Tuesday, November 30, 2010

Judges Gone Wild: Revised

I want to revise my previous post, Judges Gone Wild. First, the numbers are in error. I left out a term in my calculation. That term was near unity, so it won't make a huge difference. That term belonged in the denominator, however, so the corrected answer I will soon present below is actually more distressing.

I also decided that I tried to do too much with a single plot. I've therefore created two to replace the one. I now present them below, one for the judges ... 

 ... and one for the juries.

Before I started this, I would have been appalled by the thought of an innocent person having more than a 25% chance of wrongful conviction. I'm still appalled, but I'm now admittedly distracted by calculations that suggest an innocent person has substantially more than a 50% chance of of being convicted during a bench trial. The odds range from a "low" of 50% for forcible rape to nearly 84% for muder/manslaughter. Since judges convict 86% of all defendants in the murder/manslaughter category, the number indicates that judges are incapable of distinguishing cases of innocence from cases of guilt.

WARNING: Mathematical Addendum

At least with respect to the plot for the juries, Spencer and I agree reasonably well on the overall chance of being convicted by a jury despite being innocent. He calculates 25% for all trials combined. I calculate 28%. 

We disagree substantially, however, with respect to the overall chance of being convicted by a judge despite being innocent. He calculates 37% for all trials. I calculate 62%. The discrepancy can be understood by looking at the terms that go into the calculation.

The first term is the convictions per trial. We extract that number directly from the judge / jury agreement table. For Spencer and the NCSC data, that number was 80%.  For my work and the Kalven-Zeisel data, the number was 83%.  The two sets of data were close on this number, despite being separated in time by half a decade. 

The second term was the percentage of innocent defendants. Spencer calculated 28%. I calculated 26%. Again we are close. 

The third term was the wrongful conviction rate. Recall that the wrongful conviction rate is the number of wrongful convictions divided by the number of convictions. It is one of the primary results from our analysis of the judge / jury agreement data.  Spencer calculated 13% for judges from the NCSC data, using his methods. I calculated 20% for judges from the Kalven-Zeisel  using my methods. That's our largest discrepancy. The comparison is not great, but not terrible.

When we perform the final calculation, however, the differences combine in such a fashion as to amplify the difference of the results.

Using Spencer's numbers:  0.80 x 0.13 / 0.28  =  .37  =  37%

Using my numbers:  0.83 x 0.196 / 0.26  =  0.64  =  64%

As it turned out, when my numbers were larger, they were in the numerator. When my number was smaller, it was in the denominator. The result was a substantial difference between our calculated values for the chance of being convicted by a judge despite being innocent.

Friday, November 26, 2010

Michael Ledford: Confession Falsified by Thermodynamics

"Before I left, I lit a candle and threw it in the chair. I never wanted to hurt my family. ... I just hope my family and friends and God can forgive me."

Those words constitute the heart of Michael Ledford's spoken confession that he set fire to his apartment and was therefore responsible for the death of his one-year-old son and the serious burn injuries suffered by his wife.

Though Michael recanted those words, and his entire confession, those are the words that convicted him of first-degree murder and spared him the death sentence. The jury believed both the part about starting the fire and the part about not meaning to hurt anyone.

A confession is as good as a conviction, or quite nearly so. Those people who confess, recant, and then go to trial are almost always convicted. Jurors, i.e. the American people, simply cannot imagine themselves confessing to a heinous crime they did not commit. Since they cannot imagine they would do so, they will not believe anyone would do so.

Jurors, i.e. the American public, are wrong on both counts.

One completely logical, but amazingly ineffective means of convincing a jury that a confession is false is to show that the confession is inconsistent with the facts of the case. If the confession violates space, time, and thermodynamics, that's even better. It's better, but it's probably not good enough.

During Michael's trial, the defense tried to show that Michael's confession was inconsistent with the data. They did a poor job of it, in my opinion, but they did make a try. I'll try to do better in this post.

The photo below shows the chair into which Michael confessed to throwing a candle. The photo was taken on the same day as the fire. That day was Zachary Ledford's first birthday. In the photo, Zachary is sitting in the lap of a family friend. I wish to intrude as little as possible into their privacy, even as I publicly discuss the most tragic portion of their lives, so I have redacted the people from the photo. Click to enlarge.


