Tag Archives: crime

if everyone agrees, something is wrong

I thought I’d try to semi-derive, and explain a remarkable mathematical paper that was published last month in The Proceedings of the Royal Society A (see full paper here). The paper demonstrates that too much agreement about a thing is counter-indicative of the thing being true. Unless an observation is blindingly obvious, near 100% agreement suggests there is a hidden flaw or conspiracy, perhaps unknown to the observers. This paper has broad application, but I thought the presentation was too confusing for most people to make use of, even those with a background in mathematics, science, or engineering. And the popular versions press versions didn’t even try to be useful. So here’s my shot:

Figure 2 from the original paper. For a method that is 80% accurate, you get your maximum reliability at the third to fifth witness. Beyond that, more agreement suggest a flaw in the people or procedure.

Figure 2 from the original paper. For a method that is 80% accurate, you get your maximum reliability at 3-5 witnesses. More agreement suggests a flaw in the people or procedure.

I will discuss only on specific application, the second one mentioned in the paper, crime (read the paper for others). Lets say there’s been a crime with several witnesses. The police line up a half-dozen, equal (?) suspects, and show them to the first witness. Lets say the first witness points to one of the suspects, the police will not arrest on this because they know that people correctly identify suspects only about 40% of the time, and incorrectly identify perhaps 10% (the say they don’t know or can’t remember the remaining 50% of time). The original paper includes the actual factions here; they’re similar. Since the witness pointed to someone, you already know he/she isn’t among the 50% who don’t know. But you don’t know if this witness is among the 40% who identify right or the 10% who identify wrong. Our confidence that this is the criminal is thus .4/(.4 +.1) = .8, or 80%.

Now you bring in the second witness. If this person identifies the same suspect, your confidence increases; to roughly (.4)2/(.42+.12) = .941,  or 94.1%. This is enough to make an arrest, but let’s say you have ten more witnesses, and all identify this same person. You might first think that this must be the guy with a confidence of (.4)10/(.410+.110) = 99.99999%, but then you wonder how unlikely it is to find ten people who identify correctly when, as we mentioned, each person has only a 40% chance. The chance of all ten witnesses identifying a suspect right is small: (.4)10 = .000104 or 0.01%. This fraction is smaller than the likelihood of having a crooked cop or a screw up the line-up (only one suspect had the right jacket, say). If crooked cops and systemic errors show up 1% of the time, and point to the correct fellow only 15% of these, we find that the chance of being right if ten out of ten agree is (0.0015 +(.4)10)/( .01+ .410+.110) = .16%. Total agreement on guilt suggests the fellow is innocent!

The graph above, the second in the paper, presents a generalization of the math I just presented: n identical tests of 80% accuracy and three different likelihoods of systemic failure. If this systemic failure rate is 1% and the chance of the error pointing right or wrong is 50/50, the chance of being right is P = (.005+ .4n)/(.01 +.4n+.1n), and is the red curve in the graph above. The authors find you get your maximum reliability when there are two to four agreeing witness.

Confidence of guilt as related to the number of judges that agree and your confidence in the integrity of the judges.

Confidence of guilt as related to the number of judges that agree and the integrity of the judges.

The Royal Society article went on to a approve of a feature of Jewish capital-punishment law. In Jewish law, capital cases are tried by 23 judges. To convict a super majority (13) must find guilty, but if all 23 judges agree on guilt the court pronounces innocent (see chart, or an anecdote about Justice Antonin Scalia). My suspicion, by the way, is that more than 1% of judges and police are crooked or inept, and that the same applies to scientific analysis of mental diseases like diagnosing ADHD or autism, and predictions about stocks or climate change. (Do 98% of scientists really agree independently?). Perhaps there are so many people in US prisons, because of excessive agreement and inaccurate witnesses, e.g Ruben Carter. I suspect the agreement on climate experts is a similar sham.

Robert Buxbaum, March 11, 2016. Here are some thoughts on how to do science right. Here is some climate data: can you spot a clear pattern of man-made change?

What happened to Jack Kelly of Newsies

As my daughters are fans of the Disney play and movie, “Newsies,” and as I’ve taken interest in the early 20th century, they’ve asked me to find out what happened to Jack Kelly, the main character of the play/movie. If you’ve never seen it, Newsies is a musical about the New York newsboy strike of 1899. According to the play/ movie, as soon as the strike ends (the newsboys win), the strike leader, “cowboy” Jack Kelly goes off with Theodore Roosevelt, presumably headed to Santa Fé, New Mexico to become a real cowboy. But a simple search did not reveal what actually happened to the real Jack Kelly; here’s what I found. Noosies NYT

Without looking, I told my daughters that, if Jack Kelly had gone to Santa Fé in 1899, he would have found something very interesting: a cowboy school for young men. As it happened one of Roosevelt’s rough riders from the battle of San Juan Hill, retired to Santa Fé and set up a cowboy school for boys in the mountains above the town. He built a very outdoorsy operation in an area called “Los Alamos”. It ran until 1942 when the location was taken over to become “Site Y” of the Manhattan Project. This is where J. Robert Oppenheimer and co designed and built the first Atom Bombs. That Jack would have gone there would make for a nice, tidy story, but the truth appears to have been more messy, and more interesting. Jack got involved with William Hearst and George M. Cohan, the Titanic, a famous murder, and eventually with the fall of Tammany Hall. Here’s a picture.

Jack Sullivan

Jack Sullivan, head Newsie. He isn’t ugly, but isn’t Christian Bale either.

First, there was an actual newsboy strike in 1899; it was about raising the price the newsboys paid per paper, but the problem was that the price had been raised earlier, for the Spanish-American War, and not decreased after the war ended. The newsboys did win, and there was a leader named Jack, but according to the papers, the name of the leader was “Jack Sullivan”, not Jack Kelly or Francis Sullivan. The New York Tribune, July 22, 1899, lists Jack Sullivan as the leader of the strike Arbitration Committee and a leader of “the first group of newsboys to declare and demand their rights.” There are other leaders too: Louis “Kid Blink” Baletti, and David “Dave/ Yaller” Simmons. “Kid Blink” (he wore an eye patch and appears in the movie) got an award from the newsboys for making the best speech. I’ll guess that the Dave “the mouth” character is based on David “Yaller” Simmons, but it is not clear that he had any close relationship with Sullivan.

