Crossword Genius

Hoped to have the House go against Conservative hairsplitting (8)

Ross

I believe the answer is:

pedantic

I'm a little stuck... Click here to teach me more about this clue!

'hoped to have the house' is the definition.
I can't tell whether this defines the answer.

'against conservative hairsplitting' is the wordplay.
I cannot quite see how this works, but
'against' could be 'anti' (prefix meaning against) and 'anti' is located in the answer.
'conservative' could be 'c' (UK political abbreviation) and 'c' is found in the answer.
The remaining letters 'ped' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'go' is the link.

Can you help me to learn more?

(Other definitions for pedantic that I've seen before include "Abstruse" , "Over-concerned with minor details" , "Excessively scrupulous" , "Overly fussy" , "Excessively concerned with minor details" .)

I've seen this clue in The Times.
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