Let's examine the photo carefully. We will soon compare it to a couple of photos taken after the fire to see what we can learn.

The chair is an upholstered swivel rocker. Given that the fire occurred in Virginia in 1999, it is almost certain that the upholstery fabric was not fire-retardant. (My understanding is that California was the only state then requiring fire-retardant upholstery.) The cushions themselves consisted of polyurethane foam, a petroleum product. I've seen polyurethane referred to as solid gasoline. When burning it releases, among other gases, hydrogen cyanide and carbon monoxide. Both are deadly.

There is an ottoman sitting in front of the chair. The ottoman burned but is not particularly relevant to the story.

Behind the chair and at the right of the photo is the sole entry door to the apartment. Virginia argued that Michael set the fire near the front door to block escape, and that proved intent to murder. Because the victim was under 14 years of age and Michael was more than 20 years of age, the location of the fire near the door proved not only intent to murder, it proved capital murder. Virginia therefore asked the jury for permission to execute Michael Ledford.

To the left of the door is a light switch. It controls an outlet near the floor behind the couch. That outlet will be critical to the story. I will speak of it again in future posts.

Directly behind the chair is a quilt rack. It has several quilts and an Afghan draped across it. The quilts and the Afghan will soon burn and add substantially to the fuel load.

Above the quilt rack is a picture hanging on the wall. The photo captures just the very bottom of the picture frame. That picture will provide a clue. It will try to tell us something. I'm not yet sure what it's trying to tell us, but time and effort will reveal its clue.

To the left of the chair is an end table, of sorts. The end table is actually a portion of the sofa in which the back cushion can be folded forward to form the end table as shown.

On the table is a lamp with a glass base and a hooped shade that seems to be made of paper. The lamp is plugged into the outlet behind the sofa. If the lamp switch is in the "On" position, flipping the light switch near the door will turn the lamp on and off.

There are several framed pictures on the table. I assume they are family photos. There is also a doily resting there.

At the front of the table are two drinking vessels of some sort. They look to me to be one bottle and one tall can. I think they are inconsequential. They will be gone by the time of the fire.

Not seen on the table are two taper in candle holders. They should have been there at the time of the fire if Michael's confession is to be believed.

Michael said the candles were long and slender rather than short and stubby. "White ones about this high, this big around ... " [indicates by forming circle with his thumb and index finger] "... and probably about that tall." [indicates by separating hands by approximately five inches]

He said they were in candle holders. "They were candle holders that we got for a wedding present."

He said they were on the corners of the table. "We're always careful of where we put the candles, but we just set them on the corners that night. ... We both did. I set one on the corner and she set the other."

He said he then threw the candle in the chair and left. "After Elise went to bed, I turned the light on in the living room, and I told her that I would blow out the candles. I blew out the one, made sure that Zach’s door was closed -- that way he wouldn’t get hurt. I even made sure that our bedroom door was closed. I lit -- I kept the candle lit, and I threw it in the chair."

We know that Michael was talking about the table beside the chair, because early in the interrogation, he suggested the candles must have fallen off the table and into the chair when he shut the door. "When I left, I shut the light, I turned the light back on and I'm pretty certain, up to this point in time, now mainly, because I was scared, that I did blow out the candles. But now I'm thinking that apparently I didn't and something caused one of the candles, at least one them to fall. That's the God honest truth."

Perhaps the candles were placed on the table after the birthday party was over but before Michael left the apartment. We'll look at the photos taken after the fire to see if we can find evidence of them there.

Below, I've included a photo taken after the fire. This photo was taken by the insurance investigator two days after the fire. The police investigator had moved the chair and quilt rack to photograph behind them. The police investigator or the insurance investigator had also removed almost everything from the table. The insurance investigator returned the chair and quilt rack to their positions during the fire, based on the markings left on the carpet. He also returned the lamp to the table before taking this picture.

I've edited the photo only by making it lighter and brighter than the one I received. Click to enlarge.


The tops of the cushions are burned, as are the tops of the end table and the coffee table. The front and the sides of the sofa and chair, at least those portions shown, are not burned. The polyurethane foam in the seat cushions is generally intact, unconsumed by the fire. The seat back, however, is completely gone. You can see right through where the back cushion used to be, and see the quilt rack. The rack remains. The quilts and Afghan are mostly consumed.

