There is a crime with one and only one piece of circumstantial evidence found, which can be rated a 9.5 on a scale of 1 to 10 as to its reliability in proving who committed the crime. There is a similar crime, where 100 pieces of circumstantial evidence are found, each with a ranking of 0.095. And of course, 100 x 0.095 = 9.5. If it makes sense to convict in the first scenario, does it also make sense to convict in the second?
I’ve got a vague hunch that the question cannot be answered as written, and other factors have to come into play, although quite frankly I don’t know what they would be. Actually, I just thought of something but I won’t go back and add it. It will be interesting to see if someone else brings it up. If it can be answered, please do so. If it cannot, please add whatever is necessary as you see fit, and explain.
Mods: As I’m sure you will, please move this to the appropriate forum, it this isn’t it.
Good thing you don’t have 116 pieces of evidence with the same “ranking”. Else your scale would go up to 11 and Spinal Tap jokes ensue.
Probability doesn’t work this way. Esp. when you are vague about “reliability” and don’t mention whether the pieces are independent or not. E.g., 100 tracks in the snow made by the same person are not 100 independent pieces of evidence.
The legal question about standards of proof is a complicated one, and if this thread ends up focusing on that, it might need to be moved.
But mathematically, one must also consider whether the separate pieces of evidence are independent. Suppose there’s a murder case, where Jane Doe is dead. One of Jane’s friends said that, before the murder, she seemed to be afraid in the presence of Richard Roe. OK, that’s circumstantial evidence that Richard Roe might have been the murderer.
Now suppose that Jane’s sister said that Jane always tried to avoid Richard, and Jane’s hairdresser said that Jane told her that she didn’t trust Richard, and Richard’s co-worker said that he saw Jane crossing the street whenever Richard came by, and so on. These are also all circumstantial evidence against Richard. But no matter how many people come forward with statements like this, all it means is that Jane was worried about Richard; it doesn’t mean that Jane was correct.
Furthermore, you don’t want to just add up the values of all of the pieces of circumstantial evidence. If you argue that nine pieces of 10% evidence add up to 90%, then what do you get when you have 11 pieces of 10% evidence? The better way to combine them would be for each piece to take away some percentage of the remaining doubt, so 11 pieces of 10% evidence would leave 0.9^11 doubt, or about 31% doubt.
And then you need to take a Bayesian look. There was one case where the prosecution argued that the perpetrator was part of a mixed-race couple, which was 1 in whatever, and drove a red compact car, which was 1 in some other number, and so on, and the defendant matched all of these criteria, which was only a 1 in 5 million chance, so it was almost certain that the defendant was guilty. But the defendant appealed, and pointed out that this happened in a city of 15 million people, so there were probably about three people in the city who would match all of that, and one of the others could just as well have been the perp.
Thanks, and of course to whomever else would like to respond. This is what I was looking for. For the record, the vagueness of the reliability scale is what I thought of as described in the OP. And I was working on this whole crime scenario, with specific pieces of evidence, details of the crime, etc. But I said screw it, I’ll just throw it out what I have to the Dope.
As if I don’t have enough to worry about if I ever find myself, innocent, in front of a jury of my peers. Having nothing to do with probability, there was a show on last night where the prosecutor said that because of the amount of blood at murder scene suggested an “explosive” crime, and because the defendant had an “explosive personality”, that…
It’s whatever can convince a Judge or Grand Jury to bring charges and then whatever the DA can convince a Jury with.
Strangely, the more horrific the crime, it seems the lower the burden of proof the jury wants. With a really heinous crime there seems to be a feeling that *someone *must be found guilty.
Agree with DrDeth. It’s not the sort of mathematical exercise suggested in the OP. The usual phrase is that the jury is to consider “the totality of the evidence.” Consider each bit of evidence, pro, con, and neutral, and in the overall context.
People seem to have this idea that circumstantial=weak. No. Circumstantial=indirect. It can (like any other type of evidence), be weak or strong, depending on the circumstances.
People can and have been properly convicted on the basis of circumstantial evidence.
Though, the Jane Doe/Richard Roe example given above, would never result in a conviction, not because of any question of strength, but because there isn’t a shred of evidence to suggest that Richard killed her and or her death was a murder at all.
Note that Forensic evidence, like fingerprints and DNA is considered a type of circumstantial evidence. Now before you get all excited and say “well that solid proof” the State still must show a crime was committed and there is no other explanation for that circumstantial evidence. For example, a wife is found missing. Plenty of fingerprints of the husband in their home. Well- 1. Was there a murder or another crime or did she just leave? And 2- of course there is.
