It really wouldn't at all. Couple ideas for in person and counting.
Paper ballots (never a touch screen)
No electronic counters at all. (Never be able to ensure not hacked.)
Tight ballot control at collection, open for public viewing.
Only moved at certain times and public invited to watch it.
Counting room - parcel out votes into package (example 50 ballots). HD overhead camera watching each counter. Multiple counters (not seated by each other) count the same parcel of votes until there is sufficient statistical agreement. Counters do not know who next counter will or what previous count was. (Count have a basic electronic entry or some paper slip that it given to a supervisor to verify agreement.)
Once statistical agreement is reached on a parcel. Its added to total.
Once added to total. Tight and open to public 24/7 viewing of the storage. Ready for recount.
Not sure if this would work also, but a coupon (something printed hard to counterfeit like money) you take with you of a serial number of your ballot. Openly post on internet the votes for a serial number. Can go view your vote and make sure its logged correctly. If not, you go and they find the paper, match it up to unique coupon and look at why its wrong.
Bad statistics for a counter? Watch the video to see if criminal and a minimum remove them.