New York, long home to some of the more arcane, incumbent-protecting election laws in the country, has made rapid progress in bolstering the right to vote. In recent months, the State Legislature enacted early voting, passed a measure to automatically transfer a voter’s registration if she moves within the state and gave initial authorization for a constitutional amendment to make absentee voting easier.

But when lawmakers left Albany last month, some of the work remained unfinished — 31 election-related bills that have been approved by the Legislature but have not been signed by Gov. Andrew Cuomo.

The importance of at least one of those measures has become clear since last month’s Democratic primary for district attorney in Queens ended with a razor-thin margin that set off an automatic recount.

Tiffany Cabán, a public defender, declared victory on election night, June 25, with a margin of some 1,100 votes. But several days later, after election officials reviewed the roughly 6,300 paper ballots cast, Borough President Melinda Katz was ahead by 20 votes.