What is the test for a defendant to successfully appeal against a Rule 11 error?

When a defendant raises a Rule 11 error for the first time on appeal, this court reviews the claim for plain error. United States v. Vonn, 535 U.S. 55, 59 (2002). Under the plain error standard, the defendant must demonstrate "that (1) there was error, (2) the error was 'plain,' (3) the error prejudicially affected [her] 'substantial rights,' and the error 'seriously affect[ed] the fairness,

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integrity or public reputation of judicial proceedings.'" United States v. Flaharty, 295 F.3d 182, 195 (2d Cir. 2002) (quoting United States v. Olano, 507 U.S. 725, 732 (1993)). To demonstrate that a Rule 11 error prejudicially affected her substantial rights, the defendant must show "a reasonable probability that, but for the error, [she] would not have entered the plea." United States v. Dominguez Benitez, 542 U.S. 74, 83 (2004).

Federal Rule of Criminal Procedure 11(c)(1) provides that a district court "must not participate" in plea "discussions." The danger of a district court's participation, even if well-intentioned, in the plea process is that it "inevitably" poses "the high and unacceptable risk" that a defendant will be coerced "to accept the proposed agreement and plead guilty." United States v. Paul, 634 F.3d 668, 671 (2d Cir. 2011) (internal quotation marks omitted).