Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

11 August 2026

What Is True And What Is False About Literacy?

Jared Henderson has a thoughtful Substack post about literacy statistics and the "literacy crisis." Many statistics thrown around in the public square about this issue are misleading or ill-sourced. 

Henderson spends a lot of time revisiting his prior commentary on the issue, acknowledging that some of what he said previously was probably wrong or overstated, and sourcing the common misleading statistics. I'll skip that here.

The most essential point is that there are different levels of literacy and commonly cited statistics on point frequently don't disclose what level of literacy they are talking about. They also often cite statistics about literacy in the English language, which is appropriate for many purposes, but neglect to mention that many people in the U.S. who are not literate in English are literate in another language.



"Could not participate" is a mix of non-English language speakers, and people who have physical or cognitive disabilities too serve to interview, two very distinct populations.

Level 1 is minimal basic literacy, and about 8.1% of adults in the U.S. either could not participate in the survey or can't attain this basic level of literacy, although even some people below Level 1 literacy might be able to read a simple story to their children, recite the alphabet, or read a street sign. Many people with Level 1 literacy would struggle to graduate from high school at all.

Level 2 is the literacy level of typical non-college bound high school graduates.

Level 3 is the literacy level of a college bound high school graduate and about 57.5% of Americans have that level of literacy (other sources have put this figure as low as 46%).

Levels 4 and 5 are the literacy levels, roughly speaking, of above average college graduates and people who have graduate degrees.

An OECD report puts the United States in the middle of developed countries for literacy levels:


The United States does have a very high level of disparity between the 90th percentile and the 10th percentile in literacy (and numeracy and problem solving) compared to other developed countries, which is to say crudely that we have very literate smart people and very illiterate dumb people (using the same scale as the mean literacy levels in the chart above).


Prior to COVID, the U.S. was seeing a very gradual trend of improvement in reading and math among school children, but it took a dip (hopefully temporary and due to disrupted educational programs) in the year 2020 from which it had not yet recovered in the most recent available data.


The author describes as a separate matter the decline in the extent to which adults who used demographically used to read books do so now, but attributes this to a disinclination to read rather than a decline in the ability to read long form books. But he makes a point of distinguishing this issue from adult literacy from childhood literacy, each of which are distinct issues with distinct workable responses.

12 November 2025

Basic Skills In Decline Among Freshman At College

The UC San Diego Senate Report on Admissions documents a sharp decline in students’ math and reading skills . . . 
At our campus, the picture is truly troubling. Between 2020 and 2025, the number of freshmen whose math placement exam results indicate they do not meet middle school standards grew nearly thirtyfold, despite almost all of these students having taken beyond the minimum UCOP required math curriculum, and many with high grades. In the 2025 incoming class, this group constitutes roughly one-eighth of our entire entering cohort. 
A similarly large share of students must take additional writing courses to reach the level expected of high school graduates, though this is a figure that has not varied much over the same time span.

Moreover, weaknesses in math and language tend to be more related in recent years. In 2024, two out of five students with severe deficiencies in math also required remedial writing instruction. Conversely, one in four students with inadequate writing skills also needed additional math preparation. . . .
The math department created a remedial course, only to be so stunned by how little the students knew that the class had to be redesigned to cover material normally taught in grades 1 through 8. . . .

The report attributes the decline to several factors: the pandemic, the elimination of standardized testing—which has forced UCSD to rely on increasingly inflated and therefore useless high school grades—and political pressure from state lawmakers to admit more “low-income students and students from underrepresented minority groups.”
…This situation goes to the heart of the present conundrum: in order to holistically admit a diverse and representative class, we need to admit students who may be at a higher risk of not succeeding (e.g. with lower retention rates, higher DFW rates, and longer time-to-degree).

From Marginal Revolution. 

The deemphasis on standardized tests in admissions, which provide a means to test these skills in a way not influenced by high school specific grade inflation is probably the primary factor.

