Politics, like human consciousness, and like every human activity and physical activity is non-algorithmic. Algorithms pertain to models of phenomena and not to phenomena itself. That is where they obtain. To confuse one for the other is a category mistake.
Still, given the increasing impact of algorithms on our daily life, what is the impact of the halting problem on such algorithmic procedures?
Facebook, according to Frances Haugen, has certain algorithmic checks which it installs at election time but removes at other times.
There has been algorithmic pilitical advertsiing where a message is personalised to an large audience. So saying many different things to many different people.
There are also algorithmic trading in the city. This is part of the economy.
also algorithms in Youtube, Spotify and so on which impact the attention economy. Obviously also advertising algorithms here too. This translates into soft pilitical power.