Monday 29 February 2016

Proportional Representation in Ireland

I am not connected with politics or constitutional law in any way. I wrote this page really as an excuse to study up on something I found interesting. I have done my best to ensure that the content is accurate but if you do find any glaring errors please let me know and I will correct them. If you have any general comments/observations/suggestions about the page, I'd love to hear those also. Thanks.


Since achieving independence in 1921, we in Ireland have elected members to The Dail (one of our Houses of Parliament) using a system of voting called Single Transferrable Vote (article 16, section 2, subsection 6 of The Constitution). The purpose of this page is to explain exactly how this system works, to explain why many political scientists regard it as one of the fairest systems for conducting elections and to examine some of the mathematical anomalies which can arise from it.

Single Transferrable Vote

The basic idea underlying the Single Transferable Vote system of Proportional Representation is that any votes a candidate receives over and above the minimum necessary to be elected should not be wasted. Rather, the voters should be allowed to rank the candidates in order of preference, and any surplus votes a candidate has after being elected should be distributed to the remaining candidates in proportion to the next-highest preferences expressed by each voter.

Some history of the system to go here !

How It Works

The Vote

Voting is simplicity itself. The ballot paper will look something like this:-

Byrne, Gay
Independent Candidate
Haughey, Charles J.
Fine Gael
Lawler, Liam
Progressive Democrats
McGonigle, Eamonn
The All Night Party

The voter simply writes a number beside each of the candidates (or as many candidates as they wish) indicating the order of preference. The voter's favourite candidate will get a preference of 1, the second favourite will get a preference of 2 and so on.

Determination of the Quota

Once the voting is complete, the process of counting the votes begins. The first step is to determine the quota. This is the minimum number of votes which would be sufficient to elect only the desired number of candidates. It is a factor of

  • The number of votes cast
  • The number of people who are to be elected
It is calculated by taking the number of votes cast, dividing this by (1 + the number of seats to be filled), adding 1 to this result and discarding any fractional part. So in an area where 10,000 votes were cast and there are 2 seats, the quota would be 3,334 (= 10000 ÷ (1 + 2) + 1). It should be clear that with only 10,000 votes, it is possible for two candidates to obtain 3,334 votes, but not possible for three.

The First Count

During the first count, all of the first preference votes are counted. At the end of this, one of two things will have happened:-

Possibility #1: One or more of the candidates has reached the quota

These candidates are elected. The next step is to distribute their surplus votes (the number of votes they received over and above the quota). The idea is that these "spare" votes should not be wasted and should be transferrable to the voters' second choices

Possibility #2: None of the candidates has reached the quota

In this case, the candidate with the lowest number of votes after the first count and his/her votes are distributed to the voters' second preferences

Either way, the next step is to proceed to a second count for the purpose of distributing the surplus of the elected candidate or distributing the entire vote of the eliminated candidate.

The Distribution of the Surplus or The Elimination of the Lowest Ranking Candidate

Once a candidate is reaches the quota, any excess votes are distributed to the other candidates in proportion to the next preference votes of the elected candidate. A simple example: Assume that the quota is 3,334 (from our earlier example). Assume also, that candidate Charles J Haughey gets 4,000 votes on the first count. None of the other candidates reaches the quota at this stage. He is deemed to be elected and a second count begins for the purpose of redistributing Charlie's surplus.

At the end of the second count, it turns out that of those 4,000 voters who gave Charlie their first preference, 2,000 gave their second preference to Liam Lawler, 1,500 gave their second preference to Gay Byrne, 400 gave their second preference to Eamonn McGonigle and the remaining 100 didn't express a second preference at all.

Since the quota is 3,334, Charlie has 666 surplus votes to distribute (= 4,000 - 3,334). These will be distributed to the other candidates in the following proportions:-

CandidateTransfers from Charles Haughey
Liam Lawler(666 ÷ 4,000) × 2,000 = 333
Gay Byrne(666 ÷ 4,000) × 1,500 = 249
Eamonn McGonigle(666 ÷ 4,000) × 400 = 66

These transfers are added to each candidate's total from the first count. At this stage, the process begins again: If any candidate has now reached the quota, he/she is elected and another count begins for the purpose of distributing his/her surplus. If no candidate has reached the quota, the lowest candidate is eliminated and the next count will redistribute his/her vote to the next voters' next preferences.

There are some subtleties that arise in the distribution of quota which lead to a small element of randomness.  It can happen in three different circumstances, the most common of which is where voters haven't ranked all of the candidates (i.e. haven't written any number down against some candidates).  In that case, there may be excess votes available to be distributed (e.g. Charlie's surplus of 666) but some of those votes might not indicate a next preference.  Its probably not useful to delve into this in too much detail here: there is a very interesting analysis of this here, including an example (the Sligo-Leitrim constituency in the 1982 general election) where this randomness actually made a difference.

Interestingly, during Ireland's brief and ill-fated dalliance with electronic voting in 2002, the same random mechanism had to be built into the (electronic) counting system, even though a computer could have performed the count using a more accurate (but impractical for a manual count) system.

The Final Result

The final result is arrived at either when either:-

  • The desired number of candidates have reached the quota
  • The number of candidates remaining after the elimination of the lowest-scoring candidate at the end of a count equals the number of unfilled seats

This can happen because voters may not rank all of the candidates on the ballot paper. In our earlier example, the 100 voters who did not express a second preference will not have made any contribution to the second (or any subsequent) count.

But Is It Democratic...?

This system is regarded as among the fairest systems of the electoral systems in use in the world today. However, it is not without its imperfections. These are discussed in some length in put book reference here in considerable detail.