Admitting students who aren't academically prepared to college isn't doing them any favors.

22 August 2025

Why Do Distance Runners Have More Precancerous Colon Growths?

Are Marathons and Extreme Running Linked to Colon Cancer? A small, preliminary study found that marathoners were much more likely to have precancerous growths. Experts aren’t sure why.

From the New York Times. 

My initial take is that marathoners and extreme runners aren't dying of cardiovascular diseases or pulmonary disease (including lung cancer), but eventually have to die of something, and that something is often colon cancer.

Another non-causal explanation could be that marathoners and extreme runners are more health conscious, and hence more likely to get their colonoscopies done, causing their colon cancers to be noted statistically, while less health conscious people skip their colonoscopies (an entirely understandable sentiment) and so if they have precancerous growths at the same age, they go undetected and aren't noted statistically.

In the same vein, almost no one discovers that they have precancerous pancreatic cancer growth, or even pancreatic cancer itself, because it is usually asymptomatic until it is very advanced.

Or, it could just be a statistical fluke, which is something that is common in small studies and is further influenced by a bias towards only publishing results showing a potential positive or negative disease correlation (which creates a "look elsewhere effect"  that reduces the statistical significance of the studies that are published since only locally statistically significant outlier results get published). The look elsewhere effect is widely recognized but can be hard to quantify.

It could be more than that. It is certainly plausible that a more stressed body might be more prone to cancer, and long distance running does indeed stress your gastrointestinal system. This is especially plausible if the true effect size is modest. Indeed, the confounds noted above could turn a small effect size into a seemingly much larger one.

But it also might be just be entirely due to some of the non-intuitive aspects of how epidemiology and health statistics work. 

30 July 2025

Conclusion That Egg Consumption Reduces Alzheimer's Disease Not Very Significant

A study in the peer reviewed Journal of Nutrition claiming a 47% reduction in clinical diagnosis of Alzheimer's during life due to eating at least one egg a week, is much weaker than it appears at face value. 

The results (based upon a clinical diagnosis during life) were consistent with benefits as low as 17% within the margin of error.
 
And, the clinical diagnosis rates weren't very accurate. Post-mortem examination of the brains of more than half of the sample (578 cases) found a 56% false negative rate for clinical diagnosis during life and an 18% false positive rate for clinical diagnosis during life. This casts doubt on whether the lifetime clinical diagnosis data is meaningful at all, given its immense inaccuracy. 

The results when based on autopsies were consistent with benefits as low as 10% for two or more eggs a week.

Both these results are only modestly better than the p=0.05 statistical significance threshold, and the fact that the cases where Alzheimer's disease was accurately diagnosed showed less of a benefit, also casts doubt on the significance of this study. None of the evidence supporting the author's hypothesis that dietary choline intake was the protective factor was statistically significant, and none of the results were significant at anything close to the p=0.01 level. This significance, moreover, is overstated, because the study fails to adjust for the inaccuracy of the clinical diagnosis process or for the uncertainty in the result caused by self-reporting of what people ate. 

Dietary self-reporting is particularly problematic in a population where a large percentage of the reporters will ultimately be diagnosed with Alzheimer's disease in less than ten years. It could be that many people who don't report weekly egg consumption did so because their memory was not good enough to remember everything that they ate in the last month due to having undiagnosed or subclinical levels of Alzheimer's disease, rather than being due to actually eating fewer eggs.

The sample size is small, so the statistical significance of the result is modest. The total sample was 1024 people, and only 370 of them did not eat at least one egg a week.

Also casting doubt on the result is the fact that there was no dose-response effect (i.e. eating more than one egg a week is no better than eating one egg a week, and eating no eggs is not significantly different from eating 1-3 eggs a month) and indeed, eating more than one egg a week reduced the benefit in individuals who had post-mortem exams done, relative to those who had one egg a week.

