THE PEOPLE, Plaintiff and Respondent, v. MALCOLM RICARDO COLLINS, Defendant and Appellant.
Crim. No. 11176
In Bank. Supreme Court of California
Mar. 11, 1968.
68 Cal. 2d 319
Thomas C. Lynch, Attorney General, William E. James, Assistant Attorney General, and Nicholas C. Yost, Deputy Attorney General, for Plaintiff and Respondent.
SULLIVAN, J.—We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury‘s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.
A jury found defendant Malcolm Ricardo Collins and his wife defendant Janet Louise Collins guilty of second degree
On June 18, 1964, about 11:30 a.m. Mrs. Juanita Brooks, who had been shopping, was walking home along an alley in the San Pedro area of the City of Los Angeles. She was pulling behind her a wicker basket carryall containing groceries and had her purse on top of the packages. She was using a cane. As she stooped down to pick up an empty carton, she was suddenly pushed to the ground by a person whom she neither saw nor heard approach. She was stunned by the fall and felt some pain. She managed to look up and saw a young woman running from the scene. According to Mrs. Brooks the latter appeared to weigh about 145 pounds, was wearing “something dark,” and had hair “between a dark blond and a light blond,” but lighter than the color of defendant Janet Collins’ hair as it appeared at trial. Immediately after the incident, Mrs. Brooks discovered that her purse, containing between $35 and $40 was missing.
About the same time as the robbery, John Bass, who lived on the street at the end of the alley, was in front of his house watering his lawn. His attention was attracted by “a lot of crying and screaming” coming from the alley. As he looked in that direction, he saw a woman run out of the alley and enter a yellow automobile parked across the street from him. He was unable to give the make of the car. The car started off immediately and pulled wide around another parked vehicle so that in the narrow street it passed within 6 feet of Bass. The latter then saw that it was being driven by a male Negro, wearing a mustache and beard. At the trial Bass identified defendant as the driver of the yellow automobile. However, an attempt was made to impeach his identification by his admission that at the preliminary hearing he testified to an uncertain identification at the police lineup shortly after the attack on Mrs. Brooks, when defendant was beardless.
In his testimony Bass described the woman who ran from the alley as a Caucasian, slightly over 5 feet tall, of ordinary build, with her hair in a dark blonde ponytail, and wearing dark clothing. He further testified that her ponytail was “just like” one which Janet had in a police photograph taken on June 22, 1964.
On the day of the robbery, Janet was employed as a house
There was evidence from which it could be inferred that defendants had ample time to drive from Janet‘s place of employment and participate in the robbery. Defendants testified, however, that they went directly from her employer‘s house to the home of friends, where they remained for several hours.
In the morning of June 22, Los Angeles Police Officer Kinsey, who was investigating the robbery, went to defendants’ home. He saw a yellow Lincoln automobile with an off-white top in front of the house. He talked with defendants. Janet, whose hair appeared to be a dark blonde, was wearing it in a ponytail. Malcolm did not have a beard. The officer explained to them that he was investigating a robbery specifying the time and place; that the victim had been knocked down and her purse snatched; and that the person responsible was a female Caucasian with blonde hair in a ponytail who had left the scene in a yellow car driven by a male Negro. He requested that defendants accompany him to the police station at San Pedro and they did so. There, in response to police inquiries as to defendants’ activities at the time of the robbery, Janet stated, according to Officer Kinsey, that her husband had picked her up at her place of employment at 1 p.m. and that they had then visited at the home of friends in Los Angeles. Malcolm confirmed this. Defendants were detained for an hour or two, were photographed but not booked, and were eventually released and driven home by the police.
