THE SIXTH Amendment declares that criminal defendants will “enjoy the right to a speedy and public trial, by an impartial jury”. The guarantee is uncontroversial in theory, but recent research in cognitive science casts doubt on whether it can be plausibly provided. Thanks to Daniel Kahneman and others we have never known so much about how biased we are. Jurors, being human, are subject to “anchoring” (latching onto the first piece of information they hear and not letting go); to “priming” (being unconsciously wooed by lawyers’ manipulations); to the “halo effect” (falling for whatever the most winning witness says); and to the “availability heuristic” (gazing upon the facts of the case through prior experience and knowledge).

Courts cannot scrub these and other flaws from jurors’ minds, but they can try to keep xenophobia and overt bias out of the jury box. When a juror hears one of his peers say something racist in the jury room, a note to the judge may be enough to bring on a mistrial. But in order to cultivate open and free discussion in the jury room, both state and federal courts have protected the secrecy of deliberations and have not permitted jurors’ comments to be scrutinised after the verdict is delivered.

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In weighing the Sixth Amendment against the value of secrecy in the jury room, the justices spent much of the oral argument contemplating the relative harm of various types of juror bias and searching for a place to draw a line. Chief Justice John Roberts began by wondering why “religious bias” isn’t just as problematic as racism. “All the court needs to decide in this case today is race”, Jeffrey Fisher, Mr Peña-Rodriguez’s lawyer replied; it need not determine whether evidence of juror bias against Muslims or Catholics should also scuttle a verdict. Those biases can await a hearing another day. Not so, the chief said: “I don’t think that’s fair.” Justice Samuel Alito piled in: “You’re not being very helpful to the court in your answers”, he said. “Suppose we start with race, and the next case involves religion. Now, how would you distinguish religion from race if we were to reach an opposite conclusion in the religious case?”