The average diagnosis at 6.7 ± 4.8 years from the start of the study is also soon enough after the study began, that given strong evidence in the literature (which is not mentioned in the literature review in the study) that Alzheimer's disease starts at sub-clinical levels decades before it is diagnosed in many cases. So, the diet of the people in the study during the study period probably didn't influence the outcomes.

Finally, while the study controls for 13 potential confounding factors (of which some, like education, didn't vary significantly between the subgroups), it could easily have omitted an important factor. And, it doesn't prove cause and effect either. For example, it could be that having undiagnosed Alzheimer's disease influences your body in a way that you don't like eating eggs as much.

Thus, while the study might justify further research, its conclusion the weekly egg consumption greatly reduces Alzheimer's disease onset risk is too weak to make a life choice based upon, or to recommend clinically, despite the fact that their best fit benefit purports to be as much as a 47% reduction in the risk of getting Alzheimers. Indeed, if anything, the details of the data tend to favor some uncontrolled for confounding factor that is merely mildly correlated with egg consumption.

The failure of the study to engage with many of these issues in a forthright manner also casts doubt on the quality of the peer review at the Journal of Nutrition for this study.

The study and its abstract are as follows:
Background: Alzheimer’s disease (AD) is a neurodegenerative disorder with increasing prevalence due to population aging. Eggs provide many nutrients important for brain health, including choline, omega-3 fatty acids, and lutein. Emerging evidence suggests that frequent egg consumption may improve cognitive performance on verbal tests, but whether consumption influences the risk of Alzheimer’s dementia and AD is unknown.

Objectives: To examine the association of egg consumption with Alzheimer’s dementia risk among the Rush Memory and Aging Project cohort.

Methods: Dietary assessment was collected using a modified Harvard semiquantitative food frequency questionnaire. Participants’ first food frequency questionnaire was used as the baseline measure of egg consumption. Multivariable adjusted Cox proportional hazards regression models were used to investigate the associations of baseline egg consumption amount with Alzheimer’s dementia risk, adjusting for potential confounding factors. Subgroup analyses using Cox and logistic regression models were performed to investigate the associations with AD pathology in the brain. Mediation analysis was conducted to examine the mediation effect of dietary choline in the relationship between egg intake and incident Alzheimer’s dementia.

Results: This study included 1024 older adults {mean [±standard deviation (SD)] age = 81.38 ± 7.20 y}. Over a mean (±SD) follow-up of 6.7 ± 4.8 y, 280 participants (27.3%) were clinically diagnosed with Alzheimer’s dementia. Weekly consumption of >1 egg/wk (hazard ratio [HR]: 0.53; 95% confidence interval [CI]: 0.34, 0.83) and ≥2 eggs/wk (HR: 0.53; 95% CI: 0.35, 0.81) was associated with a decreased risk of Alzheimer’s dementia. Subgroup analysis of brain autopsies from 578 deceased participants showed that intakes of >1 egg/wk (HR: 0.51; 95% CI: 0.35, 0.76) and ≥2 eggs/wk (HR: 0.62; 95% CI: 0.44, 0.90) were associated with a lower risk of AD pathology in the brain. Mediation analysis showed that 39% of the total effect of egg intake on incident Alzheimer’s dementia was mediated through dietary choline.

Conclusions: These findings suggest that frequent egg consumption is associated with a lower risk of Alzheimer’s dementia and AD pathology, and the association with Alzheimer’s dementia is partially mediated through dietary choline.
Yongyi Pan, et al., "Association of Egg Intake With Alzheimer’s Dementia Risk in Older Adults: The Rush Memory and Aging Project" 154(7) The Journal of Nutrition 2236-2243 (2024). https://doi.org/10.1016/j.tjnut.2024.05.012.

10 January 2025

Americans Aren't Geniuses But They Aren't As Illiterate As Claimed

This meme is floating around on Facebook:


These kinds of dubious statistic are thrown out there to unjustly discredit public education and push for things like vouchers and home schooling, and to attack K-12 educators, by creating a "moral panic."

