(a) any state department, board, bureau, division, council, committee, commission, or office;
(b) any other similar state public organization established pursuant to state statutes, executive order, or other executive action for the exercise of any function of state government and to which members are appointed or elected; and
(c) any public authority or public benefit corporation a majority of whose members are appointed by the governor or serve as members by virtue of holding state offices to which they were appointed by the governor, or any combination thereof. 2. "Agency" does not include:
(a) any informal advisory organization established exclusively by a state agency to advise a commissioner, secretary, or other director of that agency on an informal basis;
(b) the state legislature; and
(c) any local government or subdivision or entity thereof. 3. The secretary of state shall maintain a compilation of persons subjected to section seventy-three-a of the public officers law and who hold policy-making positions at all state agencies, including state agencies established after the effective date of this section. Such compilation shall identify by agency the persons subjected to section seventy-three-a of the public officers law and who hold policy-making positions, the length of time such positions have been held, and a representation of policy-making positions at such agency held by women compared to policy-making positions held by men. The secretary of state shall keep such inventory in a public record available for inspection, and updated annually on the department of state website. 4. Each agency shall annually on or before January first, submit to the secretary of state all information required pursuant to this section in a manner specified by the secretary of state to facilitate the publication requirements of this section. 5. For the purposes of this section, "persons subjected to section seventy-three-a of the public officers law and who hold policy-making decisions" shall include, but not be limited to, a commissioner, a superintendent, an executive director, and other chief executive officers, positions appointed by the governor, as well as the appointments of the aforementioned whose function is essential to the policy-making processes of such agency, and any other position whose function is essential to the policy-making processes of such agency.