Late in the afternoon of the same day, Officer Kinsey, while driving home from work in his own car, saw defendants riding in their yellow Lincoln. Although the transcript fails to disclose what prompted such action, Kinsey proceeded to place them under surveillance and eventually followed them home. He called for assistance and arranged to meet other
Officer Kinsey interrogated defendants separately on June 23 while they were in custody and testified to their statements over defense counsel‘s objections based on the decision in Escobedo and our first decision in Dorado.4 According to the officer, Malcolm stated that he sometimes wore a beard but that he did not wear a beard on June 18 (the day of the robbery), having shaved it off on June 2, 1964.5 He also explained two receipts for traffic fines totalling $35 paid on June 19, which receipts had been found on his person, by saying that he used funds won in a gambling game at a labor hall. Janet, on the other hand, said that the $35 used to pay the fines had come from her earnings.6
On July 9, 1964, defendants were again arrested and were booked for the first time. While they were in custody and awaiting the preliminary hearing, Janet requested to talk with Officer Kinsey. There followed a lengthy conversation
At the seven-day trial the prosecution experienced some difficulty in establishing the identities of the perpetrators of the crime. The victim could not identify Janet and had never seen defendant. The identification by the witness Bass, who
In an apparent attempt to bolster the identifications, the prosecutor called an instructor of mathematics at a state college. Through this witness he sought to establish that, assuming the robbery was committed by a Caucasian woman with a blond ponytail who left the scene accompanied by a Negro with a beard and mustache, there was an overwhelming probability that the crime was committed by any couple answering such distinctive characteristics. The witness testified, in substance, to the “product rule,” which states that the probability of the joint occurrence of a number of mutually independent events is equal to the product of the individual probabilities that each of the events will occur.8 Without presenting any statistical evidence whatsoever in support of the probabilities for the factors selected, the prosecutor then proceeded to have the witness assume probability factors for the various characteristics which he deemed to be shared by the guilty couple and all other couples answering to such distinctive characteristics.10
Applying the product rule to his own factors the prosecutor arrived at a probability that there was but one chance in 12 million that any couple possessed the distinctive characteristics of the defendants. Accordingly, under this theory, it was to be inferred that there could be but one chance in 12 million that defendants were innocent and that another equally distinctive couple actually committed the robbery. Expanding on what he had thus purported to suggest as a hypothesis, the
Objections were timely made to the mathematician‘s testimony on the grounds that it was immaterial, that it invaded the province of the jury, and that it was based on unfounded assumptions. The objections were “temporarily overruled” and the evidence admitted subject to a motion to strike. When that motion was made at the conclusion of the direct examination, the court denied it, stating that the testimony had been received only for the “purpose of illustrating the mathematical probabilities of various matters, the possibilities for them occurring or re-occurring.”
Both defendants took the stand in their own behalf. They denied any knowledge of or participation in the crime and stated that after Malcolm called for Janet at her employer‘s house they went directly to a friend‘s house in Los Angeles where they remained for some time. According to this testimony defendants were not near the scene of the robbery when it occurred. Defendants’ friend testified to a visit by them “in the middle of June” although she could not recall the precise date. Janet further testified that certain inducements were held out to her during the July 9 interrogation on condition that she confess her participation.
Defendant makes two basic contentions before us: First, that the admission in evidence of the statements made by defendants while in custody on June 23 and July 9, 1964,
As we shall explain, the prosecution‘s introduction and use of mathematical probability statistics injected two fundamental prejudicial errors into the case: (1) The testimony itself lacked an adequate foundation both in evidence and in statistical theory; and (2) the testimony and the manner in which the prosecution used it distracted the jury from its proper and requisite function of weighing the evidence on the issue of guilt, encouraged the jurors to rely upon an engaging but logically irrelevant expert demonstration, foreclosed the possibility of an effective defense by an attorney apparently unschooled in mathematical refinements, and placed the jurors and defense counsel at a disadvantage in sifting relevant fact from inapplicable theory.
