Can someone please dumb down how the voting system works. How are quotas decided upon, how are surplus votes distrubuted etc

Lets say, first preference votes in a 5 seat cons.

x has 12,200

y has 7,800

z has 7,400

a has 4,300

b has 3,600

c has 2,100

d has 1,700

e has 1,000

f has 670

g has 410

h has 200

I has 120

I'll explain it using two different examples.

Last time out in Roscommon the total valid poll was 45680, and three seats were available. Therefore you divide 45680 by four (the number of seats plus one) and added 1 to the divided figure, to ensure that four candidates could not possibly reach the quota, i.e. 45680 / 4 = 11420, add 1 = 11421.

In that first count Denis Naughten sailed home with 13936 votes, putting him over the quota by 2515. Therefore his surplus was to be distributed on the second count of 2515. To do this they would check all of Naughten's 13936 votes, see how many votes transferred to each of the other candidates, get their totals and divide it into 2515 to get the proportionate amount to be given to each in the second count. As Naughten was an Independent this vote scattered a little, with Fitzmaurice getting the most (1214), followed Hopkins and Murphy, with the rest receiving small transfers. The contentious aspect is what happens to the surplus votes, as I understand it the votes to be added to the other candidate's piles are taken at random, i.e. they'd take any 1214 of Naughten's No 1's that went No 2 Fitzmaurice and add them in a separate bundle on top of Fitzmaurice's pile.

If every one of Naughten's No 1's were transferable then Fitzmaurice would have got 48% of Naughten's No 2's, about 6727. However it is possible that Naughten got a few No 1's that were "plumpers", i.e. just 1 for him and no other preference. But so long as at least 2516 of Naughten's votes transferred at all then those plumpers would be irrelevant and a calculation would have to be made, unlike in the later example.

Next door in Sligo/Leitrim there were two different examples of how the surplus can work. On the 11th count the Leitrim FF candidate Paddy O'Rourke was eliminated, and his transfers of 6,083 were the 12th count. So his votes would have both a party transfer and a Leitrim/local transfer element. So that count went as follows:

MacSharry (FF, Sligo town) plus 1707, total 13227 (exceeding the quota of 12468)

Reynolds (FG, Leitrim) plus 1171, total 10092

Kenny (SF, Leitrim) plus 1323, total 9294

McLoughlin (FG, Sligo) plus 112, total 10167

Scanlon (FF, South Sligo) plus 1323, total 9145

MacManus (SF, Sligo) plus 48, total 7093

MacSharry was elected but his surplus of 759 would make no difference, as it couldn't elect anyone and MacManus was too far behind to catch Scanlon or Kenny. So he was eliminated and his votes distributed. As these were SF votes and added to by Sligo town left wing transfers then Kenny was going to be the obvious beneficiary, though McLoughlin and Scanlon could pick up some of the Sligo-minded votes here too:

Reynolds +85 total 10177

Kenny +4772 total 14066 (elected)

McLoughlin +362 total 10529

Scanlon +409 total 9554

So Kenny was elected with a surplus of 1598, and as this was higher then MacSharry's, and it was now down to two seats between the three remaining candidates, it was distributed. This is where the other example I mentioned above comes in. Because it is often the case that party transfers may go 1-2-3 and no further, and especially with SF votes, then there is a possibility in later counts that not all of the surplus is transferable for the reason below.

The Kenny surplus was counted by checking only the 4772 votes that he received from his running mate MacManus in order to exceed the quota,

not all of his 14066 votes when he was elected as some might think. So they checked those 4772 votes and sure enough many didn't transfer any further, and as it happened the number that were transferable was less than 1598. So instead of doing a calculation of the votes received by each candidate and allocating the surplus proportionally, each vote that the remaining candidates got was effectively a whole vote, as follows:

Reynolds +139 total 10316

McLoughlin +381 total 10910

Scanlon +631 total 10185

Non transferable 447 - but in reality this was 3621 of the 4772 votes that didn't transfer, which meant that the candidates got 100% of the transfers that they actually got off that surplus. And as it was largely Sligo-based to begin with then Scanlon got most, with the added bonus of being FF rather than FG, and McLoughlin got a chunk too.

So the last count was to transfer the surplus MacSharry got of 759 from the first count listed above, which was the 1707 votes he obtained from his FF running mate in Leitrim. And so despite the fact that he trailed going into this count and had looked to be all but gone prior to O'Rourke's elimination, Scanlon was home and dry as these votes had already gone FF 1 FF 2, so they were almost certain to go No 3 as well:

Reynolds +101 total 10417

McLoughlin +21 total 10931

Scanlon +637 total 10822

Here the full 759 surplus was transferable which indicated that the bulk of those votes did continue past 1-2, so Scanlon could have got up to 1433 of the O'Rourke-MacSharry transfers out of the 1707 such votes. Reynolds as a Leitrim candidate did peel off some of those votes, but it wasn't enough to hold on, and with no other votes remaining to transfer McLoughlin and Scanlon were elected without reaching the quota.

It's a rather convoluted way of explaining it I know but this does hopefully show the different factors in how the counts can pan out.