1841-1901), a Belgian lawyer and mathematician.