Tallyman

In Ireland, it is common for political parties to provide private observers when ballot boxes are opened.

These tallymen keep a tally of the preferences of visible voting papers and allow an early initial estimate of which candidates are likely to win in the drawn-out single transferable vote counting process.

[1] Since the public voting process is by then complete, it is usual for tallymen from different parties to share information.

Another possible definition is a person who called to literally do a head count, presumably on behalf of either the town council or the house owners.

The title tallyman extended to the keeper of a village pound as animals were often held against debts, and tally sticks were used to prove they could be released.