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Regarding the Invisible President, isn't it frequently implied that the PM during "Yes, Minister" is female? Hacker's repeated attempts to try to reduce government spending and the size of government also suggests to me that he's Conservative ("Tory"), not Labour, so I'm even less convinced that the No Party Given trope is applicable.
The PM is clearly male, as Hacker's predecessor is often referred to as 'he' during 'Yes, Prime Minister'.
Even Word of God has, to my knowledge, never stated to which party Hacker belongs, so I think the trope applies.
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How well does it match the trope?