Original sentence: However, they now govern exactly the same territory, and have elections on the same ballot on Election Day in November of odd-numbered years; the officials of town and city interact essentially as do a single town's, or city's, officials, who have different but related responsibilities and powers
Edited sentence: However, they now govern exactly the same territory, and have elections on the same ballot on Election Day in November, the first Tuesday after the first Monday, of odd-numbered years; the officials of town and city interact essentially as do the officials of a single town or city who have different but related responsibilities and powers