We initially consider the defects in the testimony itself. As we have indicated, the specific technique presented through the mathematician‘s testimony and advanced by the prosecutor to measure the probabilities in question suffered from two basic and pervasive defects—an inadequate evidentiary foundation and an inadequate proof of statistical independence. First, as to the foundational requirement, we find the record devoid of any evidence relating to any of the six individual probability factors used by the prosecutor and ascribed by him to the six characteristics as we have set them out in footnote 10, ante. To put it another way, the prosecution produced no evidence whatsoever showing, or from which it could be in any way inferred, that only one out of every ten cars which might have been at the scene of the robbery was partly yellow, that only one out of every four men who might have been there wore a mustache, that only one out of every ten girls who might have been there wore a ponytail, or that any of the other individual probability factors listed were even roughly accurate.12
The bare, inescapable fact is that the prosecution made no attempt to offer any such evidence. Instead, through leading questions having perfunctorily elicited from the witness the response that the latter could not assign a probability factor for the characteristics involved,13 the prosecutor himself suggested what the various probabilities should be and these became the basis of the witness’ testimony (see fn. 10, ante). It is a curious circumstance of this adventure in proof that the prosecutor not only made his own assertions of these factors in the hope that they were “conservative” but also in later argument to the jury invited the jurors to substitute their “estimates” should they wish to do so. We can hardly conceive of a more fatal gap in the prosecution‘s scheme of proof. A foundation for the admissibility of the witness’ testimony was never even attempted to be laid, let alone established. His testimony was neither made to rest on his own testimonial knowledge nor presented by proper hypothetical questions based upon valid data in the record. (See generally: 2 Wigmore on Evidence (3d ed. 1940) §§ 478, 650-652, 657, 659, 672-684; Witkin, Cal. Evidence (2d ed. 1966) § 771; McCormick on Evidence, pp. 19-20; Evidence: Admission of Mathematical Probability Statistics Held Erroneous for Want of Demonstration of Validity (1967) Duke L.J. 665, 675-678, citing People v. Risley (1915) 214 N.Y. 75, 85 [108 N.E. 200, Ann. Cas. 1916 D 775]; State v. Sneed (1966) 76 N.M. 349 [414 P.2d 858].) In the Sneed case, the court reversed a conviction based on probabilistic evidence, stating: “We hold that mathematical odds are not admissible as evidence to identify a defendant in a criminal proceeding so long as the odds are based on estimates, the validity of which have [sic] not been demonstrated.” (Italics added.) (414 P.2d at p. 862.)
But, as we have indicated, there was another glaring defect in the prosecution‘s technique, namely an inadequate proof of the statistical independence of the six factors. No proof was presented that the characteristics selected were mutually independent, even though the witness himself acknowledged that such condition was essential to the proper application of the “product rule” or “multiplication rule.” (See Note,
In the instant case, therefore, because of the aforementioned two defects—the inadequate evidentiary foundation and the inadequate proof of statistical independence—the technique employed by the prosecutor could only lead to wild conjecture without demonstrated relevancy to the issues presented. It acquired no redeeming quality from the prosecutor‘s statement that it was being used only “for illustrative purposes” since, as we shall point out, the prosecutor‘s subsequent utilization of the mathematical testimony was not confined within such limits.
We now turn to the second fundamental error caused by the probability testimony. Quite apart from our foregoing objections to the specific technique employed by the prosecution to estimate the probability in question, we think that the entire enterprise upon which the prosecution embarked, and which was directed to the objective of measuring the likelihood of a random couple possessing the characteristics allegedly distinguishing the robbers, was gravely misguided.
The prosecution‘s approach, however, could furnish the jury with absolutely no guidance on the crucial issue: Of the admittedly few such couples, which one, if any, was guilty of committing this robbery? Probability theory necessarily remains silent on that question, since no mathematical equation can prove beyond a reasonable doubt (1) that the guilty couple in fact possessed the characteristics described by the People‘s witnesses, or even (2) that only one couple possessing those distinctive characteristics could be found in the entire Los Angeles area.
