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Why not institute? Which would fit as ' To make a foundation'

The proponents of recombinant DNA research have decided to (i) ______ federal regulation of their work; they hope that by making this [color=#ff0000]compromise[/color] they can forestall proposed state and local controls that might be even stiffer.

Basically the question is saying that if they do something then they will NOT have any possible issue at a local level for their research.

Therefore, if they ENCOURAGE the legislation at a FEDERAL level then they, possibly, will not have problems at a LOCAL level

Regards
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They are researchers not federal employees so they can't institute(create/lay a foundation of) federal regulation they can only encourage it and hope it helps their cause. hope this helps

The proponents of recombinant DNA research have decided to (i) ______ federal regulation of their work; they hope that by making this compromise they can forestall proposed state and local controls that might be even stiffer.

Background: Supreme court, high court and local courts. when a higher authority(Supreme court) certify you that you are inoccent then that's final, low authority courts don't bother you because your are certified by the best.

Now,

Similarly, if the supporters of DNA research encouraged the regulations from federal (highest authority) then they hope the low authorities (State and local) who are more strict and critical will not bother them in their work.

Hence, the answer is Encourage