I've converted and reformatted the 20161216.xlsx spreadsheet cited in Brythan's answer to a more portable CSV format, named 20161216.csv. The reformatting consisted of adding another field, "Election", correcting some typos, (mispellings of Committee, odd spacings), and made some field item synonyms more consistent. These changes enable using Linux utils like
csvtool for easily replicated views.
Of the 112 ties and one-vote differences:
None of the votes address matters of even statewide importance.
Of the 112 elections, 43 were ties, and 69 differed by one vote.
How many votes on average were cast? Unknown, since the spreadsheet doesn't provide vote counts. I've located one of the elections mentioned in the spreadsheet online, with 225 votes cast:
SUMMARY REPT-GROUP DETAIL Summit County, Ohio *Amended Official Results
Board of Elections
11/03/15 General Election
Run Date:12/28/15 11:46 AM
TOTAL VOTES % ABSENTEE POLL TIMELY ABS PROV
Issue 25 - Akron 3-G - Proposed Local Option
Beer, Wine, Mixed Bev and Spirit. Liq., Copley Mini Mart
(Vote for not more than ) 1
(WITH 1 OF 1 PRECINCTS COUNTED)
NO. . . . . . . . . . . . . 113 50.22 21 90 0 2
YES . . . . . . . . . . . . 112 49.78 16 92 1 3
At the polls, (including provisional ballots), it won 95 YESes to 92 NOs. But the absentee ballots turned it the other way by one vote.