From RachelDawes, a fellow SHH! member:
My answer, based on from what I gathered from various forums, is that Joker wanted to show Gotham that Dent's not different from what the criminals he incarcerated. If they've pin the murders on Joker and an investigation starts, he would just tell them the truth, he wins.
Batman and Gordon started a conspiracy here - a cover-up for Dent. If they blame the murder on Batman, the investigation would be on Batman. But then, since Batman, at this moment, could not be caught, as Gordon says, "[FONT=CourierFinalDraft,Italic]So we'll hunt him, because he can take it.", an investigation is unlikely to happen. Or if ever Dent becomes a suspect, they already have blamed it on Batman, which, in people's view, is more likely the real killer. Because he has the motive, he's a vigilante, an outlaw, people sees that he has the right reasons to do the killings.
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