This aspect of democracy is hampered when political dynasties are no longer working for public service but for family gains.

The aspect of democracy that is hampered when political dynasties are no longer working for public service but for family gains is the principle of "representative government".

Step 1: Understanding the concept of democracy Democracy is a system of government where the citizens exercise power by voting. In a representative democracy, the citizens elect representatives to create and implement laws.

Step 2: Understanding the role of political dynasties Political dynasties refer to families which have established their political dominance in a party or region over a significant period of time. Ideally, these dynasties should work for public service.

Step 3: Identifying the problem The problem arises when these political dynasties start working for their own family gains instead of public service. This means they are using their power and influence to benefit themselves rather than the citizens they represent.

Step 4: Identifying the hampered aspect of democracy When this happens, the principle of "representative government" is hampered. This is because the representatives are no longer truly representing the interests of the citizens, but are instead prioritizing their own family gains. This undermines the very essence of a representative democracy, where elected officials are supposed to work for the benefit of the public.