Examine the logical coherence between the following political philosophies and their policy inferences:
1. Evidence 1: Liberal theory posits that once a baseline standard of living is secured, free markets efficiently distribute societal rewards. Inference 1: Therefore, Liberalism relies on competition rather than total state control to manage inequality.
2. Evidence 2: Socialist doctrine asserts that concentrated economic wealth inherently subverts democratic institutions. Inference 2: Consequently, Socialists argue that economic and political inequalities are inextricably linked.
3. Evidence 3: Marxist ideology identifies private property as the root cause of systemic class dominance. Inference 3: Thus, Marxism advocates for the total privatization of core industries to empower the working class.