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Republicans said one solution would be to dock localities’ federal aid payments until they agree to cooperate fully with background investigations.

They also recommended unleashing investigators to look at online social media presence.

Current guidelines bar investigators from using the Internet for anything other than checking information such as addresses. But the Republicans’ report said investigators could learn a lot just by having access to what someone posts publicly on Twitter accounts or Facebook pages.

Under the existing background check system, responsibility is divided. An agency that wants an employee cleared asks OPM to conduct the investigation. The investigation sometimes is farmed out to private contractors. When the investigation is finished, the file is sent to the agency in question — for example, the Navy, in the case of Alexis — which makes a final determination about granting clearance.

The Defense Department is OPM’s biggest client for security clearances. It handled about 767,000 cases in 2012 and adjudicated 680,000 in 2013. The Defense Department has 460 adjudicators who decide whether clearances should be given, which works out to a staggering caseload for each adjudicator.

Overall, OPM prepared more than 2.3 million “investigative products” for federal agencies in 2012. About 30 percent of those were performed by the agency, while 70 percent were outsourced to three contractors.

The process differs depending on the level of clearance. Those like Alexis who gain secret clearance are interviewed only if their statements have inconsistencies. The clearance is good for 10 years, and there is no continuous re-evaluation. Instead, individuals are expected to self-report any problems.

In the case of Alexis, that meant that run-ins with the law, repeated breaches of Navy rules and two visits to Veterans Affairs hospitals in August were never brought to the attention of security clearance officials.

Roughly 4.9 million Americans hold security clearances ranging from classified to secret to top secret. The report said part of the problem is that executive branch agencies deem so much material classified that it creates a need for more people to be cleared. One solution, the report said, is to crack down on overclassification.