Updated: 11:48 p.m.

GOP Senate candidate Joe Miller filed suit Tuesday to keep Alaskan election officials from using their discretion in evaluating write-in votes in the race, the Associated Press reported Tuesday night.

Sen. Lisa Murkowski opted to pursue a write-in re-election campaign after Miller defeated her in the GOP primary. Write-ins held an overall lead of 11,557 on Tuesday, after Miller gained 1,882 votes over the write-in candidates following a count of early-cast and absentee ballots, the AP reported. It remains unclear how many of the write-in ballots are for Murkowski and how many are for the 159 other write-in candidates.

State officials have said they will exercise discretion when determining voter intent on write-in ballots, saying case law bolsters their stance. Miller’s campaign argues that state law establishes two criteria for a write-in vote to be counted: The ballot oval must be filled in, and either the candidate’s last name or the name as it appears on a declaration of candidacy must be written.

The Miller campaign seeks a hearing Wednesday for its suit. Election officials plan to begin counting write-in ballots Wednesday, and Lt. Gov. Craig Campbell, who oversees elections, told the AP that they would proceed as scheduled. A spokesman for the Alaska Division of Law had no immediate comment.