The white case, possibly a sewing machine case, is out of place. The front door is open. The picture that had been hanging on the wall has fallen to the floor and is visible through the now empty quilt rack.

There is no water damage from the fire-fighting effort. This fire burned rapidly and self-extinguished before the fire company arrived. It was an October night and all the doors and windows were closed. The fire used up the oxygen it needed to grow, that oxygen wasn't replaced, and the fire died out.

Zachary was at that time laying in his crib in the children's bedroom. He was unburned but died of carbon monoxide poisoning.

Elise was at that time lying on the floor in the master bedroom. She had been badly burned as she twice tried to get to the front door. She retreated to the bedroom, called 911, and collapsed to the floor just as the connection was made.

One more photo and my point will be made. This is a closeup of the area taken the day after the fire by the police investigator. We can see the chair with the missing back, the quilt rack with the missing quilts, and the picture that has fallen from the wall.


We can see what is left of the family photos.

We can see the glass base of the lamp. It fractured from the heat. We can see a metal hoop from the shade and the remnants of the doily.

The bottle and can that were in the previous photo had been replaced prior to the fire by two plastic drinking glasses. We can see them in the photo. They melted in the heat.

The insurance investigator saw in person pretty much what we can see in the photo. From his report, we find this description.
Examination of the debris on the table show the remains of a crocheted doily, a picture frame, the remains of two plastic drink cups, which are melted, a television or VCR remote control and various paper and debris.
What we don't see in the photo, what the insurance investigator did not see when he stood there and looked directly at that table are candle holders, or melted candles, or candle wax. Neither fire investigator mentioned finding any candle, any candle wax, or any candle holder anywhere in the apartment.

One might argue that the candles were consumed during the fire and that no candle wax would remain. Virginia made that argument to the jury, and the jury apparently accepted it as fact beyond a reasonable doubt. I don't believe the argument is valid, and neither does Pat Ledford, so we will be conducting testing to resolve this issue. We'll report early next year on the results.

What is not at issue, however, is that candle holders do not burn up in a fire while plastic cups sitting immediately adjacent only melt. There should be two candle holders on the table. One should be near each of the front corners of the table, where they would interfere with (and possibly burn) anyone reaching for a plastic cup. That's where Michael said they were, but I can't see them. Neither of the investigators could see them either.

If Michael's confession was factual, where are the candle holders?

Michael Ledford's confession began as denials that he had anything to do with the fire, that he had no idea how it started.
I am telling you, I did not start the fire.
I didn't do it.
I don’t know, but it wasn't me.
The only thing I can say, sir, is do what you need to do but I am going to claim my innocence ‘til the day I die.
I did not set the fire that took the life of my son and damned near took the life of my wife. There is no way in hell I'd have done that.
If I deliberately set that fire, may God strike me dead now. I did not set the fire.
I didn't set the fire. I didn't know where the fire was, plain and simple.
No. I want you to leave here knowing that I'm telling the truth. I didn't set the fire.
No, because I didn't set the fire.
I think the fire was set accidentally.
You can go to hell sir!
For hours, Michael's story did not include any mention of candles, or candle holders. He was not the first to introduce those items into the interrogation. His interrogators suggested them, and Michael acquiesced, bit by bit.

As his interrogators suggested various means and motives, as they lied about evidence tying him to the fire, as they promised to help him if he would only confess, Michael's story evolved to include a candle he thought he blew out, to a candle he might not have blown out, to a candle that might have fallen into the chair as he shut the door. Each time he tried to better explain what might have happened, the interrogators pushed harder and harder.

Suddenly Michael seemed to accept that he had tossed a candle into the chair before he left. It was shocking to behold. He figured he must be crazy. He asked to be put in a mental institution. He lost all sense of reality. He believed he needed help, and he believed they were offering help. He was, at this point, clearly delusional.
Okay. I want the agreement that I will be sent for, I want the agreement that I will be put in a psychiatric, a psychiatric hospital, to get the evaluation that I need. That's all. And afterwards, maybe help me get a trade -- not necessarily to make a good living at, but something where I will be away from people.
At that point, and only at that point, did the interrogators elect to believe him.

