**731*993A San Bernardino County jury found defendant Lee Samuel Capers guilty of the first degree murders of Nathaniel Young and Consuelo *994Patrida Young. ( Pen. Code, § 187, subd. (a).)1 As relevant here, the jury found true multiple murder, robbery-murder, and burglary-murder special circumstances. (§§ 190.2, subds. (a)(3), (a)(17), *86& (a)(17)(G).) The jury found defendant guilty of two counts of second degree robbery (§ 211), arson of property (§ 451, subd. (d)), and felon in possession of a dagger in a penal institution (§ 4502, subd. (a)). The jury found defendant personally used a deadly weapon-a handgun-within the meaning of section 12022.53, subd. (b). The jury separately tried and found defendant's five prior section 211 robbery convictions to be true.
After a penalty trial, the jury returned a verdict of death.2 The court denied the automatic motion to modify the verdict and imposed a judgment of death. (§ 190.4, subd. (e).) This appeal is automatic. (§ 1239, subd. (b).) We affirm the judgment in its entirety.
I. The Facts
A. Guilt Phase
1. Overview
The evidence showed that on Monday, November 9, 1998, defendant and three accomplices entered the Barstow T-shirt shop owned by married couple Nathaniel and Consuelo Young, robbed the store, shot and killed Nathaniel, and raped and beat Consuelo before killing her. They then set fire to both victims' bodies.
Defendant cross-examined prosecution witnesses, but presented no evidence of his own.
2. Prosecution Evidence
Nathaniel and Consuelo, who had been married for seven years, opened a T-shirt store in Barstow called "T's Galore 'N More" in 1998. Consuelo typically managed the store because Nathaniel worked on the Marine Logistics Base nearby.
Ramon Tirado lived behind the T-shirt shop and had known defendant and defendant's half-brother Anthony Leatham for years. Leatham and two other *995individuals inquired about the Barstow T-shirt shop that the Youngs owned. He asked Tirado to join them in robbing the store. Tirado declined.
On Monday November 9, 1998, Nathaniel did not arrive for his scheduled shift at the base; he had never missed work without first calling. After he missed work the next day, Margaret Carter, the base's comptroller, became concerned. She called his home and left a message on his answering machine. She then asked a superior what to do about her concern. He told her to call the Barstow Police Department and request a welfare check, which she did.
At the same time Margaret called the Barstow police, two of Nathaniel's colleagues at the base, Loretta Becknall and Nancy Derryberry, went to the T-shirt store to check on him. They could not see inside the store because soot covered the windows. The colleagues notified Margaret that there might have been a fire at the store. Margaret again called Barstow police and also spoke to Bonnie Hulse, an investigative assistant for the Criminal Investigation Division of the Marine Corps. Margaret was told to call the Provost Marshal, who had jurisdiction over the military base. The Provost Marshal's Office notified the Barstow Fire Department.
On Tuesday, November 10, 1998, Barstow Fire Department personnel inspected the victims' T-shirt store for signs of a fire. Salvatore Carrao, the Barstow Fire Department Division Chief, and Fire Engineer Steve Ross noticed heavy black soot on the inside of the store windows. They *87checked the front door, but it did not open. They checked the back door, which was unlocked, and Carrao opened it to look inside. He immediately saw two corpses and concluded there had been a fire inside. He closed the door, called law enforcement, and secured the store. **732Law enforcement soon arrived. Barstow Police Sergeant Andrew Espinoza and criminalist Randy Beasley entered the building. There they found five .45-caliber bullets and only one bullet casing. They also found a trash can that contained blood, water, and a bloody mop. Taken together, Beasley believed these items strongly suggested that someone had attempted to clean up a crime scene. Beasley found a pair of women's panties in a toilet that had been cut straight across, from one leg hole to the other. Beasley also found a wallet and a purse next to each other. The wallet, which belonged to Nathaniel, contained no money or credit cards. Consuelo's purse also contained a wallet, which, like Nathaniel's held no money. One of the bodies, tentatively identified as Nathaniel's, was stained with blood, and duct tape had been wrapped around its throat and neck. The body was partially burned.
Fire inspection specialist Rita Gay was also on the scene. She believed the fire to have been a "slow burn" that did not immediately flame up but *996smoldered for a long time. Gay observed soot on the furnishings and floor. She saw the two victims on the floor. The male victim lay prone and had golf clubs laying across his back. The female victim was more severely burned, such that the left side of her body had been largely consumed by fire. Gay detected the odor of gasoline in close proximity to the bodies. Gay did not examine either victim, but concluded that each had been separately set on fire.
Law enforcement personnel identified the second body as likely belonging to Consuelo. Her body had been largely consumed by the fire; much of her remains consisted of ashes and bones. They also discovered a large amount of blood and two metal golf clubs covered in blood. They noticed human hair on the golf clubs and deemed it to have come from Consuelo's head because she had wavy hair while Nathaniel's was more tightly curled. Catherine Wojcik, a sheriff's department criminalist, later compared the hairs found at the crime scene with the hair of both victims. Wojcik determined that the two hairs found on the golf club were similar to samples of Consuelo's hair, though she could not say definitively that they came from Consuelo. She determined Nathaniel was not the source of the two hairs.
Arson investigators later concluded the perpetrators had started two fires, each originating on the body of the two victims. A thick greasy substance was observed on the floor adjacent to the bodies; investigators concluded it might have been the victims' melted body fat.
Charlene Garcia, Nathaniel's daughter, cleaned out the T-shirt store. She informed the police that Nathaniel's gun was the only item she found missing.
Forensic pathologist and deputy medical examiner Dr. Steven Trenkle performed autopsies on both bodies. He testified that Nathaniel had been shot at least four times, and that his body contained eight entrance and exit wounds and had been moderately charred by fire. One bullet had cut through the brain stem and lodged in the base of the skull, and another went through the neck and severed the first cervical vertebrae underneath the skull. None of the injuries were consistent with having been struck with a metal golf club. Dr. Trenkle concluded Nathaniel died as a result of multiple gunshot wounds to the head, neck, and chest.
*88Dr. Trenkle explained that Consuelo had suffered extensive blunt force trauma and that her body had been significantly burned. As noted, much of her body had been consumed in the fire. The blunt force trauma had shattered the skull and facial bones. Dr. Trenkle concluded Consuelo died as a result of multiple blunt force head injuries. He could not be certain whether Consuelo was alive when her body was burned.
*997On November 15, 1998, Barstow Police Officer John Cordero notified Barstow Police Detective Leo Griego that defendant wished to speak with Griego about the T-shirt store murders. Griego spoke with defendant, first at defendant's residence and later at the Barstow Police Department. Defendant denied involvement in the murders, but said he knew two of the people involved.
Lisa Martin became acquainted with defendant a month after the murders. She let defendant stay at her home. During his stay, defendant mentioned four or five times how **733he killed a man and woman in Barstow. Defendant described how he personally shot the man, poured gasoline on both victims, and lit them on fire. He told Lisa that the woman begged and screamed for her life and that he thought it was funny. He also told her that he committed the crimes with his younger half-brother, Antonio Leatham (whom he called "Eagle"). Lisa testified that defendant kept the lighter he used to set the victims on fire and showed no remorse for killing them. Leatham also came to Lisa's house at one point and defendant mentioned the murders in front of him. Blake Martin-Ramirez, Lisa's 14-year-old son, testified that he heard defendant describe his role in killing the victims and taking their sports car. About a week after defendant told Lisa about the murders, she called defendant's mother and told her to move him out of the apartment.
