On the eve of a Metropolitan Transportation Authority board vote that may lead to the building of housing for thousands of people, and an arena for a National Basketball Association team in downtown Brooklyn, debate emerged yesterday over reports that Mayor Bloomberg has instructed his four appointees on the MTA board to opt for the bidder that plans the larger project and the one that would use bigger public subsidies.

A leader of the transit activist group the Straphangers Campaign, Neysa Pranger, said the board members must exercise “due diligence” in evaluating the proposals. “When they’re receiving orders from above, they might not do that,” she said. Governor Pataki, who has appointed six board members and who likewise has endorsed the Ratner project, will not follow Mr. Bloomberg’s lead in instructing his appointees to vote for the Ratner bid, according to a Pataki spokeswoman, Mollie Fullington.

“We respect the independence of the appointees to do their due diligence and to do what is best for the MTA,” Ms. Fullington said.

When a mayoral spokeswoman, Jennifer Falk,was asked whether it was appropriate for Mr. Bloomberg to issue voting instructions to the four MTA board members he appointed, she said: “Yes, they are his appointees.”

In the past, Mr. Bloomberg has not been tolerant of mayoral appointees who have disobeyed his voting instructions. In March 2004, he dismissed two of his appointees on the city’s Panel for Educational Policy who had indicated they were not prepared to vote for his plan to end social promotion for underachieving third-graders.

Regardless of whether Forest City Ratner or a rival firm, Extell Development Company, wins the rights to develop the MTA’s 8.4-acre rail yard, the result will be “bad news for riders” of the MTA’s trains, buses, and subways, Ms. Pranger, a coordinator for Straphangers Campaign, said.

The developer Bruce Ratner, principal owner of the New Jersey Nets, wants to move the team to an arena at the site, known as Vanderbilt Yards. He also wants to build 6,000 residential units and more than 1 million square feet of office space in the area. Extell has submitted a smaller-scale proposal to build 1,940 housing units and 116,000 square feet of office space at the site.

Forest City Ratner is offering the MTA $50 million in cash for the site, while Extell has bid $150 million in cash. But Ms. Pranger said both bids are too low to shore up the MTA’s shaky finances and avert fare hikes in the not-so-distant future. An appraiser hired by the MTA, Daniel Lane, estimated the true market value of the site at $214.5 million.

The MTA’s 17-member board will meet at the authority’s Madison Avenue headquarters this morning, and an MTA spokesman, Tom Kelly, said “there will be some kind of a vote” on Vanderbilt Yards today, although he noted that the board could choose to delay a final decision until its next scheduled meeting in September.

On Monday, Extell’s president, Gary Barnett, sent a letter to the MTA board charging that the Ratner project’s true cost to taxpayers is considerably more than the $200 million figure claimed in the Ratner bid proposal.

Mr. Barnett’s claim appears to be supported by testimony that the director of the city’s Independent Budget Office, Ronnie Lowenstein, delivered at a City Council hearing in late May.