The media occasionally give the idea that tallymen (and the media always write about tallymen) are a breed apart, able to look at a box of votes and tell you how many number 1’s are in it for each candidate While this would be a useful skill, it is entirely mythical. Tallys, or tally marks, are just an old system of counting. They have been in use, probably, for many millennia. In the vote counts in Irish election, the ‘tally’ is a running total of the votes cast in each ballot box. These are collected by volunteers whose legal role is to check the validity of the ballots.
Back up a step. When you vote in Ireland, you put your ballot paper into a box. Each box covers a certain area on the ground, maybe one housing estate, a few streets, several townlands, or even an entire village. The very first step in a count, is to take that box, inspect the seal, and open it, pouring the ballot papers onto a table. The papers are then removed one-by-one from the pile, placed face upwards on the table, and the total number of votes in that box is counted.
When they are placed face up on the table, the tally people look at each ballot to check two things. Is it a valid ballot, and for whom was the first preference vote cast on that ballot? Typically the tally people have a sheet, laid out in the same order as the ballot paper, with a table printed on it. A tally (or to be exact, a tally mark, a vertical stroke) is put beside the name of the candidate who got that vote. At the end of the process, hopefully, there is one tally for every vote in the box, and you know, quite accurately, where the first preference votes have gone from that box. Pooling these counts together for a constituency gives the tally for that constituency. These are accurate estimates of the first preference votes.
Finally, the count staff bundle the votes, usually into piles of 100 votes, held together with rubber bands. Then the bundles of votes from different boxes are mixed, and the count proper begins.
All of this has two effects, first there is a public, widely reported preliminary count. Second many kinds of wholesale ballot rigging become impossible or very very difficult. Irish elections are not perfect, but they are democratic, and the count reflects, very accurately indeed, how the Irish people have chosen to vote.