Ireland has the distinction of using one of the most complex systems of voting in the world when it comes to a General Election.

Proportional Representation by Single Transferable Vote (PR-STV) is a system that, in the simplest terms, is designed to ensure that the percentage of seats a party gets in a parliament or assembly (the Dáil in Ireland’s case) is roughly equal to the percentage of votes it gets in the election.

This is achieved by giving each voter a transferable vote, whereby their vote can go to another candidate in the same constituency if that voter’s ‘first preference’ candidate does not require that vote (either because they are already elected or they have been eliminated from the count).

This system uses multi-seat constituencies, where each constituency elects multiple candidates. In Ireland, constituencies elect either three, four or five candidates.

This system is radically different from the ‘first past the post’ system used in the UK, where each constituency elects only one candidate. First past the post does not take account of party shares in the vote. Several UK elections have seen situations where a party’s share of seats in the House of Commons was far below their share of the vote.

When voting in Ireland, you do not mark the ballot paper with a tick mark or an ‘X’. Either of these would result in a spoiled vote (invalid paper).

Instead you rank candidates according to your preference. You mark ‘1’ next to your favourite candidate, ‘2’ next to your second favourite, and so on. You can just mark ‘1’ for your favourite candidate, and leave it at that, or you can fill up the whole ballot paper, ranking all candidates according to your preference. Just be sure not to skip or repeat a number.

The first count

When the votes are being counted in a constituency count centre, the counting proceeds in different stages. In the first count, the ballot papers are sorted into parcels of first preference ballot papers for each candidate. Invalid papers are excluded and not counted.

Before anyone can be elected, the quota has to be determined. This is the number of votes a candidate needs to be sure of election (although it is possible, in certain circumstances, for a candidate to be elected without reaching the quota).

To find the quota, the total number of valid ballot papers is divided by the number of seats for the constituency plus one, then adding one to the result.

So, for example, if there is 1,000 valid papers, and four seats up for grabs, the quota would work out at 201.

A candidate whose total of votes, at any time, is equal to or greater then the quota, is elected.

Subsequent counts

All subsequent counts involve either the distribution of votes an elected candidate achieved above the quota (the surplus); or the transfer of votes from candidates who have been eliminated.

As distributing the surplus is more complex, we’ll deal with that first.

A surplus will be distributed before the elimination of the lowest candidate if the surplus, in its entirety, could elect the next highest remaining candidate or bring the lowest candidate level with or above the second lowest candidate or allow the lowest candidate to recoup their election expenses (candidates can recoup election expenses by achieving a quarter of the quota).

Distributing the surplus

To distribute the surplus of an elected candidate, the counters look at the most recent parcel of votes that candidate received (the parcel that brought them over the quota). If the candidate got in on the first count, this parcel would consist of papers where they had first preference. On subsequent counts, the last parcel may consist of second or lower preferences transferred from other candidates.

This parcel of votes is divided into sub-parcels for each candidate indicated as a next preference. If a candidate got in on their first preferences, the counters look at the second preferences on those papers. If the candidate got in on their second preference transfers, they look at the third preferences on those papers, and so on.

The votes that have an available next preference are transferable papers. Those that do not are non-transferable papers.

What happens next depends on whether the number of total transferable papers is greater than; equal to; or less than the surplus to be distributed.

In the last two of these scenarios, the process is pretty simple: the sub-parcel for each candidate receiving a next preference vote is added to their overall stack of votes.

However, in the case of the transferable papers being greater than the surplus, candidates can only receive a portion of the papers in their sub-parcels.

This portion is arrived at by dividing the surplus by the number of total transferable papers, and multiplying that number by the number of papers in each candidate’s sub-parcel. The result is then taken from a candidate’s sub-parcel and added to their total votes.

This would almost certainly result in a fractional number of papers to be transferred to a candidate, which is not possible in this method of voting. To resolve this, a candidate is transferred the ‘full’ papers (before fractions are taken into count). Then, the candidate with the highest fractional value is given another vote, with the same being applied to other candidates with a fractional value of transfers to be distributed (in descending order of the fractional values) until the entirety of the surplus is distributed.

Exclusion of lowest candidate

The exclusion of the lowest candidate is a far simpler process. If, after a count, there are no votes to transfer, the candidate with the lowest number of votes is eliminated from the count and cannot be elected. All of their transferable votes are distributed according to the next preferences on the ballot papers attributed to them.

If that distribution, in its entirety, is not enough to  bring the second lowest candidate level or above the third lowest, and would not entitle them to recoup their election expenses, they are also eliminated and their votes distributed.

The final seat

This entire process continues until such a time as all seats are filled by elected candidates who reached the quota, or until a candidate (or candidates) is/are deemed elected without reaching the quota.

This would happen in a scenario whereby a number of candidates equal to the amount of seats yet to be filled have enough votes that they cannot be overtaken by lower candidate, taking all distributions and surpluses into account.

After this, all seats are filled, and the count is over. Unless there’s a recount. Don’t get us started on recounts.