Jeremy Bentham was an English philosopher and political radical.
The 'Industrial Revolution' (with the massive economic and social shifts that it brought in its wake) the rise of the middle class, and revolutions in France and America all were reflected in Bentham's reflections on existing institutions.
While he attacked both Tory and Whig policies, both the Reform Bill of 1832 (promoted by Bentham's disciple, Lord Henry Brougham) and later reforms in the century (such as the secret ballot, advocated by Bentham's friend, George Grote, who was elected to parliament in 1832) reflected Benthamite concerns.
As to what it was that this type of knowledge had to contribute to political stability, Mill's answer was as consistent as it was unequivocal: educated individuals would come to see their own interests as being in conformity with those of "the community." Knowledge made things safer; its absence threatened political stability.
What is of importance here is that the practical locus of reform was tied to the people while the locus of the theoretical argument remained where it always had been, with appropriate knowledge, the interests of the community, and the standard-bearers of those interests.
To make the case for the inclusion of larger numbers into the political nation, on this line of reasoning, all that needed to be established was that individuals had the capacity properly to judge their own interests and that they were unencumbered in their ability to act upon them.