Griego's investigation focused on defendant and Leatham as suspects. In January 1999, Griego questioned defendant, who was incarcerated at Chino State Prison. Defendant again denied involvement in the crimes.
In December 1999, Griego collected defendant's biological samples so they could be compared to DNA samples obtained from evidence collected at the crime scene. All the DNA collected at the crime scene was matched to either Consuelo or Nathaniel.
Although defendant had denied involvement in the crimes and only talked about who he thought might have committed the T-shirt store murders, his version of events surrounding the murders changed when he met with detectives Steve Shumway and Ronald Sanfilipo on January 5, 2001. The interview, conducted at the Riverside Police Department, came about because defendant's cellmate in Riverside County Jail told authorities that defendant had discussed a Barstow double-murder where the victims had been burned. Griego watched on a video monitor in an adjoining room. After being read *998and waiving his Miranda3 rights, defendant explained he had asked to speak to them about the murders because it was "something that ha[d] been weighing [him] down."4
After a half-hour's conversation, Griego entered the interview room. Defendant again was read and waived his Miranda *89rights, and he and Griego discussed the crimes for 45 minutes to an hour. Defendant was then transported to the Barstow Police Department where detectives Griego and Keith Libby conducted an interview. During that interview, defendant, who was 24 years old (and nicknamed "Oso") at the time of the murders, explained that he committed the crimes with 15-year-old Carlos Loomis (whom he called "Bam-Bam"), 22-year-old Ruben Romero (whom he called "Wino"), and "another guy " (whom he sometimes called "the other juvenile" or "a 14-year-old kid." Defendant consistently asserted the fourth perpetrator was not his half-brother Leatham.5 He said Loomis and Romero offered him "an ounce of dope and money if he agreed to act as a lookout" during a robbery. Defendant said he agreed to be a lookout because "he was real bad on dope." Defendant maintained that Romero was in charge, and while they were all waiting around before the robbery, defendant went to Barstow Liquor and purchased a 40-ounce beer, half of which he drank immediately. Once the robbery commenced, Loomis and Romero verbally and physically abused the victims and "took the couple out of [defendant's] line of sight." About 10 or 15 minutes later, defendant **734heard gunshots. Loomis and Romero jumped into a blue or white Camaro and told defendant that they were headed to a Motel 6. Defendant then went back to his mother's house.
Detective Libby then told defendant that telling only "a little bit of the truth" would not be good for him, and that it would be best if he told the "whole truth." Libby also said that if defendant wanted him to believe that Leatham was not involved in the murders, he would have to convince him that he was telling them the "complete truth." Defendant then admitted that he entered the store and forced Consuelo and Nathaniel through the store's back door. Defendant claimed that Loomis hit Consuelo with a stick-like *999object several times. During the beating, Consuelo was pleading: "Stop please. Don't hurt us. Don't hurt us." According to defendant, Romero shot Consuelo before Loomis raped her while she was barely moving and forced Nathaniel to watch. Defendant said that during the rape, Consuelo had screamed "for a little while." During this same interview, defendant said that he beat Nathaniel a number of times after Nathaniel yelled and screamed to protect his wife.
Defendant also said that Romero then shot a .45-caliber firearm with a taped-up handle an unspecified number of times, but defendant did not say whom he shot, or how he came into possession of the gun. He said, "I know my guns ... I've been messing with guns for a long time, [so I] knew the caliber ... right off the top." Defendant also said, "I didn't pull the trigger; I didn't rape nobody; I didn't set nobody on fire." After the rape, beating, and shooting, defendant said either Romero or Loomis used gasoline and a lighter to set the bodies on fire. When asked, defendant said he could not recall anyone cleaning up the crime scene. He also said that someone, probably Loomis, had gathered up the .45-caliber shell casings.
*90After completing the robbery and murders, defendant said he and the other perpetrators stole a Camaro parked at the store and drove it to a nearby Motel 6, where they went their separate ways. At the end of the interview, defendant agreed to walk the detectives through the crime scene.
The next day, officers taped defendant's reenactment of the crimes at the T-shirt store. Defendant reiterated what he told officers during the interviews the day before and again admitted to beating Nathaniel. At the conclusion of the reenactment, defendant said, "I'm just as guilty as the man who pulled the trigger and the man who started the fire." Defendant said he felt bad for the victims, that "it wasn't supposed to happen that way to them, you know, but that still isn't going to change the fact that I was actually involved here and it's not going to change the fact, yes, I'm expecting a conviction out of this and whatever I receive, I deserve, that's it. That's all I got to say." Two weeks later, Griego contacted Leatham to speak with him about the murders before transporting Leatham to the Riverside Police Department so that he could speak with defendant before his arraignment on an unrelated offense.
During a subsequent interview on January 25, 2001, defendant took full responsibility for the crimes. Defendant assured detectives that he was now confessing because he wanted to come clean. He admitted that the crimes happened quickly and that he fired the fatal shots. He subsequently disposed of the murder weapon and the shell casings near some railroad tracks. However, he said Loomis poured the gasoline on the victims, and Romero lit them on fire. He also claimed Leatham stayed outside during the murders and *1000did not do anything. He then stated: "But just so you know, get my little brother involved with this, you know, putting him in custody, you know, I mean, where does [Loomis] and [Romero] fall into this? You know what I mean. It seems like this is just a conspiracy against me and him. Me and my brother you know?" After defendant was asked why he wanted to "take the rap" for everyone, defendant replied, "Just charge me with everything, you know what I mean?" He could not remember who he shot, but he did remember that he shot three rounds. He did not want to tell detectives where he got the gun, fearing that his "whole family would be in jeopardy and everything you know what I mean?" **735Detectives Griego and Espinoza interviewed defendant one last time at North Kern State Prison on April 16, 2002. Defendant said he met with the group to plan the robbery. During the robbery, defendant took $100 in cash and the keys to the Camaro from Nathaniel's pocket. He also stole Consuelo's wedding ring, trading it for "dope." Since Nathaniel continued yelling during the robbery, the group bound him with duct tape. Defendant then poured gasoline on the victims to scare them into giving him their money. Defendant changed his story to say that Romero then shot the victims, but defendant used a lighter to set them on fire. He said he dropped a match on them but it "didn't ignite." When asked who started the fire, defendant said, "somebody else could have ... hit them with a match or something, I don't know. I do remember that when I dropped that match it did not go up." He said he did not want to implicate anyone else because he "can't really identify the individuals with me." He also said he did not feel bad for the victims and their families because he was "gonna have to do prison time."
Detective Dennis Florence testified that a shoot-out involving a man named Jerry Corhn occurred in March 2002. Corhn *91fired on officers as they pursued him following an attempted narcotics transaction at a restaurant in Barstow. Corhn ultimately died from a self-inflicted gunshot wound to the head. Ballistics testing showed that the .45-caliber firearm recovered from Corhn's vehicle matched bullet casings recovered from the T-shirt store murders. When Griego showed defendant a photo lineup that included a picture of Corhn, defendant pointed to Corhn's picture and said he knew him because Corhn had purchased a firearm from him when he was staying in Barstow.