As for the movie showing Jack leaving with T. Roosevelt. it might have suited Roosevelt, but the real Jack appears to have stayed in New York, and appears to have taken a job as a bodyguard for William Randolph Hearst, one of the newspaper moguls who’d raised his rates and precipitated the strike. But it doesn’t end there. In 1904, Jack Sullivan, “the Boss Noosie” has gotten a charter for a Newsies Club to be set-up on 4th street in lower New York (the Bowery). A New York Times article (at left) includes an interview with Jack that fans should find pleasing, if only for his grammar. He uses the word, “papes” instead of papers or newspapers. I suspect this is a put-on affect for benefit of Times-readers, but who knows? It is sometimes the height of wisdom to appear stupid.

By 1909, Jack has lost control of his newsboy’s club. He appears to have used the club to teach boxing (how crude) and on at least one occasion used club assets to post bail for women accused of “loitering,” a jail-able offense in corrupt, Tammany-era New York. The club closed 2 years later. And then Jack gets married (November 27, 1910), and it appears that Jack’s real name was not Sullivan at all, but Reich. He marries Sarah Siegel at the Ohav Tzedek synagogue as “Jacob Reich”. The name Jacob Reich appears on his marriage license, on his death certificate, and on various court records, though he still appears as Jack Sullivan in other activities. Jack/ Jacob appears to have chosen the Irish-sounding name “Sullivan” as an homage to the leader of the Tammany (Democratic) machine, “Big Tim” Sullivan, shown in the photo below.

Turn of the century Tammany boss, "Big Tim" Sullivan, shown at right.

Turn of the century Tammany boss, “Big Tim” Sullivan, shown at right.

By March, 1912, Jack appears again in the news, this time suing two film companies for use of his story and likeness without payment to him. It’s a film called “the Gangsters.” It would be interesting to see if a copy still exists.

A month later, April 15, 1912, The unsinkable Titanic goes down, and six days after that, April 21, 1912, Jack is selling papers at a charity baseball game to benefit the survivors. The game takes place on a Sunday, normally prohibited by New York blue laws, between The New York Giants and The New York Yankees (the Yankees are still called the Highlanders in those days, but are already wearing pinstripes). In the picture below, Jack is under the red arrow with lots of “papes” under his arm, just behind famous song-writer, playwright, George M. Cohan. Both are dressed as newsies. George M. Cohan, known for the WWI song “Over there”, had four plays on Broadway at the time. He is one of the very few successful New Yorkers to have avoided major attachment to the crooked, New York political machine.

Jack Sullivan with George M Cohan, April 1912 selling a special newspaper to help survivors of the Titanic.

Jack Sullivan (arrow) with George M Cohan, April 1912 selling a special newspaper to help survivors of the Titanic.

New York Refuge

The New York house of refuge

And now Jack Kelly / Sullivan/ Reich enters history as a tragic bystander. When he got married, Jack borrowed $1000, from a Jewish gambler and gambling hall owner, Herman (Beansy) Rosenthal. Rosenthal was a good friend of his, and of “Big Tim” Sullivan, but he (and Sullivan) had enemies. Among them, the crooked police Lieutenant, Charles Becker, who headed the city vice squad and delighted in shaking down the gamblers, pimps, etc for protection money. Becker wanted Rosenthal dead, in part to keep him from going to the newspapers with stories of police corruption.

By 1912, “Big Tim” lost control of the Tammany organization and was put in seclusion under Tammany guard. Within a year he’d be dead. Someone (Becker?) then hired four hit men to kill Rosenthal (1:30 AM, July 16, 1912 in front of The Metropole Hotel). It’s an event recounted in “The Great Gatsby.” Several beat-policemen were there to see the shooting, but every one looked away. Not one shot back or took the license of the car. In fact, the police did nothing to catch the murderers except to lock up the only honest witness to keep him from testifying. Before the shooting, Becker took Jack Sullivan out for an evening at Madison Square Garden; he then dropped Jack at the Metropole just before the 1:30 shooting. Becker and the police then blamed Jack and four others for the murder based on testimony that they had concocted. In the end, Jack was acquitted, but not the other four, or Becker. All five went to the electric chair; all five protested their innocence.

Becker was the first US police lieutenant to be put to death for murder. It seems unlikely that he was innocent, but was he a murderer, or just an accomplice. As for the other four, perhaps they were guilty, perhaps not; it’s hard to tell from Tammany-era records. The judge was crooked; Police chief Devery was at least as crooked as Becker in terms of shaking down hoodlums. And Devery had as much motive as Becker to want Rosenthal dead. The witnesses were lying from a script they’d been given — that’s what justice was like in those days. Within a year of the murder, Big Tim was dead and Charles Francis Murphy had gained firm control of Tammany Hall. The police spent the next decade in criminal activities while trying to pin something on Jack, now a cigar store owner. He was busted for gambling and related offenses, but nothing much came of it. Jack cleared his name from the charge of murder only in 1936, two years before his death — three years after Fiorello La Guardia was elected mayor. Republican/ Fusion candidate, La Guardia ran against Tammany and did much to end their police corruption.

As for The Refuge, The New York House of Refuge is a real place. It sat on Randal’s Island between Manhattan, The Bronx, and Queens. The Island is now famous as the center of The Triborough Bridge. There is now a park where The Refuge was. Was The Refuge run honestly? If it was, it would have been virtually the only public institutions to run that way. Tammany was corrupt to the core.

