Aiyar said there was "arbitrariness" in the decision-making process at all levels while Karat asserted that death penalty was being used as a "political weapon".
They were participating in a discussion on 'Death Penalty and Indian Democracy' organised at the Indian Women's Press Corps here.
Karat, former General Secretary of CPI(M), also cited a resolution passed by the Karachi Congress in 1931 saying the stand against capital punishment was a part of India's freedom movement to which Aiyar remarked, "If Congress has forgotten the stand it took then, someone should remind them now."
He cited the executions of Afzal Guru and 1993 Mumbai blast convict Memon to buttress his point as opposed to the commutation of death sentences of Devinder Singh Bhullar or Rajiv Gandhi's assassins.
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"The whole of Kashmir said don't hang him (Guru). But you will listen to the political voice of Tamil Nadu and Punjab but not Kashmir," Karat said.
Aiyar questioned the judiciary taking "collective conscience" into consideration while taking any decision in this regard.
Maintaining that judiciary was "unaccountable" because of the collegium system, he asked "Has anyone ever questioned the political role played by the judiciary? The people of this country have no say over their (judges) appointments. There should be a debate going beyond Memon or any other individual."
Aiyar said the overall process in awarding someone capital punishment was vitiated by "arbitrariness and prejudice" and it was dependent on individuals holding the post of President, Home Minister or Supreme Court judges.