The major belief that united the Progressives was the idea that the American middle class was superior to other classes and should be allowed to dominate the society. Progressives felt that both the rich and the poor were deficient in some ways and that the middle class should therefore have more control over society. They believed that the government should use its power to push the rich and the poor to be more like the middle class.
The Progressives felt that middle class Americans were the group with the best values, the ones who were neither selfish and grasping nor ignorant and undisciplined. They felt that the rich were selfish and hungry for power and for wealth. They felt that the poor were not educated or disciplined enough to know what was best for them. They wanted to use the government to correct both of these problems. The reforms that they advocated came from these beliefs.
For example, the Progressives were strongly in favor of women’s suffrage and of Prohibition. Both of these were meant, in part, to curb the bad habits of the poor (particularly immigrants). The idea was that the bulk of women were good, middle class people whose votes would cancel the votes of less-educated, poor, immigrant men. This would allow the government to enact things like Prohibition. Prohibition would reform the poor by preventing them from drinking. This would make poor men better workers and fathers, just like middle class men were (in this view).
The Progressives also wanted to stop the rich from being so greedy. To this end, they instituted direct popular election of senators so the rich could not “buy” senators anymore. They also wanted the government to regulate business much more strongly. They wanted to prevent the greedy rich (as they saw it) from forming monopolies to hurt consumers. They wanted to prevent the greedy rich from being able to exploit children in their factories. They wanted to prevent the greedy rich from selling impure meats and drugs just to make a profit.
In short, the Progressives felt that society would be improved if only the government would enforce the values of the middle class. They felt the middle class was better than everyone else and that the country would be improved if the government would push everyone else to act like the middle class.