3. Defense Evidence
Defendant did not testify at trial, nor did he present any evidence. He did attempt to call one witness, Amber Renteria-Kelsey, but she successfully invoked her Fifth Amendment right against self-incrimination, and the court excused her.
*1001B. Penalty Phase
Lisa Martin and her mother, Penny Bartis, testified that on January 4, 2000, a month after he moved out of Martin's home, defendant returned with two other men and committed a home invasion robbery. Defendant knocked on the door. When Bartis answered, defendant burst into the house. His two accomplices followed and took the victims to a back bedroom. Defendant was armed and threatened to kill Martin and her family. He then stole money and personal property. Martin testified that the robbery lasted several hours, and defendant and his accomplices stole $6,000 cash as well as jewelry, expensive vases, a safe, and important papers. Martin explained that after the robbery defendant called her and told her that her son, who was also present during the robbery, was being watched. She subsequently took her son out of school. Bartis testified that after the robbery, she received four or five phone calls from defendant asking for Martin. Martin fled to Colorado, leaving her son with Bartis.
Misty Sedillo testified that in 1993, when she was 16 years old, she rode with defendant in a car. Defendant and his friends wanted to shoot at a house, but Misty asked them not to because her brother was playing in the front yard. Later during the ride, defendant pointed a gun at Misty's head.
In September 2002, a deputy sheriff found a homemade shank in defendant's jail cell. Defendant said he feared for his life and that he would not hesitate to use the shank and would make another. He also admitted that for two months he smuggled the shank into court because he planned to stab one of the witnesses who was testifying against him. Another deputy sheriff found a letter defendant tried to mail to elected District Attorney Michael Ramos. In the letter, defendant advised the prosecution to give him the death penalty or else there will be "a lot of blood" on the "County's hands." The prosecution also presented evidence of defendant's 1994 felony conviction for receiving stolen property.
Charlene Garcia, Nathanial's daughter and Consuelo's stepdaughter, testified that her **736parents' murder had a significant negative impact on her and her family.
Defendant presented the testimony of Albert Capers, his biological grandfather. Capers stated that he and his wife adopted and raised defendant, whom they loved.
*1002II. DISCUSSION
A. Issues Regarding Guilt
1. Alleged Lack of Independent Evidence
Defendant initially contends that his statements to law enforcement about *92his involvement in the T-shirt store crimes were so inconsistent and contradictory that they could not serve as corroboration of one another. He does not challenge the admission of his statements on Miranda grounds. However, he contends that because there was no physical evidence or eyewitness testimony to corroborate the trustworthiness of any one of his various confessions, his conviction must be reversed. Defendant relies on the federal common law corroboration rule intended to prevent errors in convictions based on a witnesses' untrue statement alone. ( Opper v. United States (1954) 348 U.S. 84, 93, 75 S.Ct. 158, 99 L.Ed. 101.) If applied here, the rule means that defendant's admissions or confessions may not serve as the basis for his conviction absent "substantial independent evidence which would tend to establish the trustworthiness of the [admissions or confessions]." ( Ibid. ) However, as part of the federal common law, we are not bound to follow the federal corroboration rule.
Some state courts follow the federal corroboration rule (see, e.g., Armstrong v. State (Alaska 1972) 502 P.2d 440, 447 ), but California does not. We instead apply the corpus delicti rule, which originally required independent proof of an actual crime before extrajudicial admissions could be admitted as evidence. (See People v. Alvarez (2002) 27 Cal.4th 1161, 1169-1170, 119 Cal.Rptr.2d 903, 46 P.3d 372 ( Alvarez ).) The rule derives from California common law. ( Id. at p. 1173, 119 Cal.Rptr.2d 903, 46 P.3d 372.)
In 1982, Proposition 8 abrogated much of the corpus delicti requirement when it added the Right to Truth-in-Evidence provision to article I of the California Constitution. ( Cal. Const., art. I, § 28, subd. (d), added by initiative, Primary Elec. (Jun. 8, 1982), commonly known as Prop. 8 ( section 28 (d).)6 As Alvarez observed, with certain exceptions, Proposition 8 abolished "all state law restrictions on the admissibility of relevant evidence, necessarily including the prong of the corpus delicti rule that bars introduction of an accused's out-or-court statements absent independent proof a crime was committed." ( Alvarez , supra , 27 Cal.4th at p. 1179, 119 Cal.Rptr.2d 903, 46 P.3d 372 ; see People v. Ray (1996) 13 Cal.4th 313, 341, 52 Cal.Rptr.2d 296, 914 P.2d 846.) We cautioned that the pre-2008 version of " section 28 (d) did not eliminate the independent-proof rule insofar *1003as that rule prohibits conviction where the only evidence that the crime was committed is the defendant's own statements outside of court." ( Alvarez , supra , 27 Cal.4th at p. 1180, 119 Cal.Rptr.2d 903, 46 P.3d 372.) We noted that the amount of independent evidence required is not great and may be circumstantial with only " 'a slight or prima facie showing' " that permits "an inference of injury, loss, or harm from a criminal agency, after which the defendant's statements may be considered to strengthen the case on all issues." ( Id. at p. 1181, 119 Cal.Rptr.2d 903, 46 P.3d 372.) Alvarez made it clear, however, that the pre-2008 version of " section 28 (d) did not affect the rule to the extent it (1) requires an instruction to the jury that no person may be convicted absent evidence of the crime independent of his or her out-of-court statements or (2) allows the defendant, on appeal, directly to attack the sufficiency of the prosecution's independent showing." ( Alvarez , supra , 27 Cal.4th at p. 1180, 119 Cal.Rptr.2d 903, 46 P.3d 372.) *93Even though the prosecution need satisfy only one prong of section 28(d)'s post-Proposition 8 requirement, both prongs of original section 28(d) were met here. Specifically, the record shows that the trial court **737instructed with CALJIC No. 2.72, which informed the jury that defendant's statements to law enforcement must be supported by independent evidence: "No person may be convicted of a criminal offense unless there is some proof of each element of the crime independent of any confession or admission made by him outside of this trial. [¶] The identity of the person who is alleged to have committed a crime is not an element of the crime nor is the degree of the crime. The identity or degree of the crime may be established by a confession or admission. [¶] The corpus delicti of a felony-based circumstance need not be proved independently of a defendant's extrajudicial statement." Indeed, defendant's words alone may establish the degree of his crime or his identity as the perpetrator. ( People v. Valencia (2008) 43 Cal.4th 268, 297, 74 Cal.Rptr.3d 605, 180 P.3d 351 ; People v. Ledesma (2006) 39 Cal.4th 641, 721, 47 Cal.Rptr.3d 326, 140 P.3d 657.) The jury was also instructed that it was the exclusive judge of the truth of defendant's confessions and admissions; the instruction defined both a confession and an admission and instructed that the jury should view any such statements with caution.
