Major health insurance companies seeking steep premium increases in New York have submitted memos to state officials to justify the higher rates. Now they are fighting to keep the memos from the public, saying they include trade secrets that competitors could use against them. "How these companies are setting these rates is vital for the public to know, and should not be treated like a state secret," Benjamin M. Lawsky, the state superintendent of financial services, said on Tuesday. "Transparency will promote healthy competition and enable the public to rigorously comment on proposed rates, two goals that all of us should favor." Lawsky, whose new agency oversees the state insurance division, has ordered that the memos be made public. His decision, which will go into effect by the end of November unless the companies obtain a court injunction, ends a longstanding policy that exempted the insurance companies from public access under a "trade secret" exception.