However, Michael's acquiescence became demonstrably false at the point when he began incorporating candles and candle holders into the events of that evening. One of his interrogators was, in fact, the very person who photographed the last picture I just presented. That interrogator / investigator absolutely did know (or should have known) that Michael was confabulating rather than confessing. Instead, that interrogator / investigator charged Michael Ledford with the first degree murder of his own son.

And that is why I am interested in helping.

Stay tuned for the next post in this series, when I show that Michael Ledford's confession violates not only basic thermodynamics, but space and time as well.

Thursday, November 25, 2010

Everything's Amazing and Nobody's Happy

It's Thanksgiving morning and I'm thankful for my many, many blessings. Not the least of them is my freedom.

We all fail to appreciate what we have. It's simply human nature. At least one day each year, we're reminded to think about how lucky we really are, to take stock of the miracles of everyday life that surround us.

I coincidently ran across this video this morning. It's a clip from the Conan O'Brian show, an interview with a comedian I never knew by name previously. His name is Louis CK. He talks about how everyone fails to appreciate what they have. It's funny, and like all good comedy, it makes a point.

It really gets rolling when he talks about "the crappiest generation" becoming frustrated when they don't get an immediate response on their cell phone, and it peaks when he talks about the guy in the airplane who gets pissed because he lost his internet connection at 35,000 feet above the earth.



I wish you all a grateful Thanksgiving

Wednesday, November 24, 2010

Judges Gone Wild

CAUTION: This post contains plots corrected in Judges Gone Wild, Revised.

As I work on the summary chapter for my monograph Regarding the Rate of Wrongful Conviction, I keep finding new stories in all the data I've compiled and created. I frequently find myself in awe of what is unfolding before me. I'm still wrestling with the significance of the figure I displayed in Burden of Proof As a Legal Fiction. The one I am about to show you is equally revealing and equally troubling.

I wanted a way to display the odds an innocent person faces when tried for a crime. I knew the numbers Bruce Spencer calculated from the NCSC judge-jury agreement data. (He only had one number for the judge and one number for the jury, since the NCSC data were not broken down by crime.) I also had a sense of the numbers I had for the jury on a crime-by-crime basis. I had derived them from the Kaven-Zeisel judge-jury agreement data. My jury numbers (plural) corresponded reasonably well to Spencer's jury number (singular).

I only recently (as in today) got around to deriving my judge numbers from the Kalven-Zeisel data.

Whoa!

Here you go. Click to enlarge. We'll talk after you pick yourself up off the floor.

Professor of Statistics Bruce Spencer calculated you stand a 25% chance of being convicted by a jury if you are innocent. That value corresponds to the bottom of the green horizontal bar. My calculations show that the value is sensitive to the type of crime, and is slightly less than Spencer predicted. My values are indicated by the bottom of the brown vertical bars. They range from a high of 32% for drugs to a low of 14% for forcible rape. For a substantial majority of the trials, excluding drugs, the number is around 16%. That's one chance in six. That's bad enough, but better than the one chance in four predicted by Spencer.

Bruce Spencer and I, however, disagree on the risk an innocent party faces at the hands of a judge. Spencer predicts that judges (during bench trials) convict 37% of the innocents who come before them. That's horrible, but not nearly as horrible as I calculate. My calculations indicate that those people wrongfully charged with murder are convicted in 73% of the bench trials. Instead of slightly more than one time out of three, I calculate they are convicted three times out of four.

I'm discouraged.

The best of a bad crime-category lot is forcible rape. I calculate that judges convict "only" 35% of those people wrongfully charged with and tried for forcible rape. The judges' performance for every other crime category is worse.

Worse than a 35% chance of convicting an innocent person.

Worse.

As bad as a 73% chance of convicting an innocent person.

ERRATA: This post contains plots corrected in Judges Gone Wild, Revised

Sunday, November 21, 2010

Burden of Proof as a Legal Fiction

In this post, I intend to prove to you beyond a reasonable doubt that the concept of "proof beyond a reasonable doubt" is nothing more than a legal fiction. This shouldn't take too long.

I begin by asking you to consider the burden of proof in a civil case. That burden is usually described as the "preponderance of the evidence."  It's a 50-50 type decision. If the evidence favors the plaintiff even by a  teensy weensy bit, the jury is to find in favor of the plaintiff. If, on the other hand, the evidence favors the defense even by a smidgeon, then the jury is to find in favor of the defense. It's so simple.