The People's showing of a criminal act, independent of defendant's statements, satisfies the corpus delicti rule. Here, there was substantial independent evidence of "injury, loss, or harm by a criminal agency." ( Alvarez , supra , 27 Cal.4th at p. 1171, 119 Cal.Rptr.2d 903, 46 P.3d 372.) Defendant told law enforcement that he fired the fatal shots that killed one of the victims, hid the .45-caliber gun and bullet casings, poured gasoline on the victims, and lit them on fire. Much of the physical evidence corroborates defendant's statements, including the victims' burnt bodies, .45-caliber bullets and one bullet casing recovered at the scene of the murders, and the ample physical evidence that the victims were beaten *1004before they were killed. As noted, the autopsy concluded Nathaniel died from gunshot wounds and that Consuelo died from blunt force head injuries.
Defendant, however, contends that his well-documented drug and alcohol abuse render all his recollections fatally suspect. Defendant advances a related argument, namely, that his statements were so contradictory, and his history of drug and alcohol abuse, including during the day of the crimes, is so clear, that none of his statements is trustworthy enough to even warrant corroboration. He notes he gave 10 separate statements to authorities. He recounts that in his first statements to Griego, he denied all involvement in the crimes. Later he claimed only to be a lookout. Still later, he confessed to pouring gasoline on the victims. Similarly, his description of the perpetrators changed over time and was thus unreliable.
Defendant claims that statements of someone with his history of substance abuse, who admitted to being under the influence of drugs and alcohol at the time of the event in question, do not even evidence minimal indicia of reliability and trustworthiness. Additionally, defendant asserts that when he spoke to law enforcement in 2001, he was on "psychotopic [sic ] medication."
Defendant also contends that his most inculpatory statements to law enforcement were effectively coerced, and thus even less trustworthy than some of his earlier statements because he was threatened with his half-brother's incarceration if he did not tell them what they wanted to hear. Additionally, he claims that his statements *94to Martin and Bartis lacked trustworthiness because they were biased against him because he robbed them.
Contrary to defendant's argument, considerations of trustworthiness, whether based on his ability to recall or on other factors, are the exclusive province of the jury. ( People v. Anderson (2018) 5 Cal.5th 372, 404, 235 Cal.Rptr.3d 1, 420 P.3d 825.) Thus, allowing the jury to judge the relevant evidence did not violate defendant's due process rights. ( People v. Lopez (2018) 5 Cal.5th 339, 353-354, 235 Cal.Rptr.3d 64, 420 P.3d 878.)
Initially, we note that defendant presents no evidence that investigators either tainted the evidence or coerced defendant's inculpatory statements. Rather, the jury was presented with ample evidence corroborating defendant's inculpatory statements. In addition to the physical evidence that matched defendant's **738statements, the jury heard Griego testify that law enforcement purposefully withheld from the public certain information about the crimes-e.g., the caliber of the firearm used, that Nathaniel's cause of death was by a firearm, and that Nathaniel had been bound with duct tape. Defendant's statements contained this same information. Defendant also admitted that he *1005and the others stole Consuelo's Camaro and drove it to a nearby Motel 6. As already noted, the car was found in a Motel 6 parking lot about two miles from the crime scene. In addition, Tirado testified that a week before the murders defendant and his brother spoke with him about robbing the victims' T-shirt shop, and Leatham asked if Tirado wanted to participate in the robbery, but Tirado declined. Although Tirado stated at one point that it was Leatham who did most of the talking about planning to rob the T-shirt store, his statement was consistent with defendant's admission that he and his cohorts planned the robbery.
We conclude the corpus delicti rule was satisfied here and that the jury properly considered all of defendant's independent statements regarding his participation in the robbery and murders. To the extent there was inconsistency among defendant's various statements, the court properly left it to the jury to decide the veracity of each statement. This is true whether defendant characterizes some of his statements as voluntary, internalized (from a susceptible or weak defendant), compliant (occurring during police interrogation), false confessions-or as the product of a memory rendered unreliable by years of substance abuse, by sleep deprivation, or by psychotropic drugs. Similarly, we find, despite defendant's argument to the contrary, that his statements contained sufficient indicia of reliability to satisfy what we have described as the Eighth Amendment's "heightened reliability standards for both guilt and penalty determinations in capital cases." ( People v. Cudjo (1993) 6 Cal.4th 585, 623, 25 Cal.Rptr.2d 390, 863 P.2d 635.)
2. Alleged Due Process Denial
a. Background
The prosecution's trial theory was that four people were involved in the T-shirt store murders: Defendant, Loomis, Romero, and defendant's half-brother, Leatham. The prosecution's case was that defendant's videotaped confessions supported the theory that defendant was the principal actor who had robbed and set fire to the victims.
To support his defense that he was not responsible for robbing, shooting or burning the victims, defendant sought to present the testimony of Amber Renteria-Kelsey (Renteria) who made two statements to Griego (one on May 26, 1999, and one on October 5, 1999) that she had overheard Loomis admit to another gang member *95nicknamed "Midget" that he and Romero were involved in robbing and burning down the victims' T-shirt store.
On November 1, 1999, Barstow Police Department received two handwritten letters addressed to Griego from Renteria, asserting that "there was no *1006truth" to the statements she made to the detective during their May 26 and October 5, 1999 interviews. The letters did not mention the names of the perpetrators, or specifically describe the crime. They merely stated that Renteria "was pretty much scared because I had already told you one thing and didn't know how to tell you the truth" but she could not go on lying "about this situation." In an interview with Griego in October 2003, Renteria again retracted her statements implicating both men, claiming she was on drugs when she made them, "not in [her] right state of mind," and the statements were not true. She told the detective that "What I told you at first about the two people, Bam-Bam [Loomis] and Wino [Romero] is not true."
During the trial's guilt phase and outside the presence of the jury, defense counsel stated that he intended to call Renteria as a defense witness. Renteria was in custody for an unrelated case and was present in court. The court appointed supervising deputy public defender Mark Shoup to represent Renteria and to determine if her testimony might tend to incriminate her such that she might assert her Fifth Amendment right to remain silent. Later, when the court asked if Renteria's testimony might expose her to criminal **739prosecution, Shoup stated that Renteria could be charged with committing a misdemeanor offense for falsely reporting criminal offenses to a peace officer. (See § 148.5 [falsely reporting criminal offenses to a peace officer is misdemeanor offense].)7 Counsel advised Renteria to assert her Fifth Amendment privilege. The court then noted that the prosecution could offer Renteria transactional immunity. However, the prosecutor indicated that the People were not willing to provide immunity in the case. The court upheld Renteria's privilege invocation after concluding that it could not "force her to make statements that may tend to incriminate her." The court ruled that defendant could not call Renteria as a witness. It explained that its ruling was tentative and that it would allow defense counsel to present points and authorities to support defendant's argument. The court noted that it would reopen the issue if it found "something different as far as the testimony of Renteria."
