Increase democracy in US government.
A major goal of the progressive movement was to increase democracy in US government. This was achieved through such methods as amending the Constitution to allow for the direct election of U.S. Senators (17th Amendment) and giving women the right to vote (19th Amendment).
healthier, better educated citizans.
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In social conditions
If you mean 'graft' as another word for bribery: no, progressives certainly don't support that.
Progressives wanted to make cities and factories cleaner and safer.