What is the effect of the sentencing judge's inconsistent finding by the trial court that a defendant was convicted of first-degree murder by a jury?

This second round of inconsistent factual findings by the sentencing judge may also raise double jeopardy issues. It is certainly true that where a defendant has been convicted on some counts and acquitted on others, double jeopardy principles do not prevent a sentencing court from using facts underlying an acquitted count in deciding what sentence to impose on a convicted count. (See United States v. Watts (1997) 519 U.S. 148, 154, 117 S.Ct. 633, 136 L.Ed.2d 554 ; Towne , supra , 44 Cal.4th at p. 87, 78 Cal.Rptr.3d 530, 186 P.3d 10.) But the inconsistent finding by the trial court

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here does not merely assist in selecting the length of the sentence to be imposed for a crime (first degree murder) of which defendant was properly convicted by a jury. ( Watts , at p. 155, 117 S.Ct. 633, citing Witte v. U.S. (1995) 515 U.S. 389, 401, 115 S.Ct. 2199, 132 L.Ed.2d 351.) Instead it changes the factual basis for the murder conviction from a theory the jury accepted (felony murder) to one it implicitly but necessarily rejected (premeditated murder). Where the jury has already determined that the prosecution did not prove a premeditated first degree murder beyond a reasonable doubt, on what basis can the defendant be exposed to a second hearing at which a different trier of fact applying a lesser standard will decide the same question?