During a subsequent discussion outside the presence of the jury, Shoup conceded that Renteria had no basis to assert her Fifth Amendment privilege for the section 148.5 misdemeanor offense of making the false police report to Griego because the one-year statute of limitations for that offense had run. When the court asked the prosecutor for his view whether there was a felony statute that applied to Renteria's statements, the prosecutor stated that he did not know, but that Renteria might be liable as an accessory under section 32. The court responded: "I don't know how realistic [sic ] she can be an *1007accessory ... if her initial statement to [Griego] was that something that pointed suspicion at somebody else. I don't know." Defendant's counsel then asserted that Renteria did not have a valid privilege. *96Later, the prosecutor told the court that he had spoken to Shoup, and based on that conversation, he believed Renteria would be susceptible to a section 32 charge if her intent was to protect Loomis. He also noted that he was not sure of her intent because he had never spoken with her. Shoup agreed with the prosecutor's section 32 evaluation and noted that Renteria had exposure to the criminal statute because her last contact with Griego was in October 2003, and that if it was determined she lied in 2003, the three-year statute of limitations for a violation of section 32 had yet to run. Defense counsel argued that Renteria's statement implicating Loomis and Romero would exonerate defendant. When the court asked the prosecutor to explain how Renteria could make a false statement and still be criminally liable for a section 32 violation, the prosecutor hypothesized: "She could have made up that first statement, but still know that he was involved. If she overheard another conversation that she never told Griego about, and then [lied] to Griego when she talked to him in 2003 to protect Loomis," then she could be liable as an accessory under section 32.
Shoup later interjected, "Just so the record's clear here, the only statements that I see that Amber Renteria [attributes] to Bam-Bam [Loomis] is that Bam-Bam said that he had to get out of town because he and his homie, Wino [Romero], had robbed a place on Main Street and the place burned down. And then, Renteria told me that Bam-Bam had also said that he had to burn the place to get rid of evidence. Those are the only statements that I am aware of. There is nothing in that that exonerates this defendant."
Before the commencement of the penalty phase, Renteria again testified under oath, outside the presence of the jury. She repeated her invocation of her Fifth Amendment privilege. The court stated that it would grant Renteria immunity if it had the power to do so in order to resolve the matter, and again asked the prosecutor if his office would grant the witness immunity. The prosecutor declined, explaining, "If we believe that Renteria had any credibility whatsoever, we would have used [her] statement to file on Carlos Loomis murder charges. We did not do that. We believe she has no credibility at all. That's important to put on the record." The court observed that the case was different from cases in which false testimony led to **740an erroneous conviction. (See e.g., Chambers v. Mississippi (1973) 410 U.S. 284, 298, 93 S.Ct. 1038, 35 L.Ed.2d 297.) The court then upheld Renteria's Fifth Amendment privilege and dismissed her as a defense witness. It concluded that the three-year statute of limitations for a violation of section 32 had not expired, and that Renteria was potentially exposed to criminal prosecution under section 32 for *1008her statements to Griego that she recanted. During the penalty phase, the court similarly ruled that it would not allow the defense to call Renteria.
b. Discussion
Defendant asserts that Renteria's refusal to testify and thereby admit she lied to Griego about defendant's involvement in the T-shirt store murders denied him his due process right to present a defense under the Sixth Amendment. We disagree.
The state and federal constitutions provide that a criminal defendant has the right "to have compulsory process for obtaining witnesses in his favor." ( U.S. Const., 6th Amend.; Cal. Const. art. I, § 15.) The federal compulsory process right is "so fundamental and essential to a fair trial that it is incorporated in the Due Process Clause of the Fourteenth Amendment," making it applicable to the states.
*97( Washington v. Texas (1967) 388 U.S. 14, 17-18, 87 S.Ct. 1920, 18 L.Ed.2d 1019 ( Washington ).) Under federal law, a denial of the right to present a defense occurs when the exclusion of the evidence infringes "upon a weighty interest of the accused." ( United States v. Scheffer (1988) 523 U.S. 303, 308, 118 S.Ct. 1261, 140 L.Ed.2d 413.) A weighty interest of the defendant is infringed when "[t]he exclusions of evidence ... significantly undermined fundamental elements of the accused's defense." ( Id. at p. 315, 118 S.Ct. 1261.)
Our state compulsory process right "is independently guaranteed by the California Constitution" under article 1, section 15, and is "deemed to be at least as broad and fundamental as the federal" right. ( In re Martin (1987) 44 Cal.3d 1, 30, 241 Cal.Rptr. 263, 744 P.2d 374 ( Martin ).) The government violates a defendant's constitutional right to compulsory process when it interferes with the exercise of a defendant's right to present witnesses on his own behalf. ( Ibid. ) A defendant establishes such interference when he or she demonstrates the prosecution intimidated defense witnesses by telling them they could be prosecuted for any crimes they revealed during their testimony. ( Ibid. ) Defendant must also demonstrate the misconduct was a substantial cause of his witness's refusal to testify. ( Id. at p. 31, 241 Cal.Rptr. 263, 744 P.2d 374.) Defendant additionally "must show at least a reasonable possibility that the witness could have given testimony that would have been both material and favorable." ( Id. at p. 32, 241 Cal.Rptr. 263, 744 P.2d 374.) If a defendant successfully sustains his burden of demonstrating prejudice, the verdict must be reversed. ( Id. at p. 51, 241 Cal.Rptr. 263, 744 P.2d 374.)
In Martin , we held that the defendant successfully demonstrated a compulsory process violation. ( Martin , supra , 44 Cal.3d at p. 42, 241 Cal.Rptr. 263, 744 P.2d 374.) There, the prosecutor committed prejudicial misconduct when he informed the defense witness's attorney that if the defense witness testified, he would not get *1009immunity and would be prosecuted if he implicated himself in a crime or committed perjury. ( Id. at pp. 36-37, 40, 241 Cal.Rptr. 263, 744 P.2d 374.) We found substantial causation between the misconduct and the defendant's inability to present witnesses on his own behalf because the witness stated he decided to assert his Fifth Amendment right to remain silent after he learned the prosecutor would not grant him immunity and he had an encounter with a district attorney investigator who threatened arrest and got " 'in his face.' " ( Id. at p. 37, 241 Cal.Rptr. 263, 744 P.2d 374.) Martin also held the testimony was reasonably " 'material and favorable' " because the witness's statements contradicted the testimony of another witness adverse to the defendant. ( Id. at p. 42, 241 Cal.Rptr. 263, 744 P.2d 374.)
Defendant claims the prosecutor committed prejudicial misconduct when he told Shoup that Renteria could be charged as an accessory under section 32, and that he would not grant Renteria immunity from prosecution on the ground that her statements **741and retractions were not credible. (See supra , 251 Cal.Rptr.3d at p. 96, 446 P.3d at p. 739; Martin , supra , 44 Cal.3d at pp. 37, 241 Cal.Rptr. 263, 744 P.2d 374.) Defendant would have us find prejudice because Renteria's proposed testimony was material and favorable to the defense because (1) her testimony would have exonerated him, and (2) the prosecutor's actions were a substantial factor in causing Renteria to invoke her Fifth Amendment privilege.
We find no constitutional violation or prosecutorial misconduct. It was Shoup who initially told the court that his client *98was exposed to potential misdemeanor criminal liability. The prosecutor told the court that Shoup was in the best position to determine any potential criminal liability. He also agreed with Shoup that Renteria had exposure to criminal liability. Later, in answer to a question from the court, the prosecutor opined that Renteria would be exposed to criminal liability under a different statute (§ 32) than that initially identified by Shoup. Shoup agreed with the prosecutor's assertion. There is also no indication that the prosecutor committed misconduct when he refused to grant the witness immunity. He explained to the court that Renteria had no credibility as a witness. As he pointed out, if she had any credibility, the District Attorney would also have charged Loomis with the murders.
