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Conrad doesn't actually believed what Alito told him. Conrad thinks he is playing some Jedi mind game with Alito. The way Conrad's grade school logic has it, he wins whether Alito keeps his word or not. If Alito keeps his word, it will be because Conrad made him feel like he wasn't a man of honor if he did otherwise (because he looked him in the eye and told him he would).
Of course we all know (including Conrad), that Alito, like Roberts, is not a man of honor. He will support his well-known ideologies on the bench, not the word he gave Conrad. Conrad thinks this is okay because he will be able to say that Alito lied to his face. Meanwhile, we've all lost more of our rights because Conrad was playing games with them.