Step 1: Understanding the question.
The question asks for a philosophy that advocates distributing authority because it assumes that people are competent.
Step 2: Analyzing the options.
- Span of management: This refers to the number of subordinates a manager can effectively supervise, not directly related to the dispersal of authority.
- Decentralisation: Decentralisation is the process of delegating decision-making authority to lower levels in the organisation, promoting the belief in people's competence and resourcefulness.
- Centralisation: Centralisation concentrates decision-making power at the top of the organisation, which contradicts the idea of selective dispersal of authority.
- Democratic leadership style: While democratic leadership involves participation, it doesn't specifically focus on authority dispersion in the same way decentralisation does.
Step 3: Conclusion.
The correct answer is Decentralisation, as it involves the selective dispersal of authority, believing in the capability of individuals at various levels.
Final Answer:
\[
\boxed{\text{The correct answer is (2) Decentralisation.}}
\]