Robert E. Buxbaum, October 25, 2015. Much of the information here comes from a tumbler exchange called, “newsies historical research.” I organized it and added some background about Baseball, Tammany, etc. If you like Newsies, or the era, I can recommend the novel (and movie), The Great Gatsby, or Fiorello!, a musical version of La Guardia’s unlikely rise to power. Hearst is treated somewhat positively in Newsies, but less-so as “Citizen Kane.” If someone’s seen, or has a link to “The Gangsters” please tell me.

A prison tale (fiction) by R. E. Buxbaum

I’m writing from the Michigan Department of Corrections; Mail-stop 5678 E, Jackson, MI, awaiting trial on auto-related charges. So, legally speaking, I’m still innocent, if not quite free. So, here’s my  story, and my bargain. The whole situation, it seems, is more comical than criminal. At its source, at bottom, all I was trying to do was take care of some left over issues from unofficial jobs I was doing for the city. For his honor, the mayor. That’s K.K., Kwamie Kilpatrick, the ex-mayor to you, but always his honor to me; great guy. Anyway, cars that fall in the river aren’t that unusual in this town, and it’s not like I planned to smuggle anything to Canada. You’ll notice my case doesn’t involve theft, or injuring anyone but myself. Just trespass, though I wouldn’t mind a short prison stay if it can be arranged. Sort of like Shawshank redemption.

Anyway, my minor crime was committed a week ago, Thursday, and involved a Dodge Viper. One that I own, straight-up, with a partner and the bank: a yellow, convertible viper costing some $220,000 when new. Beautiful machine; tinted glass, and capable of doing 180 mph without breaking a sweat. I use it, or did, to take care of errands for his honor. He tips nice, and helps out when I’m in a jam, so I did get paid for the work, but for the most part, it’s like I’m like a patriot-servant to the city. I’m using my own car for city business. In better days, those errands included taking judges for the occasional joy ride, to the airport or lunch, plus other deliveries. Not generally on the water, like last Thursday, and yes that’s me, waving in the photo. Shame about the car.

As to how I got the viper, I got it at the dealer on Woodward, just over the 8 mile bridge, and paid for it mostly myself, with a loan from First Federal. At the time I had a good job running errands for his honor, as I mentioned. Now I’m so of unemployed. What sort of errands? The sort of ones you’d want to run in a viper, Duh. Aside from driving judges to meetings, there were girl errands; some boy errands; some money errands. Occasionally a disposal — nothing illegal, but embarrassing maybe. When you’re disposing of city property, you don’t look too carefully at the item. When you’re carrying something big, or someone’s wife or girlfriend, or a lot of money, it’s nice to be able to move quickly. Judges and senators like to move fast too, behind tinted windows. They still do.

Anyway, after his honor goes to prison (real shame, that), and my job becomes near-ended. There’s still some errands to to, but not so many, and I’ll grant that the viper has become more of a liability than an asset. Not that there’s insurance fraud behind me ending up in the river, just good-ole fun, and maybe a little reckless driving. I’m owing like 165k still on the machine, and my brother and I came up with this great plan for a movie — no fraud intended. There’s this great spot that we know by Zug Island, where the Rouge meets the Detroit river. It’s pretty well deserted, with a pier and a boat ramp. We used it all the time, back in the day for meetings and such. No-one goes there because of the smells. There’s always an oil slick and the water there will dissolve most anything metal. The Zug Island folks make sure of there are no cameras or loiterers either — just so no-one steals their secrets. Anyway, my brother and I figured that, if I got the viper up to about 30- 40 mph on the pier we could sail it out over the rocks and garbage into the river, land softly in the water, and make for a great movie. We never planned to file an insurance claim like we’d lost the car or it was stolen. Anyway, the water’s only about 8′ below the end of the pier, so it’s sort of like a high-dive. I figured I’d get out of the sinking car swim up to the boat ramp, and walk to my brother’s car on the street. The car would dissolve to rust in a week; the water’s pretty nasty there. He’d film the whole thing. I’d dry off; we’d drive home, have a beer or two, then sell the film. Probably pull the rust out of the river in a week, just to keep everything in it’s pure, pristine state. Though, now that I think of it, insurance might still cover most of the value of the car. You never know.

So the first part goes OK. We drive to the pier about 9:00 PM, Thursday, just as the sun’s setting. There’s that good, reddish light over the Windsor skyline, and the pier is empty. There are two winos off far from my intended route. My brother and I take down the top and line up the vehicle so I avoid unwanted bumps and garbage as I sail out on my way to glory. And, with a shot of Jack, and a wave to my brother (It’s on the film), I go shooting out down the pier and over the water. Fine. No bumps, no rocks. Nice flight. No soft landing, though. The car hits water like a pumpkin on concrete. Ouch! The thing bends in the middle sealing the door shut and me inside. There’s hardly any spring to the seats anyway, and what little there once was is lost. My back gets twisted into the steering wheel. I can barely turn and I can’t quite get out. Then, about 5 minutes later, the air bag goes off. Guess they didn’t design for this accident. My back, is now twisted into the sat-back, and I’m in pain.

I think it’s some sort of Sprite Healey fracture like Kevin Everett got last year. I can walk, thanks, but it needs medical attention that I’m not likely to get on Medicaid. Anyway, like I said, I’m trapped inside the vehicle, and suppose I’d be dead if the car sank like we planned, bit it don’t sink. The thing floats. Like, forever. The car weighs like two tons and it floats! Who knew. I’m carried by my momentum and by some random Rouge current out past Zug Island into the main channel between Detroit and Windsor where I’m almost run down by an ore boat. Anyway, the yellow metal Viper-dingy I’m in gets noticed by the boat lookout and by some fishermen, but no one helps. Everyone’s seems to think it’s really funny. They’re all taking pictures, and texting, and calling their friends. And everyone is laughing but me. It’s funny, like a fart in a space suit. Meanwhile my brother’s been driving along by the river, filming everything and hoping I get out and can somehow swim to safety, and I keep floating off to Canada. Finally, someone calls the coast guard, but when the come, it turns out I’m in Canadian waters. So the Canadians come, and they’re all think it’s a boot. I’m a celebrity with pictures of me in my car floating all over the internet. And well, here I am, a relatively innocent man, with a junked car and a bad back. And I’m ready to make a deal. I’ll admit it looks like I was planning to defraud someone, but there’s no evidence. I’ll admit to trespass if you like, but not fraud or endangerment. There was no one there to endange, and no one endangered, except of me. And I won’t press charges (little joke).