Eyewitness testimony (the most common sort of direct evidence) is frequently unreliable, actually. Witnesses can be bought or threatened, they can be biased, and memories are quite unreliable- and cant be changed by questioning.
For example, say the police want to prove a Usual Suspect did the crime. The witness describes a robbery, where there is a getaway car. The police know the Usual Suspect uses a red car. “When the suspects drove off in the red car, which direction was it going?”. The witness will then "remember’ the car was red- even if it was actually blue.
Wiki gives some interesting examples of: The 2004 murder trial of Scott Peterson was another high-profile conviction based heavily on circumstantial evidence. Another case that relied on circumstantial evidence was that of Nelson Serrano. The 2015 murder trial of Ivan Chan Man-sum was a conviction based solely on circumstantial evidence[13][14] without finding the body.[15]
As to Peterson, this will answer the Ops question:*They based their verdict on “hundreds of small ‘puzzle pieces’ of circumstantial evidence that were revealed during the trial, from the location of Laci’s body to the myriad lies her husband told after her disappearance”. *
Since I semi-regularly make this point about probabilities as regards evidence vs. “a smoking gun”, I’ll just throw in on the view that it’s a more complicated matter than simply assigning a probability to each item in the folder and running some math. Just assigning the number is quite difficult, if you want to do it properly - the “wisdom of the masses” be as it may, there are some things that people have a poor intuition for. And, as people have noted here, the independence of evidence is also a large factor. There are probably also cases where there is a partial independence which, I’m sure that there’s some math for, but I don’t believe that it’s commonly utilized. Regression models, for example, usually try to exclude variables that might be correlated rather than try to figure out some means to split them into the non-overlapping component (if any).
But, an example like multiple accusers for the same crime would generally fall under the heading of an independent item of evidence. Even if we given each accuser a fairly low probability of truth telling, if there are twenty of them, that does add up.
Also, note that the math isn’t a simple addition operation. If there’s a 60% chance that a person is telling the truth, and there are two people, there isn’t a 120% probability that one of them is telling the truth. If I’m correct, I believe that it’s 84% that at least one is telling the truth and only 36% that both are.
A simple way to visualize this for two pieces of evidence is to split a square horizontally and vertically, coloring in one of the divisions in one color and the other division in the other color, and figure out the area of the overlaps, overflow, and white space. You then divide that area by the area of the total square. If you have three pieces of evidence, then you have to move up to a cube, and then on up into hypercubes and such.
Well, it shouldn’t result in a conviction, that was my point. But there is still a shred of evidence: all of that circumstantial evidence adds up to a pretty strong conclusion that Jane feared Richard, and she may well have had some good reason for that.
I was assuming that the fact that she’d been killed by someone had already been established. Maybe her body was found with a knife stuck in her chest, or something. There’s usually not much doubt about the fact of murder itself in a murder trial-- Usually the big question is just who did it.
No. They first need to link him to her death in time and space. In Scott Peterson’s case that was obviously simple.
Here not so much. Only once the link is made then can you even begin to consider the rest.
As you say, it’s more complicated than just running the math, so I’ll throw out a couple of caveats in case they need to be pointed out to anybody.
First, this calculation is only valid if the two events are independent—and that doesn’t just mean that the two people didn’t directly influence one another. To be independent means that the probability that Person B is telling the truth remains the same regardless of whether or not person A is telling the truth. So, for example, if the two people are saying things that are mutually contradictory, the probability that both are telling the truth is 0; they’re not independent.
Second, probability calculations like this are “garbage in, garbage out”: the 84% and 36% you came up with are no more reliable than the 60% you started with. And what does it even mean that someone has a 60% probability of telling the truth? How is that determined?
Simple? Yes, they lived together as husband and wife. The 'evidence" against him was crappy. (Oh, he likely did it, sure, but the evidence was crap, the DA appealed to emotions, not logic).
I’ll finish up the math from the OP. There are 100 pieces of evidence, all **independent **from each other, each with 0.095 out of 10 probability. The probability of each independent event is 0.095, or 9.5% (probabilities are usually expressed as a portion of one, or 100%).
Probability that **all **the events are true is 0.095 raised to the 100th power. This is a very small number (over 100 zeros ‘in front’).
Probability that **any **of the events are true is one minus the probability that they are all false… so 1 - (.915 ^ 100) = 99.986%.
