Former U.S. Sen. Mark Begich announces that he’s staying in the race for governor in Anchorage on Tuesday, the deadline for candidates to withdraw and have their names taken off the ballot. Also pictured: His son Jacob Begich, wife Deborah Bonito and lieutenant governor running mate Debra Call. The three-way race includes Gov. Bill Walker, an independent, former state Sen. Mike Dunleavy, a Republican, and Begich, a Democrat. (Photo by Liz Ruskin/Alaska Public Media)Former U.S. Sen. Mark Begich announced that he’s staying in the race for governor. This sets up a three-way race between Begich, former state Sen. Mike Dunleavy and Gov. Bill Walker.Listen now“Alaska’s never given up on me, and I won’t give up on Alaska,” Begich said at a press conference in Anchorage on Tuesday. “For those that are wondering, I’m staying in this race for governor.”Both power brokers and conflicted voters have expressed concern that the Democratic Begich and independent Walker will compete for the same voters.A recent poll commissioned by the Alaska AFL-CIO found Dunleavy, a Republican, would win a three-way race by 10 points, but would lose to both Walker and Begich in a two-way race.Both Begich and Walker resisted calls to withdraw. Begich said he will fight for women’s right to make their own health care decisions. He also highlighted his support for protecting permanent fund dividends. And he said he would work to fully fund education and to reduce crime.“It’s a three-way race, so get used to it,” he said. “We are focusing on what this race is about: the people of Alaska. Alaskans will need to make their choice of who they will support and vote accordingly. You cannot cut a deal on your values, just to make sure that one person or another becomes governor.”Begich wouldn’t answer questions about how his decision to stay in the race could lead to Dunleavy winning.Begich has criticized recent cuts to PFDs made by Walker and the Legislature. Walker and lawmakers said they made the cuts to help close the gap between what the state spends and what it raises in oil royalties, taxes and fees.Both Begich and Walker have said they would make up for any long-lasting budget gap with new revenue. Neither have campaigned on a specific tax proposal.Dunleavy opposes new taxes. He has said he would use permanent fund earnings to pay for higher PFDs. But he hasn’t said how deeply he would draw down permanent fund earnings.Four years ago, Democratic nominee Byron Mallott joined his ticket with Walker, and the Alaska Democratic Party supported Walker and Mallott.