Heartlessly send mate to smaller house? (6)

I believe the answer is:

senate

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'house?' is the definition.
(I have seen 'Second house ' mean 'senate' so perhaps 'house' could also mean 'senate')

I don't understand how the rest of the clue works.

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(Other definitions for senate that I've seen before include "State assembly" , "Second house of the Oireachtas" , "Legislative body" , "House where politicians" , "Upper council of university" .)

I've seen this clue in the Sydney Morning Herald.

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