In contrast to the trial court in Martin , the court here did not deny defendant the right to "put on the stand a witness who was physically ... capable of testifying ... and whose testimony would have been relevant and material to the defense." ( Washington , supra , 388 U.S. at p. 23, 87 S.Ct. 1920.) Renteria's testimony would not have exonerated defendant, or been material to his defense, either by tending to prove he did not commit the crimes charged or by diminishing his involvement. In fact, Renteria's proposed testimony would have reiterated the prosecution's theory, based in part on defendant's admissions, that defendant committed the crimes with Loomis and Romero. Even if *1010her statement had been admitted, she could have been impeached with her subsequent recantation and comments that she was on drugs when she implicated Loomis and Romero in the murders. Renteria's decision not to testify, upheld by the court, did not deny defendant the right to present a defense nor his Eighth Amendment right to have the jury hear all mitigating evidence at the penalty phase.
3. Alleged Fifth Amendment Privilege
Apart from asserting a compulsory process violation, defendant also claims the court erred in granting Renteria's Fifth Amendment privilege because the statute of limitations to charge her had run on any violation of section 32 before she was to be called as a witness. Defendant asserts that the statute of limitations started running on a section 32 violation in October 1999, when Renteria sent her first retraction letter to the police and not when she retracted her inconsistent statements in October 2003.
The Attorney General responds that defendant forfeited this argument because he did not raise it in the trial court. Defendant effectively concedes he never raised the claim in the trial court but contends he did not forfeit his claim because it is based on "undisputed facts" contained in one of Griego's reports that states: "Renteria later (on 10-29-99) sent me a letter at the Barstow Police Department 'retracting' her statements." (See Williams v. Mariposa County Unified School District (1978) 82 Cal.App.3d 843, 850, 147 Cal.Rptr. 452 [if facts supporting new contention on appeal are undisputed, court may entertain the contention as a question of law on those facts].) Defendant also contends that although defense counsel might have been aware of Renteria's 1999 retraction letter and yet failed to raise it as a defense to her exposure to criminal liability, the prosecution team, including Griego, "had an independent duty to make sure that the trial court was made aware of Renteria's earlier retraction." Defendant's claims fail. Even if we were to assume that Renteria's testimony would have assisted defendant's defense, and that he did not forfeit his claim regarding the 1999 retraction letter, he has stated no constitutional or prosecutorial violations.
*99The standards governing defendant's contention that the court erred in granting Renteria's Fifth Amendment assertion are well established. The Fifth Amendment privilege provides that "[n]o person ... shall be compelled in any criminal case to be **742a witness against himself." ( U.S. Const., 5th Amend.; Cal. Const., art. I, § 15.) The high court has held that the privilege "marks an important advance in the development of our liberty." ( Kastigar v. United States (1972) 406 U.S. 441, 444, 92 S.Ct. 1653, 32 L.Ed.2d 212.) It "must be accorded liberal construction in favor of the right it was intended to secure." ( Hoffman v. United States (1951) 341 U.S. 479, 486, 71 S.Ct. 814, 95 L.Ed. 1118 ( Hoffman ).) Recognizing that the trial court *1011must determine whether there is reasonable cause for the privilege to extend to the witness, Hoffman left it to the court to determine whether the witness's "silence is justified." ( Ibid. ) Hoffman instructed: "To sustain the privilege, it need only be evident from the implications of the question, in the setting in which it is asked, that a responsive answer to the question or an explanation of why it cannot be answered might be dangerous because injurious disclosure could result. The trial judge in appraising the claim 'must be governed as much by his personal perception of the peculiarities of the case as by the facts actually in evidence.' " ( Id. at pp. 486-487, 71 S.Ct. 814.) Our state jurisprudence incorporates the broad Hoffman standard. (See People v. Seijas (2005) 36 Cal.4th 291, 304, 30 Cal.Rptr.3d 493, 114 P.3d 742 ( Seijas ).)
Our Evidence Code implements the privilege as follows: "Whenever the proffered evidence is claimed to be privileged under Section 940 [privilege against self-incrimination], the person claiming the privilege has the burden of showing that the proffered evidence might tend to incriminate him; and the proffered evidence is inadmissible unless it clearly appears to the court that the proffered evidence cannot possibly have a tendency to incriminate the person claiming the privilege." ( Evid. Code, § 404.)
We conclude that the federal and state constitutions supported the trial court's decision to grant Renteria her Fifth Amendment privilege whether or not the court was aware of the 1999 retraction letter that Renteria had sent to Griego. (See Seijas , supra , 36 Cal.4th at p. 304, 30 Cal.Rptr.3d 493, 114 P.3d 742.) On review of a witness's successfully invoking the Fifth Amendment privilege, we look only to see whether it is evident from the "implications of the question, in the setting in which it is asked, that a responsive answer to the question or an explanation of why it cannot be answered might be dangerous because injurious disclosure could result." ( Hoffman , supra , 341 U.S. at pp. 486-487, 71 S.Ct. 814.) In fact, a trial court may deny Fifth Amendment privilege only if it is " 'perfectly clear, from a careful consideration of all the circumstances in the case, that the witness is mistaken, and that the answer[s] cannot possibly have such tendency' to incriminate." ( Id. at p. 488, 71 S.Ct. 814, italics omitted.) Our state jurisprudence is equally strong in its protection of the right and holds that the Fifth Amendment does not allow "the court to assess the likelihood of an actual prosecution in deciding whether to permit the privilege." ( Seijas , supra , 36 Cal.4th at p. 305, 30 Cal.Rptr.3d 493, 114 P.3d 742 ; see Evid. Code, § 404.)
Renteria and her counsel could reasonably have concluded that Renteria would be subject to criminal prosecution under section 32 for her statements to Griego about what she overheard if compelled to testify. Section 32 subjects a person to criminal liability for aiding a principal in *100avoiding conviction or punishment for a crime. Renteria's inconsistent statements could have a tendency to incriminate her because it is possible they could *1012have supported a charge that she sought to help Loomis and Romero in avoiding prosecution of the crimes at issue. (See § 32; Evid. Code, § 404.) We find the court did not err when it granted Renteria her Fifth Amendment privilege. ( Hoffman , supra , 341 U.S. at p. 488, 71 S.Ct. 814.)
We also find that the prosecution did not engage in misconduct in failing to raise Renteria's 1999 retraction earlier during the trial court's colloquy about Renteria's asserted Fifth Amendment privilege. We have held that "[a] prosecutor's conduct violates the federal Constitution when it infects the trial with such unfairness as to make the resulting conviction a denial of due process. Conduct by a prosecutor that does not rise to this level nevertheless violates California law if it involves the use of deceptive or reprehensible methods to attempt to persuade either the **743court or the jury." ( People v. Whalen (2013) 56 Cal.4th 1, 52, 152 Cal.Rptr.3d 673, 294 P.3d 915.) Even though the statute of limitations had passed on Renteria's initial alleged lie to Detective Griego in 1999, it had not passed when she allegedly lied in her second retraction of 2003. Here, there is no indication that the prosecutor's conduct rendered the trial so unfair as to deny defendant due process, or that his silence on the issue misled the court in order to persuade it in violation of California law. ( Ibid. ) The prosecutor thoroughly discussed the effect of Renteria's 2003 statement with the court in the presence of defendant's counsel as well as Renteria's counsel, as discussed supra , at pages 95 to 96, 446 P.3d at pages 738 to 739. Additionally, the prosecution's theory was based on defendant's own statements that he had committed the crimes with Loomis and Romero. There is simply no indication that awareness of the 1999 retraction letter would have changed the court's decision to grant Renteria's right to silence or would have otherwise infected the trial with such unfairness that defendant's conviction amounted to a denial of due process.