What with all the publicity, I figure you want to press more than just trespass, and what I was thinking of is reckless driving. I’ll admit to that with no contest. Looked at the right way, that’s like a 60 day sentence, maybe 90 days, and that’s just fine with me. I don’t have the cleanest record, but it’s not like I’ve done this before. I think it would be fair if I got 60 to 90-days of incarceration with medical benefits and job rehabilitation. I’d like to learn a new trade, like auto repair. That’s a win-win for everyone. You close the case, and I get cured and put my job skills to work just as soon as I get out. But I really need the medical though. My health insurance doesn’t cover injury-in-performance-of-a-crime — it’s right there on page 28. And Medicare is garbage. Next time you get insurance, your honor, make sure to read the contract.

Anyway, you have the tape and the pictures, and can check with my brother. We have plenty of people who will testify for us, even folks in congress and in the police department. They’ll all tell you, we’re just a couple of good fellows, somewhat down on our luck, waiting to get out and go straight. Thanks for your help, and God-bless.

R. E. Buxbaum. Sept 30, 2015. Some weeks ago, I wrote an essay, “What is comedy.” So I thought I’d try writing one. Tell me how you think I did. No one in the story is meant to be anyone real, except for “his honor,’ who’s meant to be a fictional version of His Honor.

Criminal Punishment Theory

I’ve often wondered about the theory of criminal punishment. How long should sentences be? For which crimes and external circumstances should people be let off, for which should there be alternative punishments, like civic work, or a fine instead of jail time. I’ve a few ideas, but here are some thought cases:

Someone steals an expensive handbag from a clothing store. What should the punishment be for (a) a ghetto black with no job, (b) a middle-class, college sophomore (c) a famous actress? Should it be the same for all? Is jail the best punishment — it costs money, and doesn’t help the criminal or the store. If jail, how long is appropriate? Should the length of stay correspond to the cost of the bag? If the punishment is money or civic service, how should the fine vary with the wealth of the thief, or if the person is a repeat offender? Many countries have corporal punishment — why or why not?

My sense is that sentences should be shorter for less-expensive items, and longer for more expensive. My sense is that a fine or civic service is appropriate for most first offenses, and while jail seems necessary for serious crimes, if only to keep criminals off the streets, the sentences should be reasonably short and include rehabilitation. I suspect that long sentences don’t help the criminal or society. I suspect that victimless crimes, e.g. prostitution or drug sales should have very short sentences or non-jail punishments, and I’m not quite sure what to do if the thief reforms in prison or appears to.

The US leads Russia, China, South Africa, and all of Europe in terms of percent of population is prison.

The US leads Russia, China, Cuba, India, and all of Europe in terms of percent of our population in prison. The main cause is very long sentences, a product of fixed minimums. Strangely, our crime rate is low. Chart from the international business times.

Regarding prostitution perhaps it should be policed by the clergy, that’s why they get tax breaks. And why is sex between consenting adults punished as prostitution if money changes hands but not otherwise, or if the only pay is dinner? Why should the professional offender (the prostitute) pay more than the casual (the john). Why is drug use punished more than alcohol. Many drug and alcohol users live happy productive lives. To the extent that these crimes should be punished, it seems to me that fines, community service, or corporal punishment might be appropriate — I can not see prison healing a moral failing or reforming a victimless criminal.

And then there is rape. As a crime, the definition of rape has a long slippery slope, but the punishment does not. It isn’t quite clear where consensual become criminal, but the punishment is strict and undivided. We treat some cases as extreme crimes and others are let completely free. We have cases where the sex-criminal man or woman marries his or her underage partner, but is still guilty of statutory rape, and is then listed forever as a sex-criminal.

Children under 21 can not drink alcohol in the US, but they can in many other countries, and in some countries even older people can not drink at all. Is Saudi Arabia a very productive country; is Germany falling apart because of young drinkers? It seems not, so why is 21 the drinking age when you can choose to marry or join the army at 18. Soldiers are allowed to drink earlier than non-soldiers, but young marrieds are not afforded the same benefit. I don’t see why. The punishment for underage drinking varies too, as does the punishment for underage driving.

The Bible has some enlightened ideas on punishment, prescribing the use of fines of double or four or five times the value going to the victim (the thief pays 4 times for a stolen sheep, 5 times for a stolen cow, for example), but in other cases, it’s positively draconian prescribing death for homosexuality, violating the sabbath or for taking God’s name in vain. A seducer has to marry his seducee, but can not divorce her (assuming she agrees) but what if it’s an unhappy marriage? There is no room for judicial leniency in the bible, but there is in traditional applications; I’m not sure that’s not an improvement.

Robert E. Buxbaum, May 30, 2014. I’ve been wondering about the theory of appropriate punishment for at least 35 years. Are we protecting society, extracting vengeance, helping the criminal or doing some vague combination. My sense is we’re just bumbling blindly, and sorry to say, I have no answers.

Stoner’s prison and the crack mayor

With the release of a video of Rob Ford, the Mayor of Toronto, smoking crack while in office, and the admission that at least two US presidents smoked pot, as did the Beatles, Stones, and most of Hollywood, it seems worthwhile to consider the costs and benefits of our war on drugs, especially pot. Drugs are typically bad for productivity and usually bad for health. Thus, it seems worthwhile to regulate it, but most countries do not punish drug sale or use nearly as harshly as we do in the US.

