Falk was the the Democratic nominee for Treasurer; it seems his name was swapped with that of Johnson on some ballots in Brown County.
Candidates' party affiliations obtained from the 11/4/1881 Iowa County Democrat. https://chroniclingamerica.loc.gov/lccn/sn86086852/1881-11-04/ed-1/seq-1/
Source for Popular Vote data: Wisconsin Board of State Canvassers, "Secretary of State," Tabular Statement of the votes...at the General Election (Madison, 1881)