B. Issues Regarding Penalty
1. Constitutionality of California's Death Penalty Statute
Defendant asserts numerous challenges to California's death penalty law that we have repeatedly rejected. We reiterate our previous decisions.
a. Whether Penal Code section 190.2 is impermissibly broad
Defendant asks that we reconsider our well-established holding that "special circumstances listed in section 190.2 that render a murderer eligible for the death penalty, which include felony murder and lying in wait, are not so numerous and broadly interpreted that they fail to narrow the class of death-eligible first degree murderers as required by the Eighth and Fourteenth *1013Amendments." ( People v. Brooks (2017) 3 Cal.5th 1, 114-115, 219 Cal.Rptr.3d 331, 396 P.3d 480 ; see ibid . [upholding the current version of section 190.2 which is very similar to version defendant was convicted under]; People v. Stanley (1995) 10 Cal.4th 764, 842-843, 42 Cal.Rptr.2d 543, 897 P.2d 481.) We decline to do so.
b. Whether Penal Code section 190.3 is arbitrary and capricious
We have repeatedly rejected the claim that section 190.3, factor (a), which requires the jury to consider as evidence in aggravation the circumstances of the capital crime, arbitrarily and capriciously imposes the death penalty under the Fifth, *101Sixth, Eighth, and Fourteenth Amendments to the United States Constitution. (See Brooks , supra , 3 Cal.5th at p. 115, 219 Cal.Rptr.3d 331, 396 P.3d 480.) We decline defendant's request to review our prior holdings.
c. Whether unanimous jury findings are required
As we have many times held, "[t]he jury's reliance on unadjudicated criminal activity as a factor in aggravation under section 190.3, factor (b), without any requirement that the jury unanimously find that the activity was proved beyond a reasonable doubt, does not deprive a defendant of any federal constitutional rights, including the Sixth Amendment right to trial by jury and the Fourteenth Amendment right to due process." ( Brooks , supra , 3 Cal.5th at p. 115, 219 Cal.Rptr.3d 331, 396 P.3d 480.) We have also held that the federal Constitution does not require unanimous jury findings for imposing the death sentence, nor must the jury agree on the existence on any one aggravating factor. ( People v. Hamilton (2009) 45 Cal.4th 863, 960, 89 Cal.Rptr.3d 286, 200 P.3d 898.) Defendant contends that we must reconsider these holdings and others, including People v. Prieto (2003) 30 Cal.4th 226, 263, 133 Cal.Rptr.2d 18, 66 P.3d 1123 ( Prieto ), in light of Ring v. Arizona (2002) 536 U.S. 584, 602, 122 S.Ct. 2428, 153 L.Ed.2d 556 ( Ring ), which followed Blakely v. Washington (2004) 542 U.S. 296, 303-305, 124 S.Ct. 2531, 159 L.Ed.2d 403 (and Apprendi v. New Jersey (2000) 530 U.S. 466, 490, 120 S.Ct. 2348, 147 L.Ed.2d 435 ), to hold that any fact that increases the penalty for a crime beyond the prescribed statutory maximum, other than the fact of a prior conviction, must be submitted to a jury and proved beyond a reasonable **744doubt before its decision that death is the appropriate sentence.
Defendant makes the same argument as the defendant made in Prieto , that Ring undermines our previous holdings that: "(1) the jury need not find that the aggravating circumstances outweigh the mitigating circumstances beyond a reasonable doubt; (2) the jury need not find each aggravating factor beyond a reasonable doubt; (3) juror unanimity on the aggravating factors is not *1014necessary; and (4) written findings are not required." ( Prieto , supra , 30 Cal.4th at p. 275, 133 Cal.Rptr.2d 18, 66 P.3d 1123.) As we explained in Prieto , the jury's penalty determination is normative, not factual, and is "analogous to a sentencing court's traditionally discretionary decision to impose one prison sentence rather than another." ( Ibid . )
Defendant also asserts that the high court's decision in Hurst v. Florida (2016) 577 U.S. ----, 136 S.Ct. 616, 193 L.Ed 2d 504 ( Hurst ), which invalidated Florida's capital sentencing scheme, also invalidates California's capital sentencing scheme. Like Ring , Hurst requires a jury to find each fact necessary to impose the death sentence. (Ibid .) Further, defendant claims that Hurst makes it clear that our sentencing determination violates the Sixth Amendment because it collapses "the weighing finding and the sentence-selection decision into one determination and labeling it 'normative' rather than factfinding" by a jury beyond a reasonable doubt. It does not. ( People v. Rangel (2016) 62 Cal.4th 1192, 1235 & fn. 16, 200 Cal.Rptr.3d 265, 367 P.3d 649.) Our cases have consistently rejected similar arguments. ( Ibid. ) The California sentencing scheme is materially different from that in Florida, which, in contrast to our death penalty statutes, mandates that the trial court alone must find that sufficient aggravating circumstances outweigh the mitigating circumstances. ( Hurst , supra , 577 U.S. ----, [136 S.Ct. at p. 622] ; see *102Fla. Stat. § 775.082(1).) Once the jury renders a verdict of death, "our system provides for an automatic motion to modify or reduce this verdict to that of life imprisonment without the possibility of parole. ( Pen. Code, § 190.4.) At the point the court rules on this motion, the jury 'has returned a verdict or finding imposing the death penalty.' " ( Rangel , supra , 62 Cal.4th at p. 1235, fn. 16, 200 Cal.Rptr.3d 265, 367 P.3d 649.) We do not find that Hurst in any way undermines our previous rulings upholding the constitutionality of our death penalty scheme. (See People v. Becerrada (2017) 2 Cal.5th 1009, 1038, 216 Cal.Rptr.3d 662, 393 P.3d 114 ; see also People v. Brown (1985) 40 Cal. 3d 512, 541, 230 Cal.Rptr. 834, 726 P.2d 516 [jury may reject death sentence even after it has found aggravation outweighs mitigation].)
d. Validity of California's Death Penalty Jury Instructions
i. Reasonable doubt
Defendant contends that the trial court erred when it did not instruct the jury that the prosecution bore the burden of proof. He argues that his "jury should have been instructed that the State had the burden of persuasion regarding the existence of any factor in aggravation, whether aggravating factors outweighed mitigating factors, and the appropriateness of the death penalty, and that it was presumed that life without parole was an appropriate sentence." Alternatively, defendant asserts that if there is no burden of proof, *1015the jury should have been informed that the prosecution has no burden of proof in capital sentencing.
