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Mattis has a bachelor's degree in history from Central Washington University.

Earlier, Trump said he will make Rep. Tom Price, R-Ga., his nominee to be the next secretary of the Department of Health and Human Services, and Steven Mnuchin, a film finance company executive, to be the secretary of the Treasury Department.

Related: 5 things to know about Trump HHS shaper Paula Stannard

At press time, Trump had not yet announced the name of his pick to be the next Labor secretary.

Here are some reasons why, if Mattis is confirmed, he could end up being another shaper of how the United States goes about starting a new chapter in efforts to improve its health care and health finance systems:

1. Job-related needs

As Defense secretary, Mattis would be the head of one of the biggest buyers of employee health benefits and retiree health benefits in the world.

Health care and health insurance for active-duty military personnel and their dependents cost the Defense Department about $41 billion in the 12-month period ending Sept. 30, or about 7.7 percent of the department's discretionary base budget, and the department also contributes to a fund that's supposed to supplement health benefits for military retirees who are eligible for Medicare.

Mattis would also run an organization that depends heavily on the health of the U.S. population.

In the past, one argument for reforming the health care and health finance systems has been that obesity, lack of exercise and other public health problems have been hurting the military's ability to find qualified recruits.

2. Big bureaucracy experience

Trump seems to have operated more as the head of a small company that controls many other companies than inside the machinery of a big, bureaucratic organization.

Tom Price, Trump's pick for Health and Human Services secretary, has been an orthopedic surgeon and a member of Congress. He may have worked mainly inside relatively small units inside much larger organization.

Mattis, in contrast, has worked inside the Pentagon and has received extensive military training on how to operate inside a giant organization. He may have insight into how other giant organizations in the health care space, such as HHS and the HHS Centers for Medicare & Medicaid Services division, actually work.

3. Post-military experience

Since leaving the military, Mattis has served on the boards of Palo Alto, California-based Theranos Inc., a home medical test kit company that has faced criticism of its quality-control practices, and of Falls Church, Virginia-based General Dynamics Corp.

While serving on the board of Theranos, Mattis may have a unique perspective on how the U.S. Food and Drug Administration, an HHS unit, operates when it has concerns about quality.

While on the board of General Dynamics, Mattis may have heard presentations on General Dynamics' work running call centers for the Affordable Care Act public exchange system.

4. Strategic concerns

In January, when Mattis testified before the Senate Armed Services Committee, he said one thing the United States has to do to stay strong is to get spending and budget deficits under control, according to a written version of his remarks.

Getting overall health care spending under control is important to solving federal budget deficit problems, because health spending accounts for about one-quarter of federal spending.