The Freak Brothers by Gilbert Shelton. Clearly these boys were not improved by drugs, but perhaps we could do better than incarcerating them, and their fans, for years, or life.

The Freak Brothers by Gilbert Shelton. Clearly these boys were not improved by drugs, but perhaps we could do better than incarcerating them, and their fans, for years, or life.

While US penalties vary state by state, most states have high minimum penalties that a judge can not go below. In Michigan, where I live, medical marijuana is legalized, but all supply is still illegal. Marijuana cultivation, even for personal medical use, is a felony carrying a minimum punishment of 4 years in state prison and a $20,000 fine. For cultivation of more than 20 plants the minimum sentence is 7 years in prison and $500,000; and cultivating 200 or more plants results in 15 years plus a $10,000,000 fine. These are first-time, minimum sentences where the judge can not consider mitigating circumstances, like a prescription, for a drug that was accepted for use in the US in the 70s, is legal in Holland, legalized in Colorado, and is near-legal in Belgium. While many pot smokers were not served by the herb, many went on to be productive, e.g. our current president and the Beatles.

In Michigan, the mandatory minimums get worse if you are a repeat offender, especially a 3 time offender. Possession of hard drugs; and sales or cultivation of marijuana makes you a felon; a gun found on a felon adds 2 years and another felony. With three felonies you go to prison for life, effectively, so there is little difference between the sentence of a repeat violent mugger and a kid selling $10 rocks of crack in Detroit. America has more people in prison than Russia, China, or almost every industrialized nation, per capita, and the main cause is long minimum sentences.

In 2011, Michigan spent an average of $2,343 per month per prisoner, or $28,116/year: somewhat over 1.3 billion dollars per year in total. To this add the destruction of the criminal’s family, and the loss of whatever value he/she might have added to society. Reducing sentences by 10 or 20% would go a long way towards paying off Detroit’s bankruptcy, and would put a lot of useful people back into the work-force where they might do some good for themselves and the state. 60.8% of drug arrestees were employed before they were arrested for drugs, with an average income of $1050/month. That’s a lot of roofers, electricians, carpenters, and musicians — useful people. As best we can tell, the long sentences don’t help, but lead to higher rates of recidivism and increased violent behavior. If you spend years in jail, you are likely to become more violent, rather than less. Some 75% of drug convicts have no prior record of violent crime, so why does a first-time offense have to be a felony. If we need minimums, couldn’t it be 6 months and a $1000 fine, or only apply if there is violence.

Couldn’t we allow judges more leeway in sentencing, especially for drugs? Recall that Michiganders thought they’d legalized marijuana for medical use, and that even hard-drugs were legal not that long ago. There was a time when Coca-Cola contained cocaine and when Pope Leo was a regular drinker of cocaine laced wine. If the two presidents smoked pot, and the Mayor of Toronto could do a decent job after cocaine, why should we incarcerate them for life? Let’s balance strict justice with mercy; so the fabric of society is not strained to breaking.

Robert Buxbaum, Jan 16, 2014. Here are some other thoughts on Detroit and crime.

Near-Poisson statistics: how many police – firemen for a small city?

In a previous post, I dealt with the nearly-normal statistics of common things, like river crests, and explained why 100 year floods come more often than once every hundred years. As is not uncommon, the data was sort-of like a normal distribution, but deviated at the tail (the fantastic tail of the abnormal distribution). But now I’d like to present my take on a sort of statistics that (I think) should be used for the common problem of uncommon events: car crashes, fires, epidemics, wars…

Normally the mathematics used for these processes is Poisson statistics, and occasionally exponential statistics. I think these approaches lead to incorrect conclusions when applied to real-world cases of interest, e.g. choosing the size of a police force or fire department of a small town that rarely sees any crime or fire. This is relevant to Oak Park Michigan (where I live). I’ll show you how it’s treated by Poisson, and will then suggest a simpler way that’s more relevant.

First, consider an idealized version of Oak Park, Michigan (a semi-true version until the 1980s): the town had a small police department and a small fire department that saw only occasional crimes or fires, all of which required only 2 or 4 people respectively. Lets imagine that the likelihood of having one small fire at a given time is x = 5%, and that of having a violent crime is y =5% (it was 6% in 2011). A police department will need to have to have 2 policemen on call at all times, but will want 4 on the 0.25% chance that there are two simultaneous crimes (.05 x .05 = .0025); the fire department will want 8 souls on call at all times for the same reason. Either department will use the other 95% of their officers dealing with training, paperwork, investigations of less-immediate cases, care of equipment, and visiting schools, but this number on call is needed for immediate response. As there are 8760 hours per year and the police and fire workers only work 2000 hours, you’ll need at least 4.4 times this many officers. We’ll add some more for administration and sick-day relief, and predict a total staff of 20 police and 40 firemen. This is, more or less, what it was in the 1980s.

If each fire or violent crime took 3 hours (1/8 of a day), you’ll find that the entire on-call staff was busy 7.3 times per year (8x365x.0025 = 7.3), or a bit more since there is likely a seasonal effect, and since fires and violent crimes don’t fall into neat time slots. Having 3 fires or violent crimes simultaneously was very rare — and for those rare times, you could call on nearby communities, or do triage.

In response to austerity (towns always overspend in the good times, and come up short later), Oak Park realized it could use fewer employees if they combined the police and fire departments into an entity renamed “Public safety.” With 45-55 employees assigned to combined police / fire duty they’d still be able to handle the few violent crimes and fires. The sum of these events occurs 10% of the time, and we can apply the sort of statistics above to suggest that about 91% of the time there will be neither a fire nor violent crime; about 9% of the time there will be one or more fires or violent crimes (there is a 5% chance for each, but also a chance that 2 happen simultaneously). At least two events will occur 0.9% of the time (2 fires, 2 crimes or one of each), and they will have 3 or more events .09% of the time, or twice per year. The combined force allowed fewer responders since it was only rarely that 4 events happened simultaneously, and some of those were 4 crimes or 3 crimes and a fire — events that needed fewer responders. Your only real worry was when you have 3 fires, something that should happen every 3 years, or so, an acceptable risk at the time.