As to the first inherent failing we observe that the prosecution‘s theory of probability rested on the assumption that the witnesses called by the People had conclusively established that the guilty couple possessed the precise characteristics relied upon by the prosecution. But no mathematical formula could ever establish beyond a reasonable doubt that the prosecution‘s witnesses correctly observed and accurately described the distinctive features which were employed to link defendants to the crime. (See 2 Wigmore on Evidence (3d ed. 1940) § 478.) Conceivably, for example, the guilty couple might have included a light-skinned Negress with bleached hair rather than a Caucasian blonde; or the driver of the car might have been wearing a false beard as a disguise; or the prosecution‘s witnesses might simply have been unreliable.16
The foregoing risks of error permeate the prosecution‘s circumstantial case. Traditionally, the jury weighs such risks in evaluating the credibility and probative value of trial testimony, but the likelihood of human error or of falsification obviously cannot be quantified; that likelihood must therefore be excluded from any effort to assign a number to the probability of guilt or innocence. Confronted with an equation which purports to yield a numerical index of probable guilt, few juries could resist the temptation to accord disproportionate weight to that index; only an exceptional juror, and indeed only a defense attorney schooled in mathematics, could successfully keep in mind the fact that the probability com-
As to the second inherent failing in the prosecution‘s approach, even assuming that the first failing could be discounted, the most a mathematical computation could ever yield would be a measure of the probability that a random couple would possess the distinctive features in question. In the present case, for example, the prosecution attempted to compute the probability that a random couple would include a bearded Negro, a blonde girl with a ponytail, and a partly yellow car; the prosecution urged that this probability was no more than one in 12 million. Even accepting this conclusion as arithmetically accurate, however, one still could not conclude that the Collinses were probably the guilty couple. On the contrary, as we explain in the Appendix, the prosecution‘s figures actually imply a likelihood of over 40 percent that the Collinses could be “duplicated” by at least one other couple who might equally have committed the San Pedro robbery. Urging that the Collinses be convicted on the basis of evidence which logically establishes no more than this seems as indefensible as arguing for the conviction of X on the ground that a witness saw either X or X‘s twin commit the crime.
Again, few defense attorneys, and certainly few jurors, could be expected to comprehend this basic flaw in the prosecution‘s analysis. Conceivably even the prosecutor erroneously believed that his equation established a high probability that no other bearded Negro in the Los Angeles area drove a yellow car accompanied by a ponytailed blonde. In any event, although his technique could demonstrate no such thing, he solemnly told the jury that he had supplied mathematical proof of guilt.
Sensing the novelty of that notion, the prosecutor told the jurors that the traditional idea of proof beyond a reasonable doubt represented “the most hackneyed, stereotyped, trite, misunderstood concept in criminal law.” He sought to reconcile the jury to the risk that, under his “new math” approach to criminal jurisprudence, “on some rare occasion . . . an innocent person may be convicted.” “Without taking that risk,” the prosecution continued, “life would be intolerable . . . because . . . there would be immunity for the Collinses, for people who chose not to be employed to go down and push old ladies down and take their money and be
In essence this argument of the prosecutor was calculated to persuade the jury to convict defendants whether or not they were convinced of their guilt to a moral certainty and beyond a reasonable doubt. (
We conclude that the court erred in admitting over defendant‘s objection the evidence pertaining to the mathematical theory of probability and in denying defendant‘s motion to strike such evidence. The case was apparently a close one. The jury began its deliberations at 2:46 p.m. on November 24, 1964, and retired for the night at 7:46 p.m.; the parties stipulated that a juror could be excused for illness and that a verdict could be reached by the remaining 11 jurors; the jury resumed deliberations the next morning at 8:40 a.m. and returned verdicts at 11:58 a.m. after five ballots had been taken. In the light of the closeness of the case, which as we have said was a circumstantial one, there is a reasonable likelihood that the result would have been more favorable to defendant if the prosecution had not urged the jury to render a probabilistic verdict. In any event, we think that under the circumstances the “trial by mathematics” so distorted the role of the jury and so disadvantaged counsel for the defense, as to constitute in itself a miscarriage of justice. After an examination of the entire cause, including the evidence, we are of the opinion that it is reasonably probable that a result
In view of the foregoing conclusion, we deem it unnecessary to consider whether the admission of defendants’ extrajudicial statements constitutes error under the rules announced in Escobedo and Dorado. Upon retrial, the admissibility of these or any other extrajudicial statements sought to be introduced by the prosecution must be determined in the light of the rules set forth in Miranda v. Arizona (1966) 384 U.S. 436 [16 L. Ed. 2d 694, 86 S. Ct. 1602, 10 A.L.R.3d 974]. (People v. Doherty (1967) 67 Cal. 2d 9, 12, 17-21 [59 Cal. Rptr. 857, 429 P.2d 177].) As we have pointed out, the trial herein took place between our first and second Dorado decisions (see fn. 4, ante). Although defense counsel was commendably alert in basing objections to the admission of the statements upon the decisions in Escobedo and Dorado, he of course did not have the benefit of our numerous decisions beginning with the second Dorado decision expounding various facets of the exclusionary rule. In the event any extrajudicial statements made by defendant are offered in evidence on retrial, the parties will have an opportunity to make a record on pertinent issues subject to prior determination by the court in the light of Miranda rules before such statements are received in evidence. It would be fruitless for us to essay such a task at this point when such record does not yet exist.