I present the idealized concept of preponderance of the evidence in the figure below. Click to enlarge.
Matters are a little more confusing for jurors in a criminal case. They are asked to decide if the evidence proves the State's case beyond a reasonable doubt. The jurors must figure out how heavily the evidence favors the prosecution AND they must figure out what the hell the term reasonable doubt means AND they must decide whether the weight of the evidence provided by the prosecution exceeds the reasonable doubt threshold.

Courts are of almost no help in determining the meaning of reasonable doubt. One thing they absolutely will not do is apply any numeric value to reasonable doubt. They never suggest anything such as "you must be 90% certain."

Never. Ever.

Not now. Not ever.

Instead, they give you a reasonable doubt instruction something along the line of:
The question naturally is what is a reasonable doubt. The words almost define themselves. It is a doubt based upon reason and common sense. It is a doubt that a reasonable person has after carefully weighing all of the evidence. It is a doubt which would cause a reasonable person to hesitate to act in a matter of importance in his or her personal life. Proof beyond a reasonable doubt must be proof of such a convincing character that a reasonable person would not hesitate to rely and act upon it in the most important of his own affairs.
There you go. I'm sure that clarified things.

Legal scholars, and I've been reading a lot of their scholarly work on this issue recently, recognized that if you are to quantify the number, it should be greater than 50%. That after all is the standard for civil cases, and the burden of proof in criminal cases is supposed to be substantially greater. Legal scholars tend to throw out a value of 90% as a starting point. This corresponds roughly to William Blackstone's 250 year old claim that it is "better that ten guilty persons escape than that one innocent suffer."

That traditional view is portrayed in the figure below.
Those legal scholars who believe that figure portrays reality are full of scholarly beans.

When Rita Simon and Linda Mahon asked 106 judges to put a non-legally-binding number to proof beyond a reasonable doubt, those judges gave a number (presumably on average) of 89%. Since that's almost identical to the number the full-of-beans legal scholars provided, I declare that judges too are full of judicial beans, at least with respect to this concept.

Simon and Mahon also asked 25 jurors to put a number to the concept. Those jurors put the number at 79%. That number is not far from a couple other studies I've seen where jurors put the number around 75%, assuming they are asked before they deliberate in a mock trial. If they are asked after they deliberate, the put the number closer to 55%. The suggestion is that they wanted to convict, the evidence didn't support conviction at even a 75% standard, so they reduced the standard.

Even though the students eventually put the standard just barely above a civil suit "preponderance of the evidence" standard, I declare my fellow jurors to be full of deliberative beans, at least with respect to this issue.

I'll allow the judges and jurors to make my point for me. During the NCSC judge-jury agreement study used by Bruce Spencer to establish a wrongful conviction rate around 10%, the judges and jurors were asked to provide their estimate of the strength of the evidence used to convict (or acquit) a defendant. I'll simply provide a summary plot of the results below, and move away from the keyboard a bit as you study the plot and say "What the hell?" Click to enlarge.
Okay. I'm back. The first thing the Skeptical Spouse said when I showed her this plot was "That's not right!!?"  She was pointing to the portion where the jurors voted more frequently to convict when the strength of evidence was 1 than when it was 2. I replied with something equally as scholarly, something along the lines of "Screw that. They're voting to convict a third of the time when by their own admission the evidence strongly favors the defense."

Even when the evidence favors neither the prosecution nor the defense, both judge and jury are voting two out of three times to convict. Anyone who studies the chart for more than a minute and  still believes that we presume defendants to be innocent, or that we burden the prosecution with proof beyond a reasonable doubt, is full of blog-reading beans.

This one simple plot, based directly on data provided by judges and juries, demolishes dozens of scholarly works I've read regarding quantifying reasonable doubt. This plot causes me to propose an alternative hypothesis of jury behavior. It may not be scholarly, but it better explains the data. Here goes.


Besides destroying much scholarly work and putting the lie to some of the most fundamental principles of our judicial system, the plot also tells you that those who guess and those who divide are pretty much wrong when they arrive at wrongful conviction rates of 1 or 2 or 3%. There is no way that the behavior portrayed in the chart would result in such low error rates.

I'll add one final chart, then I'll step away from the keyboard. In the chart below, I simply overlay the idealized and realized worlds of proof beyond a reasonable doubt. I'll allow the chart to speak for itself.