Before going to what caused this model of police and fire service to break down as Oak Park got bigger, I should explain Poisson statistics, exponential Statistics, and Power Law/ Fractal Statistics. The only type of statistics taught for dealing with crime like this is Poisson statistics, a type that works well when the events happen so suddenly and pass so briefly that we can claim to be interested in only how often we will see multiples of them in a period of time. The Poisson distribution formula is, P = rke/r! where P is the Probability of having some number of events, r is the total number of events divided by the total number of periods, and k is the number of events we are interested in.

Using the data above for a period-time of 3 hours, we can say that r= .1, and the likelihood of zero, one, or two events begin in the 3 hour period is 90.4%, 9.04% and 0.45%. These numbers are reasonable in terms of when events happen, but they are irrelevant to the problem anyone is really interested in: what resources are needed to come to the aid of the victims. That’s the problem with Poisson statistics: it treats something that no one cares about (when the thing start), and under-predicts the important things, like how often you’ll have multiple events in-progress. For 4 events, Poisson statistics predicts it happens only .00037% of the time — true enough, but irrelevant in terms of how often multiple teams are needed out on the job. We need four teams no matter if the 4 events began in a single 3 hour period or in close succession in two adjoining periods. The events take time to deal with, and the time overlaps.

The way I’d dealt with these events, above, suggests a power law approach. In this case, each likelihood was 1/10 the previous, and the probability P = .9 x10-k . This is called power law statistics. I’ve never seen it taught, though it appears very briefly in Wikipedia. Those who like math can re-write the above relation as log10P = log10 .9 -k.

One can generalize the above so that, for example, the decay rate can be 1/8 and not 1/10 (that is the chance of having k+1 events is 1/8 that of having k events). In this case, we could say that P = 7/8 x 8-k , or more generally that log10P = log10 A –kβ. Here k is the number of teams required at any time, β is a free variable, and Α = 1-10 because the sum of all probabilities has to equal 100%.

In college math, when behaviors like this appear, they are incorrectly translated into differential form to create “exponential statistics.” One begins by saying ∂P/∂k = -βP, where β = .9 as before, or remains some free-floating term. Everything looks fine until we integrate and set the total to 100%. We find that P = 1/λ e-kλ for k ≥ 0. This looks the same as before except that the pre-exponential always comes out wrong. In the above, the chance of having 0 events turns out to be 111%. Exponential statistics has the advantage (or disadvantage) that we find a non-zero possibility of having 1/100 of a fire, or 3.14159 crimes at a given time. We assign excessive likelihoods for fractional events and end up predicting artificially low likelihoods for the discrete events we are interested in except going away from a calculus that assumes continuity in a world where there is none. Discrete math is better than calculus here.

I now wish to generalize the power law statistics, to something similar but more robust. I’ll call my development fractal statistics (there’s already a section called fractal statistics on Wikipedia, but it’s really power-law statistics; mine will be different). Fractals were championed by Benoit B. Mandelbrot (who’s middle initial, according to the old joke, stood for Benoit B. Mandelbrot). Many random processes look fractal, e.g. the stock market. Before going here, I’d like to recall that the motivation for all this is figuring out how many people to hire for a police /fire force; we are not interested in any other irrelevant factoid, like how many calls of a certain type come in during a period of time.

To choose the size of the force, lets estimate how many times per year some number of people are needed simultaneously now that the city has bigger buildings and is seeing a few larger fires, and crimes. Lets assume that the larger fires and crimes occur only .05% of the time but might require 15 officers or more. Being prepared for even one event of this size will require expanding the force to about 80 men; 50% more than we have today, but we find that this expansion isn’t enough to cover the 0.0025% of the time when we will have two such major events simultaneously. That would require a 160 man fire-squad, and we still could not deal with two major fires and a simultaneous assault, or with a strike, or a lot of people who take sick at the same time. 

To treat this situation mathematically, we’ll say that the number times per year where a certain number of people are need, relates to the number of people based on a simple modification of the power law statistics. Thus:  log10N = A – βθ  where A and β are constants, N is the number of times per year that some number of officers are needed, and θ is the number of officers needed. To solve for the constants, plot the experimental values on a semi-log scale, and find the best straight line: -β is the slope and A  is the intercept. If the line is really straight, you are now done, and I would say that the fractal order is 1. But from the above discussion, I don’t expect this line to be straight. Rather I expect it to curve upward at high θ: there will be a tail where you require a higher number of officers. One might be tempted to modify the above by adding a term like but this will cause problems at very high θ. Thus, I’d suggest a fractal fix.

My fractal modification of the equation above is the following: log10N = A-βθ-w where A and β are similar to the power law coefficients and w is the fractal order of the decay, a coefficient that I expect to be slightly less than 1. To solve for the coefficients, pick a value of w, and find the best fits for A and β as before. The right value of w is the one that results in the straightest line fit. The equation above does not look like anything I’ve seen quite, or anything like the one shown in Wikipedia under the heading of fractal statistics, but I believe it to be correct — or at least useful.

To treat this politically is more difficult than treating it mathematically. I suspect we will have to combine our police and fire department with those of surrounding towns, and this will likely require our city to revert to a pure police department and a pure fire department. We can’t expect other cities specialists to work with our generalists particularly well. It may also mean payments to other cities, plus (perhaps) standardizing salaries and staffing. This should save money for Oak Park and should provide better service as specialists tend to do their jobs better than generalists (they also tend to be safer). But the change goes against the desire (need) of our local politicians to hand out favors of money and jobs to their friends. Keeping a non-specialized force costs lives as well as money but that doesn’t mean we’re likely to change soon.

Robert E. Buxbaum  December 6, 2013. My two previous posts are on how to climb a ladder safely, and on the relationship between mustaches in WWII: mustache men do things, and those with similar mustache styles get along best.