The ranking is, as noted, grossly inaccurate - there is a huge difference between 36th place and 125th place in a world with 195 countries. This flaw should undermine the credibility of the entire meme.

The definition used is also problematic.

What is the "6th grade level"? The 54% read below the 6th grade level figure is surely not referring to the reading level of the median 6th grader, which would be 50% in 6th grade, as the term would naively imply without a definition.

The high school graduation rate is 87% and 61% of adults over age 25 have some college. While many people don't improve a whole lot in reading ability between 6th grade and 12th grade, or after graduating from high school and then going to college but not graduating, more than 4% of people, for example, people who were slightly below average in 6th grade but ultimately graduate from high school and then go to college for a year or so, improve at least beyond the level of the median 6th grader in their next six to nine years of formal education after the 6th grade.

The statistics claiming that 54% of adults read below the 6th grade level also can't be squared with other data showing that 20% of adults read below the 5th grade level uncritically quoted by some advocated in the same breath (which is about the reading level at which general public oriented regional newspapers like the Denver Post are written). The literacy acquisition curve is not a mesa that gets super steep for one year and then almost completely flattens out. Other studies claim that the average American reads at the 8th or 9th grade level, a statistic which shares the same definition issues but less acutely.

The 54% read at the 6th grade level statistic must really based on measuring what some overoptimistic education researcher believes a 6th grader should be able to read that is divorced from reality. It is probably closer to the median reading level of 9th graders which is commonly used as a benchmark for functional literacy.

Also, the true literacy rate in the U.S. is well over 90%. Almost all adults (even those who are legally developmentally disabled) know the alphabet and can read street signs, children's books, etc. in their native language. "Functional literacy" set at a level needed to function reading things like medicine labels and tax forms and instructions for purchases that adults sometimes need to know is shared at a lower rate (and is about the reading level of the median 9th grader).

Yes, the average person is less functionally literate than the average functionally literate person believes, and yes, it would be better if more people had a higher level of literacy. But we aren't nearly as far gone as this meme implies.

08 December 2024

MIT Students Make Up 80% of Putnam Competition Winners

One of the biggest national contests in math for college students in the U.S. and Canada is the Putnam competition. About 80% of the winners attend MIT. Many of the rest attend Harvard, a few hundred yards away. The prize is nominal, but the reputational benefits of winning and scholarships are immense for anyone interested in pursuing a career in mathematics and it can open the door to large merit scholarships as well. Per the Wikipedia link above:

It is widely considered to be the most prestigious university-level mathematics competition in the world, and its difficulty is such that the median score is often zero or one (out of 120) despite being primarily attempted by students specializing in mathematics.

21 August 2024

Home Prices And Political Identity

It isn't a perfect fit, but high home prices are strongly correlated with voting blue and low home prices are strongly correlated with voting red. Note also Zillow's novel statistic.

03 October 2022

High School Exit Exams Don't Matter

Conditioning the award of a high school diploma on passing a high school exit exam is designed to provide a signaling benefit to those who pass it relative to those who don't, given the fact of having earned a diploma more value in the economic and educational marketplace. 

But that doesn't seem to be what actually happens.

This suggests that IQ matters more than the signal of earning a diploma for these students who often receive a "certificate of completion" that the market treats as a high school diploma, even though it is not a true diploma.

Part of why high school dropouts perform so much worse that high school graduates who just barely graduate in the job market is that usually dropping out of high school reflects delinquency and a failure to conform to social norms, rather than serving as a measure of IQ. The diploma signals something, but not academic ability.

For the same reason, even though earning a GED requires more IQ than the average high school graduate, a GED is a less desirable credential than a high school diploma since it is so often earned by someone who is incarcerated, a negative mark that outweighs proving that one has a minimum level of intellectual capacity.

