"An estimated 20,000 persons, or more, ... are in prison for crimes to which they pleaded guilty but did not in fact commit."

And those are conservative numbers according to Judge Jed Rakoff, who has written a compelling piece explaining that innocent people are pleading guilty to crimes that they have not committed.  There is a lot to blame for this phenomenon but he offers this solution:

What can we do about it? If there were the political will to do so, we could eliminate mandatory minimums, eliminate sentencing guidelines, and dramatically reduce the severity of our sentencing regimes in general. But even during the second Obama administration, the very modest steps taken by Attorney General Eric Holder to moderate sentences have been met by stiff opposition, some from within his own department. For example, the attorney general’s public support for a bipartisan bill that would reduce mandatory minimums for certain narcotics offenses prompted the National Association of Assistant US Attorneys to send an “open letter” of opposition, while a similar letter denouncing the bill was signed by two former attorney generals, three former chiefs of the Drug Enforcement Administration, and eighteen former US attorneys.

Reflecting, perhaps, the religious origins of our country, Americans are notoriously prone to making moral judgments. Often this serves salutary purposes; but a by-product of this moralizing tendency is a punitiveness that I think is not likely to change in the near future. Indeed, on those occasions when Americans read that someone accused of a very serious crime has been permitted to plea bargain to a considerably reduced offense, their typical reaction is one of suspicion or outrage, and sometimes not without reason. Rarely, however, do they contemplate the possibility that the defendant may be totally innocent of any charge but is being coerced into pleading to a lesser offense because the consequences of going to trial and losing are too severe to take the risk.
I am driven, in the end, to advocate what a few jurisdictions, notably Connecticut and Florida, have begun experimenting with: involving judges in the plea-bargaining process. At present, this is forbidden in the federal courts, and with good reason: for a judge to involve herself runs the risk of compromising her objectivity if no bargain is reached. For similar reasons, many federal judges (including this one) refuse to involve themselves in settlement negotiations in civil cases, even though, unlike the criminal plea bargain situation, there is no legal impediment to doing so. But the problem is solved in civil cases by referring the settlement negotiations to magistrates or special masters who do not report the results to the judges who handle the subsequent proceedings. If the federal rule were changed, the same could be done in the criminal plea bargain situation.
As I envision it, shortly after an indictment is returned (or perhaps even earlier if an arrest has occurred and the defendant is jailed), a magistrate would meet separately with the prosecutor and the defense counsel, in proceedings that would be recorded but placed under seal, and all present would be provided with the particulars regarding the evidence and issues in the case. In certain circumstances, the magistrate might interview witnesses or examine other evidence, again under seal so as not to compromise any party’s strategy. He might even interview the defendant, under an arrangement where it would not constitute a waiver of the defendant’s Fifth Amendment privilege against self-incrimination.
The prosecutor would, in the meantime, be precluded from making any plea bargain offer (or threat) while the magistrate was studying the case. Once the magistrate was ready, he would then meet separately with both sides and, if appropriate, make a recommendation, such as to dismiss the case (if he thought the proof was weak), to proceed to trial (if he thought there was no reasonable plea bargain available), or to enter into a plea bargain along lines the magistrate might suggest. No party would be required to follow the magistrate’s suggestions. Their force, if any, would come from the fact that they were being suggested by a neutral third party, who, moreover, was a judicial officer that the prosecutors and the defense lawyers would have to appear before in many other cases.
Would a plan structured along these lines wholly eliminate false guilty pleas? Probably not, but it likely would reduce their number. Would it present new, unforeseeable problems of its own? Undoubtedly, which is why I would recommend that it first be tried as a pilot program. Even given the current federal rules prohibiting judges from involving themselves in the plea-bargaining process, I think something like this could be undertaken, since most such rules can be waived and the relevant parties could here agree to waive them for the limited purposes of a pilot program.
I am under no illusions that this suggested involvement of judges in the plea-bargaining process is a panacea. But would not any program that helps to reduce the shame of sending innocent people to prison be worth trying?