Requirement 2 is achieved with the use of a ballot paper and ballot box. The ballot paper acts as a kind of token indicating that the holder has been authenticated, but which gives no clue as to their identity. The ballot box ensures that the voter's paper cannot be viewed by anyone other than the voter himself.
Requirement 3 is met by providing a paper with a simple and familiar interface. During the vote collection phase, ballot boxes are at all times visible to polling station staff and interested observers. Their transport is supervised by members of the Garda Síochana and representatives of running candidates - or sides, in a referendum. This means that requirement 4 is fulfilled because any manipulation of the ballots would be detected. The tabulation process involves many people, again being supervised closely. The ballots are retained so that they can be used in recounts. The combination of the two fulfills requirement 5.
The sixth and final requirement is fulfilled, again by the fact that the whole process is supervised. The familiarity of the electorate with the system, and their belief that it has worked up until now also contribute to their confidence.