Also, perhaps this is because attempting college and not getting a diploma has been widely adopted as a signal to distinguish high school graduates who are more or less academically capable. Students who just barely pass a high school exit exam aren't likely to attempt to go to college.
Clark and Marotell (2014) . . . compare the career earnings of students who barely passed and those who barely failed high school exit exams - those who failed did not get a diploma, but those who passed did (these were at the end of their education, so a big effect here would give credence to the signalling thesis). They find little evidence of there being a signal effect, and you can see the visualisations . . . below.

From Sam Atis, "Quasi-experiments and Education" Samstack (September 29, 2022) (comparing linear regression to "Regression Discontinuity Design" [where] "an arbitrary cut-off can give you the equivalent of the treatment group and a control group that you get in a randomised control trial.").

If there were a signaling effect from passing a high school exit exam, you would expect that there would be a discontinuity in the trend at the zero line that divides students who passed the exit exam from those who failed it in the charts above. But, there isn't one. 

Two other RDD students on the benefits of education are also interesting:
  • Banks and Mazzona (2012) exploit a 1947 change to the minimum school leaving age in the United Kingdom, and find a large and significant effect of one year of education on male memory and executive functioning in old age.

    Ozier (2018) exploits the fact that the probability of admission to a government secondary school sharply increases if a child gets a score close to the national mean, finding that completing secondary school increases scores on a cognitive ability test by 0.6 standard deviations. Education also seems to increase employment rates and decrease the chance of teen pregnancy among women - although this would be consistent with the signalling thesis.

    These studies also point out another issue. One way to conceptualize a content free IQ test administered to a child is, at least in part, as a potential to benefit from education that still requires education to be fully realized.

04 August 2022

Don't Solve For The Equilibrium

One of the classic catch phrases of both economics and physics is "solve for the equilibrium". It is easier, mathematically and simpler, in  principle, to solve a problem with formulas in which everything has to balance out, than it is to solve a problem and predict a result where everything is out of equilibrium.

But, in the 21st century, we are in a context in which most questions worth asking in the social sciences involves circumstances that are further from an equilibrium state than at almost any other time in human history.

Technology, the fundamentals and system self-interactions that drive economics, the climate, the ecological balance of nature, parenting, dating, marriage, gender, racial identities, the way the political system works, military realities, and more are in intense flux.

Only a handful of political regimes anywhere in the world are more than five generations old. The first powered fixed wing aircraft flew four generations ago in 1903, commercial aircraft entered wide use about a generation later, and two generations later a man had walked on the Moon. Internal combustion engine vehicles fueled with refined petroleum became predominant by 1908 and will probably be a minority of vehicles on the road by 130 years later - the vast majority of non-transportation uses of petroleum have already largely been phased out (except heavy heating oil in a few regions, electricity generation in Hawaii and Alaska, lubricants, plastics, and fertilizers). General Relativity and quantum mechanics are less than four generations old, and when they were invented, Armies still had horse cavalry. Most of the national boundaries in the Middle East were drawn shortly after World War II. 

Jews started to return to Israel in the 1920s, after by tradition, about 1850 years in the diaspora, and the State of Israel came into being in 1948. Hebrew was an exclusively a liturgical language and a language used by religious scholars from about 200 CE to 1880 CE, was spoken by a community of about 34,000 people during World War I, and did not start to become a widespread living first language until the 1920s in the British Mandate in Palestine and first became a national language in 1948, about two generations after it started to be revived, when Israel became an independent state (at which point about 80% of Jews spoke it as a first language, and 15% spoke it as a second language).

The home that I live in was built less than a hundred years ago, in 1925 with coal fired steam heat boiler made popular by then recent global Spanish flu pandemic, had a door in the kitchen wall to receive ice deliveries, had a garage sized for a Model T, had galvanized steel pipes, didn't have electricity until it was added in later renovations, and was in a neighborhood that got its start as a streetcar suburb of Denver called "South Denver" before it was annexed by the City of Denver. Coal is now used predominantly to generate electricity in large power plants, in which it has a rapidly decreasing market share, and for "coke" in the steel production process.

