Introducing last night’s debate between the four candidates competing to take the state house seat being vacated after 20 years by Eric Turkington, host Judy Crawford noted the absence of a Republican candidate as a complicating factor.

The choice would have been much easier, said the president of the League of Women Voters of Martha’s Vineyard, if the contest was simply between a Republican and a Democrat. But the presence of three independents made the whole thing far more complex.

And foremost among the complexities was the question of how many independents there really are in the race, and how many Democrats. If there was one recurring motif and one issue that provoked a little heat during the generally amiable debate, it was the question of who was a “real” Democrat.

Dan Larkosh of West Tisbury, the candidate who won the September primary and has the backing of the party machine, including the state governor and a host of unions, insisted it was him. He suggested he was more deeply Democrat than any of the others, although he also suggested everyone on the stage was essentially one.

Then there is the independent Tim Madden of Nantucket, who has worked for the past decade as legislative liaison for Representative Turkington, and who ran as a write-in candidate in the Democratic primary. Even as a write in, he swept Nantucket in September, losing to Mr. Larkosh 1,722 votes to 1,401, and he will sit as a Democrat is he wins.

Melissa Freitag of Falmouth, who is now unenrolled, but who also will register as a Democrat if elected, bridled at Mr. Larkosh’s suggestion that she was not the genuine party article.

Jacob Ferreira of Vineyard Haven is a true independent, but on the issues last night he was virtually indistinguishable from the three Democrats except for his support for the death penalty.

The contenders were asked first how they distinguished themselves from one another.

Ms. Freitag stressed her academic background (she is currently a teacher of government and history at Cape Cod Community College), saying that made her capable of researching and negotiating, which suited her to helping keep the state at the “forefront of progressive legislation in the country.”

Mr. Madden recited his record of service as legislative liaison, as chairman of the Nantucket selectmen and on numerous town committees, as well as experience as a business owner and manager. He knows how to work with people, he said.

Mr. Larkosh relied on his deep Democratic roots, his outspoken opinions on issues, and his background as a lawyer representing working families.

And Mr. Ferreira cited character and leadership abilities. He has a bachelor of science in business administration and a master’s in leadership. His education and military background (he was a Coast Guard officer) prepared him for the challenges of government, he said.

In light of the $1.4 billion state budget cut announced this week, candidates were asked to name their spending priorities.

Mr. Larkosh nominated local aid for protection, and said he would look to merge areas of different departments to reduce administration costs. He said he would cut funding for a smoking cessation program.

Mr. Madden said he thought Gov. Deval Patrick had targeted his spending cuts well. Local aid, schools and health spending should not be touched, he said.

Mr. Ferreira said he would protect funding for law enforcement, for small business and entrepreneurship.

Ms. Freitag was the most specific. She said education, health and emergency services should be quarantined from cuts, and was enumerating various small local programs like $500,000 for a new boat ramp in Falmouth and $1 million for an underwater archeology project, when her time to answer ran out.

Next came the casino question.

Mr. Madden is firmly opposed to casino gambling. Mr. Larkosh opposes gambling as a revenue raiser, calling it pernicious and devastating to families. Of $12 million spent on scratch tickets on this Island, he said, only $300,000 came back. Think what could be done for affordable housing with $12 million, he said. But he was more open to the idea of the Wampanoags getting a casino.

Ms. Freitag said people should have the right to gamble, although she said it is not part of her personal values. Mr. Ferreira confessed to a bit of gambling and said he didn’t buy the social ills argument.

Candidates also answered questions about offshore power generation, and the state’s efforts to regulate it through the new Oceans Act.

On the controversial Cape Wind project, Mr. Larkosh is unequivocally in favor of it. Ms. Freitag also backs it; Mr. Madden opposes it, and Mr. Ferreira said he had concerns, but that it was hard to stand in the way of the project.

All four said the new Oceans Act should and would give full regulatory power over future energy projects within three miles of the shores of the Vineyard to the Martha’s Vineyard Commission. Mr. Larkosh said he supported a move to grant similar regulatory powers to Nantucket.

On the Steamship Authority, an issue on which Mr. Larkosh is under considerable pressure, he sought to distance himself from a statement he made during his primary campaign that he supports a state takeover of the boat line.

“I want to make it clear I absolutely do not support any dilution of . . . control

of the Steamship Authority,” Mr. Larkosh said.

The other three candidates supported the status quo for the SSA, although Ms. Freitag said she would like to see the boat line engage in “a little more dialogue” with other parties.

The candidates were asked about their views on charter schools, and whether there should be a separate line item in the state budget for them.

Once again, Mr. Larkosh was the odd one out; he said the idea had merit. Mr. Ferreira expanded his answer to relate to educational opportunities more generally on the Island, saying he would like to see more education here for law enforcement officers, teachers and medical staff.

All four candidates vehemently oppose a question on the November ballot to eliminate the state income tax. They agree on the need for a housing bank, although Ms. Freitag had concerns about its introduction in the current economic climate.

In the end the candidates were invited to quiz one another. Ms. Freitag asked the others to outline what they had personally done to reduce their carbon footprints. Mr. Ferreira mentioned his business venture, growing sustainable vegetables. Mr. Larkosh mentioned new insulation and low energy lights in his house, while Mr. Madden regaled the audience with a description of a new dual-flush toilet.

Answering her own question, Ms. Freitag said she cycles to work, uses biofuel to heat her home and recycles campaign materials.