The judgment is reversed.
Traynor, C. J., Peters, J., Tobriner, J., Mosk, J., and Burke, J., concurred.
MCCOMB, J.—I dissent. I would affirm the judgment in its entirety.
APPENDIX
If “Pr” represents the probability that a certain distinctive combination of characteristics, hereinafter designated “C,” will occur jointly in a random couple, then the probability that C will not occur in a random couple is (1 — Pr). Applying the product rule (see fn. 8, ante), the probability that C will occur in none of N couples chosen at random is (1—Pr)N, so that the probability of C occurring in at least one of N random couples is [1 — (1—Pr)N].
By subtracting the probability that C will occur in exactly one couple from the probability that C will occur in at least one couple, one obtains the probability that C will occur in more than one couple: [1 — (1 — Pr)N] — [(N) X (Pr) X (1 — Pr)N-1]. Dividing this difference by the probability that C will occur in at least one couple (i.e., dividing the difference by [1 — (1 — Pr)N]) then yields the probability that C will occur more than once in a group of N couples in which C occurs at least once.
Turning to the case in which C represents the characteristics which distinguish a bearded Negro accompanied by a ponytailed blonde in a yellow car, the prosecution sought to establish that the probability of C occurring in a random couple was 1/12,000,000—i.e., that Pr = 1/12,000,000. Treating this conclusion as accurate, it follows that, in a population of N random couples, the probability of C occurring exactly once is [(N) X (1/12,000,000) X (1 — 1/12,000,000)N-1]. Subtracting this product from [1 — (1 — 1/12,000,000)N], the probability of C occurring in at least one couple, and dividing the resulting difference by [1 — (1 — 1/12,000,000)N], the probability that C will occur in at least one couple, yields the probability that C will occur more than once in a group of N random couples of which at least one couple (namely, the one seen by the witnesses) possesses characteristics C. In other words, the probability of another such couple in a population of N is the quotient A/B, where A designates the numerator [1 — (1 — 1/12,000,000)N] — [(N) X (1/12,000,000) X (1 — 1/12,000,000)N-1], and B designates the denominator [1 — (1 — 1/12,000,000)N].
Hence, even if we should accept the prosecution‘s figures without question, we would derive a probability of over 40 percent that the couple observed by the witnesses could be “duplicated” by at least one other equally distinctive interracial couple in the area, including a Negro with a beard and mustache, driving a partly yellow car in the company of a blonde with a ponytail. Thus the prosecution‘s computations, far from establishing beyond a reasonable doubt that the Collinses were the couple described by the prosecution‘s witnesses, imply a very substantial likelihood that the area contained more than one such couple, and that a couple other than the Collinses was the one observed at the scene of the robbery. (See generally: Hoel, Introduction to Mathematical Statistics (3d ed. 1962); Hodges & Leymann, Basic Concepts of Probability and Statistics (1964); Lindgren & McElrath, Introduction to Probability and Statistics (1959).)
Notes
| Characteristic | Individual Probability |
| A. Partly yellow automobile | 1/10 |
| B. Man with mustache | 1/4 |
| C. Girl with ponytail | 1/10 |
| D. Girl with blond hair | 1/3 |
| E. Negro man with beard | 1/10 |
| F. Interracial couple in car | 1/1000 |