‘’Hi. This is Dr. Cora Stack again. I'm still on a roll with my trying to explain the mathematics behind Ireland's PR-STV voting system.’’
Mairead Kenny: Hello everyone. Mairead Kenny, Politics and More podcast. I'm here with Dr. Cora Stack. We’re talking about Ireland’s PR-STV Electoral Voting System. That’s the proportional representation - Single Transferable Vote electoral system. Ireland uses a Proportional Representation (PR)[1] system[2] for voting in elections, with each voter having a Single Transferable Vote (STV). We saw this in action in the recent Dublin Central[3] and Galway West[4] Bye-Elections[5]. This podcast explains the operation and maths behind this. I’m talking to Dr. Cora Stack whose an expert in Mathematics! Welcome Cora.
Dr. Cora Stack: I will explain the mathematics behind the PR-STV system hopefully in a clear and logical way.
Mairead Kenny: PR-STV is a candidate-based system. This means voters can choose to vote for as many, or as few candidates as they like, in order of their preference. The voter’s first preference vote, the candidates they give their number 1 vote to is most important and is always counted.
A voter’s second and further preferences may be counted if their preferred candidate is eliminated at the end of a round of counting or if their preferred candidate is elected with a surplus. These are known as transfers. Transfers will be explained also in this podcast.
Continued in Transcript.
Dr. Cora Stack, The Mathematics Behind Ireland’s PR-STV System: Valid Votes, Quotas, Transfers, Surpluses, and Election Counts available here.
http://maireadkenny.ie/wp-content/uploads/2026/05/The_Mathematics_Behind_Irelands_PR_STV_S.pdf
Dr. Cora Stack, Explaining PR-STV in Ireland: Valid Votes, Quotas, Transfers, Surpluses, and Election Counts available here.
http//maireadkenny.ie/wp-content/uploads/2026/05/Explaining_PR_STV_in_Ireland_Valid_Votes.pdf
Dr. Cora Stack, The Droop Quota in PR-STV: The Least Threshold Sufficient to Secure Election.
http://maireadkenny.ie/wp-content/uploads/2026/05/The_Droop_Quota_in_PR_STV_The_Least_Thre.pdf
[1] https://www.citizensinformation.ie/en/government-in-ireland/elections-and-referenda/voting/proportional-representation/
[2] https://www.electoralcommission.ie/irelands-voting-system/
[3] Dublin Central Bye Election, Notice of Poll, 14 Candidates at https://www.dublincityreturningofficer.com/index.php/dublin-central-bye-election-2026/78-notice-of-poll-may-2026
[4] Galway Central Bye Election, Notice of Poll, 17 Candidates at https://galwayreturningofficer.com/by-election-galway-west-2026/notice-of-poll-may-2026
[5] https://data.oireachtas.ie/ie/oireachtas/communications/education/2026/2026-05-19_what-is-a-bye-election_en.pdf
https://www.citizensinformation.ie/en/government-in-ireland/elections-and-referenda/voting/proportional-representation/
https://www.electoralcommission.ie/irelands-voting-system/
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