What political ideology of a gradual transition from a capitalism to socialism
The change from capitalism to Socialism (classless stateless society based on production for use) will have to be sudden and revolutionary.
Democratic Socialism
I wouldn’t call it an ideology, but Socialism (classless stateless society based on production for use) is the opposite of the state capitalist dictatorship that Stalin presided over.
The official ideology is socialism and one political party ruling.
In Western nations, the ideology of capitalism brought on wealth and prosperity to the rich although a middle class was developing. A competing ideology was various types of socialism and Marxism.
Political ideology (Maoism vs. National Socialism), mainly.
It depends what you mean by "most powerful". If you mean "most advanced", Communism was the most advanced stage of society posited by Karl Marx and Engels. The progression was from Feudalism to Capitalism to Socialism to Communism. If by powerful you mean the most influential paradigm and ideology today, it would be capitalism in its neoliberal flavor.
Sure capitalism is based on a set of ideas = ideology. The main IDEAS behind capitalism are the closely connected 'inflation' and 'infinite growth'
If Capitalism did not need Ideology, then it wouldn't be ideology at all. Ideology is the organized ideas which give a new direction to the people in society for revolution and because Capitalism is being able to own private land, businesses and organizations; there must be entrepreneur and because entrepreneur come up with ideas, there is the ideology. The free market economy, in essence, is basically the source of ideology in capitalism.
Mussolini originally adhered to socialism and was a prominent member of the Italian Socialist Party. However, he later broke away from socialist ideals and formed his own political ideology known as fascism. This ideology emphasized authoritarian rule, nationalism, and the complete subordination of individual interests to the state.
Adam Smith favored the ideology of classical liberalism, particularly advocating for free markets, limited government intervention, and the idea of self-interest leading to the common good. His book "The Wealth of Nations" is considered a foundational text for the principles of modern capitalism.
Political ideology
John Stuart Mill favored the ideology of utilitarianism, which emphasizes maximizing overall happiness and well-being for the greatest number of people. Mill believed in individual freedoms, limited government intervention, and the importance of individuality and self-development.