irish voting problem

I have a couple of issues with the way transfers are handled in Ireland.

The main problem I have is the way the surplus votes are transfer based on those last received pile of votes.

This leads to a random selection and not proportional representation at all. If we continue to use this method we need to change the name.

I found a very interesting paper on the Mathematical Aspects of the Irish Election that pointed out these problems and I'll attempt to visualise it as best I can.

Scenario 1
3 seater constituency, 39,996 votes and a quota of 10,000. And 5 candidates running.

The boxes are opened and the first count:



We know Dennis is VERY popular. So popular he has 2nd preference votes from ALL of Albert, Barry and Cian voters (28,990). The only people who don't like Dennis are Evan voters (2,006). They all voted exactly the same with Albert, Barry and Cian as 2nd, 3rd and 4th preferences.

Evan is eliminated and votes redistributed for the second count.



Albert is elected! Looking at his 12,000 votes, next preference candidates are Dennis (9,994 votes/83%) and Barry (2,006 votes/17%).

Count 3 and surplus of 2,000 is redistributed, but it is taken from the top, meaning that only the top 2,000 votes (which came from Evan) are redistributed, all going to Barry.



Barry is elected! Looking at his 11,001 votes, next preference candidates are Dennis (9,001 votes/81%) and Cian (2,000 votes/18%).

Count 4 and surplus of 1,001 is redistributed, but it is taken from the top, meaning that only the top 1,001 votes (which came from Albert, which came from Evan) are redistributed, all going to Cian.



Now Cian is elected and all 3 seats filled.

Having received the most 1st preference votes, and the vast majority of 2nd preference votes from the 3 runners up in count 1, Dennis fails to get elected.

Scenario 2
3 seater constituency, 19,996 votes and a quota of 5,000. And 4 candidates running.

The boxes are opened and the first count and John is elected on first count.



We know Paul is popular, almost reaching the quota.

Looking at John votes, the majority of 2nd preference votes go to George and Ringo for 3rd preference. But there is some support for Paul, giving him their 2nd vote. Perhaps 5% (300 votes) but they are hidden somewhere in pile of 6,000 votes.

Second count and the 1,000 surplus votes are taken from John's top pile and redistributed. Since this is random and just happen to be the last votes counted, these contain no votes for Paul.



George is elected! Like last time, the surplus of 501 votes, which came from John are distributed and all go to Ringo for count 3.



And Ringo is elected and all seats filled.

If you're interested in this I urge you to read the paper and question is this way of voting unacceptable?