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In the distant future, the human race has become extinct, leaving behind the machines they created. These robots are very similar to us and are run by separate AI. They share our emotions and language, and also the concepts of friend and family relationships. They are also curious about the universe, and are programmed to collaborate with one another in order to achieve a common goal.

Why would they be interested in politics? Isn't it better for them to avoid having different perspectives on issues so that there won't be any disagreements or conflicts of interest?

Extra info: In my story, the extinction of humans is due to political issues

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The mere fact that they share our behaviors indicate that they will not succeed in arriving at such a common perspective, but I'm sure that's insufficient.

If they are anything like us, they have some concept of themselves. This means they can have wants and aspirations. What one AI thinks is "good" another AI may think is "bad." This is reasonable. However, the reconciliation process for these disagreements may be untenable. There's plenty of NP problems out there, so if the reconciliation includes one of them, it may take exponential time to resolve. Even if you can prove that there exists an answer which makes everyone happy, finding it may take so long, digitally, that its more effective to rely on less technical approaches, like politics.

Digging further, if they are self-aware, there are actually fundamental disagreements that may be unresolvable in a mathematically provable way, depending on how your particular AIs are constructed. However, demonstrating the existence of such limits involves invoking the work of Tarski or Godel, which is not always easy to do.

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Politics would probably not make too much sense to robots. Make a set of rules. Follow it. Thus is the way of AI. The bigger group acts like video game characters and gets rid of or overpowers the minority, reprogramming it. They can be friendly, but they don't have to agree. No politics, just a universal mindset that will take a while to attain.

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