UK European elections 2019: Remain candidates

2014 D'Hondt counting grid

Party1st seat2nd seat3rd seat4th seat5th seat6th seat7th seat8th seat
Lib Dem105,48752,74435,16226,37221,09717,58115,07013,186

Numbers are rounded and smaller parties have been left out for ease of reading.

2014 result

Labour, UKIP, Conservative, Labour, UKIP, Labour, Conservative, UKIP

How to read the grid

How do we get that result from this grid? First we need to understand the simple formula behind the D'Hondt system:

quotient = votes / (seats won so far + 1)

In other words, every party starts off with the full number of votes it received, and the first comparison is done between these votes. Look at the first column of numbers in the grid: the party that received the highest vote wins the first seat.

Now, for the second seat, we repeat the comparison, except that the winner of the first round now has its vote divided by 2 (the number of seats that party has won so far + 1).

So we're still looking at the first column of numbers for most of the parties, but the second column (marked '2nd seat') for that one party that already won a seat.

As parties win multiple seats, we move across to the other columns for that party only as the seat allocation continues.

The process is repeated until all seats available in this area have been allocated.

Isn't there an easier way?

Yes! Once you understand the grid, all you need to do is look at the highest numbers in the entire grid (the highlighted numbers) for however many seats there are. (For example, to allocate 8 seats, look at the 8 highest numbers overall.)