Soviet style communism lasted less than 75 years in Europe, where it no longer exists. Many countries in East Asia and Southeast Asia still have nominally communist political systems (none of which are yet 75 years old), but their economies have adopted so many market economy reforms that their economies aren't really communist anymore. These nominally communist regimes are still authoritarian one-party states, but collective ownership of the means of production, and distribution of the fruits of production according to need, is a Marxist pipe dream that Asian regimes that are nominally communist have largely abandoned.

Around the time that my parents were born, the Great Depression wasn't over yet, the airship industry was collapsing, most of Africa and Asia was governed by European colonial powers, the Communists were just an upstart political party in China, and the Soviet Union was alive and well. My in-laws were born during World War II and experienced the Korean War in ways that put their lives at risk. The farm my father grew up on used a horse for farm labor when he was a child. The entire nuclear dimension of military affairs came into being at a time when my parents could read about it in the newspaper, as did the political regimes in Europe, Asia, and Africa. 

When my parents started high school, Latin was a mandatory subject for every college bound high school student and public schools in the South were still segregated by race as a matter of law. All Roman Catholics in the world conducted their church services in Latin at a time when my parents had both finished their undergraduate educations. My parents were first generation college students who earned PhDs. Co-ed dorms didn't exist when my parents were in college. At the time my father served in the Army, it was just in the process of desegregating. 

Long term mortgages and employment based health insurance were first widely used in my parent's lifetimes. My father-in-law was one of the first doctors to use radiology machines more sophisticated than X-Rays and his parents were first generation Christians. 

Over the course of my parents lives, the Republican party went from being a liberal leaning Northern party to a conservative party of the South and rural America. At my father's first job as a professor in Atlanta, Georgia, many of his students had spent at least some of their school years in segregated schools, and some of their African-American friends had first been able to vote in a Presidential election just four years before they arrived in Georgia as a consequence of the Voting Rights Act of 1965. 

My father was on the committee that organized the first Earth Day. My parents were peers of Elvis Presley and disliked the Beatles and pretty much all other kinds of rock musics, well into their 30s, when rock music started to become predominant. Big band music, more than one sub-genres of jazz music, rock music, and the music of "crooners", like Frank Sinatra featured on the Lawrence Welk show on TV, all came into being during their lifetimes before I was born.

Most of the hydroelectric, geothermal, and nuclear power plants in the world were built during my parents lifetimes before I was born, or when I was a child. The vast majority of the wind, solar, tidal power and natural gas fueled power plants powering the electrical grid in the world has come online in my lifetime, and a majority of the wind, solar and tidal power powering the electrical grid in the world has been added during my children's lifetimes.

Polio afflicted tens of thousands of people a year in the United States until after my parents were finished with college; there were ten cases of polio that originated in the United States in the first decade of my life, and there has only been one case of polio from any source in the United States in the last twenty-nine years, which was this year. The concept of autoimmune diseases as a coherently class of ailments was developed after my parents had graduated from college (and after my aunt was first diagnosed with M.S. an autoimmune disease whose true cause has only been ascertained in the last few years).

When I was born, most cars ran on leaded gasoline, most physics and engineering calculations were still done with slide rules, computers took up whole rooms, the primary method of putting information into a computer was a punchcard, formulas in physics journal articles were written by hand, and many rural areas were still served by "party line" telephone service. Early computers (in my lifetime) with the power of my cell phone would have taken the same amount of electricity to operate as a skyscraper. Computer processor power and memory has increased exponentially, and has seen power consumption decrease exponentially, for my entire life. The core components of the Standard Model of Particle Physics were invented in my lifetime. "No fault" divorce, legal recognition for LGBT rights, females making up more than low single digit percentages of lawyers and doctors and professors, the modern concept of attention deficit disorder, the generalized concept of post-traumatic stress disorder, widespread use of statins to control cholesterol, widespread use of student loans for higher education, and the modern environmental movement all came into existence, for all practical purposes, in my lifetime. Obesity rates for both children and adults in the U.S. have roughly tripled from their long term historical norms to current levels during my lifetime. 