Improving Bankrupt Detroit

Detroit is Bankrupt in more ways than one. Besides having too few assets to cover their $18 Billion in debts, and besides running operational deficits for years, Detroit is bankrupt in the sense that most everyone who can afford to leaves. The population has shrunk from 2,000,000 in 1950 to about 680,000 today, an exodus that shows no sign of slowing.

The murder rate in Detroit is 25 times the state average; 400/year in 2012 (58/100,00) as compared to 250 in the rest of the state (2.3/100,000). The school system in 2009 scored the lowest math scores that had ever been recorded for any major city in the 21 year history of the tests. And mayor Kwame Kilpatrick, currently in prison, was called “a walking crime wave” by the mayor of Washington DC. The situation is not pretty. Here are a few simple thoughts though.

(1) Reorganize the city to make it smaller. The population density of Detroit is small, generally about 7000/ square mile, and some of the outlying districts might be carved off and made into townships. Most of Michigan started as townships. When they return to that status, each could contract their children’s education as they saw fit, perhaps agreeing to let the outlying cities use their school buildings and teachers, or perhaps closing failed schools as the local area sees fit.

This could work work well for outlying areas like the southern peninsula of Detroit, Mexicantown and south, a narrow strip of land lying along Route 75 that’s further from the center of Detroit than it is from the centers of 5 surrounding cities: River Rouge, Ecorse, Dearborn, Melvindale, and Lincoln Park. This area was Stillwell township before being added to Detroit in 1922. If removed from Detroit control the property values would likely rise. The people could easily contract education or police with any of the 5 surrounding cities that were previously parts of Stillwell township. Alternately, this newly created township might easily elect to join one of the surrounding communities entirely. All the surrounding communities offer lower crime and better services than Detroit. Most manage to do it with lower tax rates too.

Another community worth removing from Detroit is the western suburb previously known as Greenfield, This community was absorbed into Detroit in 1925. Like the Mexicantown area, this part of Detroit still has a majority of the houses occupied, and the majority of the businesses are viable enough that the area could reasonably stand on its own. Operating as a township, they could bring back whatever services they consider more suitable to their population. They would be in control of their own destiny.

 

Detroit Teachers are not paid too much

Detroit is bankrupt financially, but not because the public education teachers have negotiated rich contracts. If anything Detroit teachers are paid too little given the hardship of their work. The education problem in Detroit, I think, is with the quality of education, and of life. Parents leave Detroit, if they can afford it; students who can’t leave the city avoid the Detroit system by transferring to private schools, by commuting to schools in the suburbs, or by staying home. Fewer than half of Detroit students are in the Detroit public schools.

The average salary for a public school teacher in Detroit is (2013) $51,000 per year. That’s 3% less than the national average and $3,020/year less than the Michigan average. While some Detroit teachers are paid over $100,000 per year, a factoid that angers some on the right, that’s a minority of teachers, only those with advanced degrees and many years of seniority. For every one of these, the Detroit system has several assistant teachers, substitute teachers, and early childhood teachers earning $20,000 to $25,000/ year. That’s an awfully low salary given their education and the danger and difficulty of their work. It’s less than janitors are paid on an annual basis (janitors work more hours generally). This is a city with 25 times the murder rate in the rest of the state. If anything, good teachers deserve a higher salary.

Detroit public schools provide among the worst math education in the US. In 2009, showing the lowest math proficiency scores ever recorded in the 21-year history of the national math proficiency test. Attendance and graduation are low too: Friday attendance averages 71.2%, and is never as high as 80% on any day. The high-school graduation rate in Detroit is only 29.4%. Interested parents have responded by shifting their children out of the Detroit system at the rate of 8000/year. Currently, less than half of school age children go to Detroit public schools (51,070 last year); 50,076 go to charter schools, some 9,500 go to schools in the suburbs, and 8,783, those in the 5% in worst-performing schools, are now educated by the state reform district.

Outside a state run reform district school, The state has taken over the 5% worst performing schools.

The state of Michigan has taken over the 5% worst performing schools in Detroit through their “Reform District” system. They provide supplies and emphasize job-skills.

Poor attendance and the departure of interested students makes it hard for any teacher to handle a class. Teachers must try to teach responsibility to kids who don’t show up, in a high crime setting, with only a crooked city council to look up to. This is a city council that oversaw decades of “pay for play,” where you had to bribe the elected officials to bid on projects. Even among officials who don’t directly steal, there is a pattern of giving themselves and their families fancy cars or gambling trips to Canada using taxpayers dollars. The mayor awarded Cadillac Escaldes to his family and friends, and had a 22-man team of police to protect him. On this environment, a teacher has to be a real hero to achieve even modest results.

Student departure means there a surfeit of teachers and schools, but it is hard to see what to do. You’d like to reassign teachers who are on the payroll, but doing little, and fire the worst teachers. Sorry to say, it’s hard to fire anyone, and it’s hard to figure out which are the bad teachers; just because your class can’t read doesn’t mean you are a bad teacher. Recently a teacher of the year was fired because the evaluation formula gave her a low rating.

Making changes involves upending union seniority rules. Further, there is an Americans with Disability Act that protects older teachers, along with the lazy, the thief, and the drug addict — assuming they claim disability by frailty, poor upbringing or mental disease. To speed change along, I would like to see the elected education board replaced by an appointed board with the power to act quickly and the responsibility to deliver quality education within the current budget. Unlike the present system, there must be oversight to keep them from using the money on themselves.

She state could take over more schools into the reform school district, or they could remove entire school districts from Detroit incorporation and make them Michigan townships. A Michigan township has more flexibility in how they run schools, police, and other services. They can run as many schools as they want, and can contract with their neighbors or independent suppliers for the rest. A city has to provide schools for everyone who’s not opted out. Detroit’s population density already matches that of rural areas; rural management might benefit some communities.

