When members of Dow Jones & Co.'s controlling Bancroft family gathered 10 days ago for a meeting at a Boston hotel, they expected a fight. Some wanted to entertain a $5 billion bid for the company by Rupert Murdoch's News Corp. , but Michael Elefante, a powerful Dow Jones director and family trustee, had opposed it.

Instead of a rebuff, the family members got a huge surprise: Mr. Elefante had switched sides.

Mr. Elefante, a partner at a law firm that had represented the family for decades, told the group that for Dow Jones to remain competitive, he now believed the family needed to explore a sale to Mr. Murdoch or another bidder, according to people familiar with the presentation.

A look inside the family's deliberation shows four crucial factors laid the groundwork for the Bancrofts' dramatic change of position. One was the shift by Mr. Elefante, a Boston lawyer who oversees the family's trusts. A rift in the 34-member family widened as an increasingly noisy wing, especially those in the younger generation, agitated for Mr. Murdoch's offer to be considered. In a presentation to the board weeks earlier about the deal's pros and cons, Dow Jones Chief Executive Richard Zannino had starkly laid out to the family the downside of shutting the door. Finally, competition was getting fiercer than ever, with business-information providers Reuters Group PLC and Thomson Corp. announcing merger plans. All this made it harder for the family to resist the rich premium of Mr. Murdoch's offer.

On Thursday evening, the new stance surfaced at a special Dow Jones board meeting. The Bancroft family said in a statement that it wants to meet Mr. Murdoch to discuss his bid, and it will consider other bidders as well. (Read the statement.) The family, which controls 64% of Dow Jones's voting power, cautioned that a sale isn't a certainty. But it said the "mission of Dow Jones may be better accomplished in combination or collaboration with another organization, which may include News Corp."