Source: https://www.theracetothebottom.org/rttb/duka-v-sec-and-the-constitutionality-of-administrative-law-j-3.html
Timestamp: 2019-04-25 19:01:05+00:00

Document:
The Appointments Clause provides that the President has the authority to appoint Officers of the United States but allows Congress to vest the appointment of "inferior officers" "in the President alone, in the Courts of Law, or in the Heads of Department." To the extent that ALJs at the SEC are "inferior officers" (as opposed to employees), therefore, they must be appointed by the Commission.
With respect to the appointment of ALJs, each agency is allowed to determine the number that it needs. See 5 U.S. Code § 3105 ("Each agency shall appoint as many administrative law judges as are necessary for proceedings required to be conducted in accordance with sections 556 and 557 of this title. . . .").
After having determined the number, the actuall appointment process involves substantial input from the Office of Personnel Management ("OPM"). OPM screens the candidates and must approve a selection or povide a list of eligible candidates. See 5 CFR § 930.203a ("An agency may make an appointment to an administrative law judge position only with the prior approval of OPM, except when it makes its selection from a certificate of eligibles furnished by OPM.").
OPM, however, emphatically disavows any final decision making with respect to ALJs. See 5 CFR 930.201 ("OPM does not hire administrative law judges for other agencies"). The law seems clear, therefore, that agencies, not OPM, select ALJs.
Within each agency, the system for appointment often rests with the head of the agency. See 42 U.S.C.A. § 2000e-4 (Chairman of EEOC, on behalf of the Commission, approves ALJs); 50 U.S.C.A. § 2412(c)(4) ("An administrative law judge referred to in this subsection shall be appointed by the Secretary [of Commerce] from among those considered qualified for selection and appointment"); 29 U.S.C.A. § 661(e)("The Chairman [of OSHA] shall be responsible on behalf of the Commission for the administrative operations of the Commission and shallappoint such administrative law judges and other employees as he deems necessary to assist in the performance of the Commission's functions"); 30 U.S.C.A. § 823 ("The [Federal Mine Safety and Health Review] Commission shall appoint such additional administrative law judges as it deems necessary to carry out the functions of the Commission."); 20 U.S.C.A. § 1234 ("The administrative law judges (hereinafter "judges") of the Office shall be appointed by the Secretary [of Education] in accordance with section 3105 of Title 5.").
The appointment process at the SEC, however, is less clear.

References: § 3105
 § 930
 § 2000
 § 2412
 § 661
 § 823
 § 1234