In a municipal Council of 24 people, your one elected independant can do squat and be held responsible for nothing.
In fact they use this as a means of avoiding responsibility. Say for example you Town want to put a dump in your back yard. Your counilor will vote against it, vehiminetly, yet it will still be dumped there because the majority vote will go against him.
They can take turn dumping garbage, or stealing money, and each one will votes against it when its their ward affected in turn, and no one can evern blame anyone for anything.
Elected representatives can only be held responsible in groups, because they never have enough say in any decision to overrule a majority. They take turn being part of the majoroty when they are all independant, so no one can be said to stand out to attrct responsibility.
The entire council or group or committee has to be blamed and the only way to deal with groups of politicians at election time is by their party.
In a control and opposition set up you also have one group making decisions and the other group criticizing them, so that the public can know what's going on for next time we vote.