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Compared to the 0.228 average for all U.S. districts, Maryland came in at 0.081.

“The governor has given us a lemon of a map,” Mr. Parrott said. “You can’t really get any worse than this map.”

Michael McDonald, co-project leader of the Public Mapping Project and an associate professor at George Mason University said what was curious about the referendum was that at its heart, “it tells you the amount of money [Republicans] are willing to invest in trying to change the outcome of one congressional district, and even then it’s not a guarantee,” he said. “In the end, I think it’s a sign of the times how flush with cash the parties are.”

Looking to November, Mr. Parrott acknowledged that the petition was “not an emotional issue but it’s a logical issue,” a fact not lost on the redistricting experts.

“The map itself is such a detail-oriented thing and redistricting is not an issue people are thinking about,” said Tim Storey, a redistricting analyst for NCSL. “Your average people going to work every day, they care a lot about police, schools, health care, street lights; very tangible, real things. The things they do in Annapolis like redistricting, are a step removed from people’s everyday lives.”

Mr. McDonald said the referendum process wasn’t the best method of reform, and saw it more as “an unending game of passing a new map, referendum, passing a new map, referendum.”

But the uncommon quality of the referendum could have far-reaching effects, he said.

“If this succeeds, if Marylanders reject this map, it may just be that tipping point necessary to bring about national reform.”