We have never held that the Sixth and Fourteenth Amendments require a jury instruction regarding the burden of proof in capital sentencing. (See People v. Williams (1988) 44 Cal.3d 883, 960, 245 Cal.Rptr. 336, 751 P.2d 395.) As the Attorney General observes, the only burden of proof applicable at the penalty phase "relates to aggravating evidence of other crimes under factor (b) [ People v. Foster (2010) 50 Cal.4th 1301, 1364, 117 Cal.Rptr.3d 658, 242 P.3d 105 ], and aggravating evidence of prior convictions under factor (c). (See [People v.] Williams , supra , [ (2010) ] 49 Cal.4th [405] at p. 459 [111 Cal.Rptr.3d 589, 233 P.3d 1000].)" Otherwise, our cases do not require that a burden of proof be applied to aggravating evidence. (See **745People v. Lewis (2009) 46 Cal.4th 1255, 1319, 96 Cal.Rptr.3d 512, 210 P.3d 1119.)
ii. Unanimous agreement on aggravating factors
Defendant contends the trial court violated his rights under the Sixth, Eighth, and Fourteenth Amendments when it failed to instruct the jury that it must unanimously agree on the same factors in aggravation. We have "consistently held that unanimity with respect to aggravating factors is not required by statute or as a constitutional procedural safeguard." ( People v. Taylor (1990) 52 Cal.3d 719, 749, 276 Cal.Rptr. 391, 801 P.2d 1142 ( Taylor ).)
The same is true for prior unadjudicated criminal activity. We have repeatedly rejected claims that the jury's findings of prior unadjudicated crimes must be unanimous in relation to evidence admitted under section 190.3, factor (b). ( People v. Foster (2010) 50 Cal.4th 1301, 1364-1365, 117 Cal.Rptr.3d 658, 242 P.3d 105.)
iii. Alleged vague instructions
Contrary to defendant's assertion, California's death penalty jury instructions are not unconstitutionally vague, because they provide that a jury "must be persuaded that the aggravating circumstances are so substantial in comparison *103with the mitigating circumstances that it warrants death instead of life without parole." ( CALJIC No. 8.88, italics added.) The " 'so substantial' " language does not violate the Eighth and Fourteenth Amendments. ( People v. Ghobrial (2018) 5 Cal.5th 250, 292, 234 Cal.Rptr.3d 669, 420 P.3d 179.)
iv. Requiring written findings
We also decline defendant's request that we reconsider our prior holdings that do not require jurors to submit written findings during a capital case's penalty phase. ( Taylor , supra , 52 Cal.3d at p. 749, 276 Cal.Rptr. 391, 801 P.2d 1142.)
*1016v. Converse principle instruction
Contrary to defendant's view, it is unnecessary for the trial court to instruct the jury that if it determines mitigation outweighs aggravation, it must return a verdict of life without the possibility of parole. ( People v. Kopatz (2015) 61 Cal.4th 62, 95, 186 Cal.Rptr.3d 797, 347 P.3d 952 ( Kopatz ).)
vi. Jury Unanimity on mitigation
We continue to reject the contention raised here that a jury must be instructed regarding the standard of proof and the lack of a need for jury unanimity as to mitigating circumstances. ( Kopatz , supra , 61 Cal.4th at p. 95, 186 Cal.Rptr.3d 797, 347 P.3d 952, citing People v. Streeter (2012) 54 Cal.4th 205, 268, 142 Cal.Rptr.3d 481, 278 P.3d 754.)
vii. Presumption of life instruction
Consistent with our cases, we affirm the view that the trial court, contrary to defendant's argument, is not required to instruct the jury that the law favors a presumption of life in the penalty phase. (See People v. Arias (1996) 13 Cal.4th 92, 190, 51 Cal.Rptr.2d 770, 913 P.2d 980.)
viii. Failure to delete inapplicable sentencing factors
As we held in People v. Cook (2006) 39 Cal.4th 566, 618, 47 Cal.Rptr.3d 22, 139 P.3d 492, "[th]e trial court has no obligation to delete from CALJIC No. 8.85 inapplicable mitigating factors." We decline to reconsider our decision as defendant requests.
ix. Failure to instruct that statutory mitigating factors are relevant solely as potential mitigators
We also decline to reconsider our conclusion that the jury need not be advised which sentencing factors in CALJIC No. 8.85 are aggravating and which are mitigating. As we have held, the court does not need to define the statutory factors because the "nature of those factors is self-evident within the context of each case." ( People v. Hillhouse (2002) 27 Cal.4th 469, 509, 117 Cal.Rptr.2d 45, 40 P.3d 754.)
e. Inter-case Proportionality Review
As we have stated before, neither California's death penalty law nor the federal **746and state constitutions require inter-case proportionality review. *1017( People v. Virgil (2011) 51 Cal.4th 1210, 1289-1290, 126 Cal.Rptr.3d 465, 253 P.3d 553 ; People v. Hillhouse (2002) 27 Cal.4th 469, 511, 117 Cal.Rptr.2d 45, 40 P.3d 754.)
f. Equal Protection and California's Capital Sentencing Scheme
Consistent with our precedent, California's capital sentencing scheme does not, as defendant contends, violate the Equal Protection Clause of the federal Constitution because capital defendants and noncapital defendants "are not similarly situated." ( *104People v. Williams (2013) 58 Cal.4th 197, 295, 165 Cal.Rptr.3d 717, 315 P.3d 1.) Consequently, it is permissible for noncapital defendants to have more procedural protections than capital defendants.
g. International Law
Contrary to defendant's contention, international law does not prohibit application of the death penalty in the United States. Although the United States is a signatory to the International Covenant on Civil and Political Rights, "it signed the treaty on the express condition '[t]hat the United States reserves the right, subject to its Constitutional constraints, to impose capital punishment on any person (other than a pregnant woman) duly convicted under existing or future laws' " allowing capital punishment. ( People v. Thompson (2016) 1 Cal.5th 1043, 1130, 210 Cal.Rptr.3d 667, 384 P.3d 693, citing People v. Brown (2004) 33 Cal.4th 382, 403-404, 15 Cal.Rptr.3d 624, 93 P.3d 244.)
2. Alleged Cumulative Error
Defendant contends the alleged errors at trial cumulatively make his trial unfair and hence resulted in a miscarriage of justice, violating due process.
Cumulative error is present when the combined effect of the trial court's errors is prejudicial or harmful to the defendant. ( People v. Winbush (2017) 2 Cal.5th 402, 487, 213 Cal.Rptr.3d 1, 387 P.3d 1187 ; People v. Hinton (2006) 37 Cal.4th 839, 897, 913, 38 Cal.Rptr.3d 149, 126 P.3d 981.) Although a defendant is entitled to a fair trial, he or she is not entitled to "a perfect one." ( People v. Cunningham (2001) 25 Cal.4th 926, 1009, 108 Cal.Rptr.2d 291, 25 P.3d 519.) Even though the cumulative error rule recognizes the value in the efficient administration of justice, it does not elevate it above the protection of individual rights. ( People v. Cuccia (2002) 97 Cal.App.4th 785, 795, 118 Cal.Rptr.2d 668.)
We conclude that defendant has not established cumulative error. There are no errors to aggregate. The corpus delicti rule was vindicated, and Renteria's *1018failure to testify did not represent a compulsory process violation. The court also did not err prejudicially in sustaining Renteria's Fifth Amendment privilege. Renteria's proposed testimony had no tendency in fact to lessen defendant's criminal culpability and the jury heard overwhelming evidence of defendant's guilt.
III. CONCLUSION
For the foregoing reasons, we affirm the judgment in its entirety.
We Concur:
CANTIL-SAKAUYE, C. J.
CORRIGAN, J.
LIU, J.
CUÉLLAR, J.
KRUGER, J.
GROBAN, J.