Representative Don Young, for example, a Republican who has represented Alaska’s lone House district since 1973 and is running for re-election, is considered a master of the personal touch and has a goal of shaking every Alaskan’s hand. He is still working on it, though there are more hands now to shake, with 735,000 residents in Alaska, more than double the number when Mr. Young first ran for office.

Mr. Sullivan and Mr. Begich will each try to assemble a coalition on that landscape, politicians and residents said. Mr. Sullivan will be working to woo libertarians and voters who hate Washington and think its bureaucrats overly restrict development of mineral resources; Mr. Begich will try to attract rural voters and supporters of abortion rights.

The urban areas, especially Anchorage, will decide the contest, people in both parties said, with the ability to make a personal connection with voters being the determining factor. The cities have oil industry workers who might lean toward Mr. Sullivan’s more conservative approach, but liberals and newcomers may lean toward Mr. Begich, and there are lots of independents who could go either way.

Whether television advertising even works well in Alaska is also an open question. The primary campaign that finished Tuesday was the most expensive in state history, with outside groups pouring in millions of dollars in support or attack. Though there are few good independent polls, a spokesman for Mr. Begich, Max Croes, said that because the campaign had responded forcefully to attacks, not a lot of opinions seemed to have changed.