In order to find a particular job in the government which grants you major bargaining power with no qualifications you could try a number of different approaches:
1. Consult your network. Talking to anyone who works in the government or knows someone who does is a great first step.
2. Check your country's Occupational Shortage List. This will give you an idea for what labor is in demand in your country. In-demand occupations offer the employee more leverage when it comes to negotiating wages, benefits and working conditions. 
3. Just ask a random government worker on the street how they got their job and if they feel they have major bargaining power.
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