I would like to see the curriculum modified to be more financially relevant. Detroit schools could reinstate classes in shop and trade-skills. In effect that’s what’s done at Detroit’s magnet schools, e.g. the Cass Academy and the Edison Academy. It’s also the heart of several charter schools in the state-run reform district. Shop class teaches math, an important basis of science, and responsibility. If your project looks worse than your neighbor’s, you can only blame yourself, not the system. And if you take home your work, there is that reward for doing a good job. As a very last thought, I’d like to see teachers paid more than janitors; this means that the current wage structure has to change. If nothing else, a change would show that there is a monetary value in education.

Robert Buxbaum, August 16, 2013; I live outside Detroit, in one of the school districts that students go to when they flee the city.

Crime: US vs UK and Canada

The US has a lot of guns and a lot of murders compared to England, Canada, and most of Europe. This is something Piers Morgan likes to point out to Americans who then struggle to defend the wisdom of gun ownership and the 2nd Amendment: “How do you justify 4.8 murders/year per 100,000 population when there are only 1.6/year per 100,000 in Canada, 1.2/year per 100,000 in the UK, and 1.0/year per 100,000 in Australia — countries with few murders and tough anti-gun laws?,” he asks. What Piers doesn’t mention, is that these anti-gun countries have far higher contact crime (assault) rates than the US, see below.

Contact Crime Per Country

Contact crime rates for 17 industrialized countries. From the Dutch Ministry of Justice. Click here for details about the survey and a breakdown of crimes.

The differences narrow somewhat when considering most violent crimes, but we still have far fewer than Canada and the UK. Canada has 963/year per 100,000 “most violent crimes,” while the US has 420/year per 100,000. “Most violent crimes” here are counted as: “murder and non-negligent manslaughter,” “forcible rape,” “robbery,” and “aggravated assault” (FBI values). England and Wales classify crimes somewhat differently, but have about two times the US rate, 775/year per 100,000, if “most violent crimes” are defined as: “violence against the person, with injury,” “most serious sexual crime,” and “robbery.”

It is possible that the presence of guns protects Americans from general crime while making murder more common, but it’s also possible that gun ownership is a murder deterrent too. Our murder rate is 1/5 that of Mexico, 1/4 that of Brazil, and 1/3 that of Russia; all countries with strong anti-gun laws but a violent populous. Perhaps the US (Texan) penchant for guns is what keeps Mexican gangs on their, gun-control side of the border. Then again, it’s possible that guns neither increase nor decrease murder rates, so that changing our laws would not have any major effect. Switzerland (a country with famously high gun ownership) has far fewer murders than the US and about 1/2 the rate of the UK: 0.7 murders/ year per 100,000. Japan, a country with low gun ownership has hardly any crime of any sort — not even littering. As in the zen buddhist joke, change comes from within.

Homicide rate per country

Homicide rate per country

One major theory for US violence was that drugs and poverty were the causes. Remove these by stricter anti-drug laws and government welfare, and the violent crime would go away. Sorry to say, it has not happened; worse yet, murder rates are highest in cities like Detroit where welfare is a way of life, and where a fairly high fraction of the population is in prison for drugs.

I suspect that our welfare payments have hurt Detroit as much as they’ve helped, and that Detroit’s higher living wage, has made it hard for people to find honest work. Stiff drug penalties have not helped Detroit either, and may contribute to making crimes more violent. As Thomas More pointed out in the 1500s, if you are going to prison for many years for a small crime, you’re more likely to use force to avoid risk capture. Perhaps penalties would work better if they were smaller.

Charity can help a city, i think, and so can good architecture. I’m on the board of two charities that try to do positive things, and I plant trees in Detroit (sometimes).

R. E. Buxbaum, July 10, 2013. To make money, I sell hydrogen generators: stuff I invented, mostly.

Detroit: maximum punishment

Some moths ago, I argued that getting rid of its extra-high minimum wage was perhaps the single best thing that Detroit could do to improve its bankrupt finances and to provide jobs for its youth. I argued that this living wage of $11 or $14/hr, depending on whether healthcare was provided, was too much for the city to pay for it’s minimal skill workers. I also argued that a lower minimum wage would help the city finances, and would allow the unskilled of Detroit to find jobs: it would provide the first rung of a ladder. Well, sort-of good news: Detroit’s living wage has been declared unenforceable by the Michigan Supreme court.

Unenforceable does not mean that wages will lower immediately: anyone working for the city will keep their high salary job, so the finances of the city will remain strained. Also, private companies can not lower anyone’s contracted wages. The only difference is that workers on non-city jobs who agree to be paid $7.50 to $14/hr, can no longer sue to recover additional dollars to meet Detroit’s “living wage.” Bit by bit I expect that more low-skilled workers will be hired, and that their wages will stabilize downward to a free-market value.

The next big things that are needed are reduced crime and increased population who are employed in businesses other than selling drugs or themselves. One way to reduce crime, I think is to have less-stiff minimum penalties for non-violent crimes like drug possession and driving with a suspended license. Currently the penalty for possession runs to 15-20 years. No one who spends that much time in prison will fit back into society. Let’s do them and ourselves a favor by reducing minimum sentences so that the normal sentence is only 1-5 years (ideally with < 1 oz marijuana possession punished by a fine).

Another horror is the penalty for driving with a suspended license. It’s $3000 for a start (a reasonable amount, I think), but then the state adds a $4000 per year penalty for the next 3 years: a total of $15,000. That’s too much for a minimum-wage earner to pay, but the minimum wage earner needs a car to get to work. So he/she can’t work, or he/she drives without a license or insurance. Is this what we want? Lets give a second chance and lower the penalty to produce more working, law-abiding citizens. There is nothing wrong with Detroit that could not be fixed by 200,000 more, law-abiding, employed Detroiters.

R.E. Buxbaum owns REB Research, a maker of hydrogen purifiers and hydrogen generators. We used to be located in Detroit, but are now in Oakland county, 1/2 mile north of the Detroit border.