The first time I met someone who was openly gay was in college, which is also the first time that I used the Internet, and the first time I'd encountered Muslims face to face, and the first time I'd eaten tofu. The Soviet Union ceased to exist when I was in college. Crime rates hit all time highs around the time that I was in college and have since declined to half century lows. Divorce rates which were once low across the board soared to record highs during my lifetime, then experienced a class divide with divorce rates for college educated couples plummeting and divorce rates for couples without any college educations reaching levels never before seen that continue to rise checked only by couples not bothering to get married when living together and having children at all.

MTV came and went in my lifetime, as did disco, New Wave, eight track tapes, cassette tapes, videodisks, compact disks (CDs), DVDs, and analog broadcast television. Broadcast satellite TV and radio came into wide commercial use in my lifetime and I doubt that either will still be in wide commercial use when I die. Rap and Hip hop were invented in my lifetime and remain vibrant. The proportion of Americans who identify as non-religious has increased by a factor of ten in my lifetime. 

Commercial supersonic aircraft came into being and then ceased to exist in my lifetime, and will renter the market again in a few years.

"Smart bombs", guided missiles, stealth aircraft, and unmanned military drones all entered regular military use in my lifetime.  Amphibious assaults, air to air combat between fighter aircraft in "dog fights", ship to ship battles, submarine to ship battles, ship to submarine battles, and the use of nuclear weapons in war, have become vanishingly rare or non-existent in my lifetime.

The death penalty in the United States was abolished nationally, and then reinstated on a much more restricted basis, in my lifetime. Abortion was first constitutionally protected after my brother and I were born, and has now been denied constitutional protection in my lifetime. Marital rape was criminalized, and domestic violence  and acquaintance rape first began to be taken very seriously by the criminal law in my lifetime, and gay sex between consenting adults was legalized by becoming constitutionally protected in the United States in my lifetime. Serious drunk driving penalties and major reductions in tobacco use both arose in my lifetime.

At my first job as a summer law clerk with a law firm, lawyers were not allowed to use computers or typewriters, we had to dictate everything that we didn't write longhand, leaving typing for a large and almost entirely female corps of secretaries who knew how to use typewriters and early word processors (even though the youngest lawyer in the firm and the law clerks knew how to do so themselves). Legal research, including checking cases to make sure that they had not been overruled or narrowed by subsequent cases, was done almost entirely with dead tree books, because computerized legal research while it existed, was very expensive per minute or per search. At the end of each day, a recent high school graduate would rush to hand deliver all of the firm's court filings to the local court clerk before the office closed at five p.m., and to mail copies of those documents before five p.m. at the local post office that this courier had spent all afternoon photocopying to every party of record in the case and the court with an extra copy to be pinned down with metal clamps in a hard copy paper pleadings file. Lawyers needed to finish their dictations and final handwritten revisions to court documents by three or four o'clock in the afternoon, to allow time for them to be typed by the secretaries, photocopied, delivered to the court clerk, and mailed, before the hard five o'clock deadlines for doing so. All court hearings were held in person.

Now those jobs are gone. All lawyers except men in their sixties or older type their own first drafts of court documents subject to only light editing and proofreading by staff (younger lawyers do their own advanced typesetting as well, while older ones rely on secretaries or paralegals for these formatting tasks), after personally researching cases and statutes online, and then they either personally, or with one paralegal serving several lawyers, e-file the documents to the court and to all other parties in the case by midnight deadlines, often without the final draft ever being printed or manually signed or filed. The client gets an email copy and often there is no paper pleadings file in a case at all. Many non-evidentiary court hearings like status conferences and pre-trial conferences are conducted remotely, as are many mediation sessions (something that also was rare back then, but now is required in almost every case).

Back in the day, many court documents needed to be notarized, in person, with a red ink stamp with a raised embossed seal. Now, the documents that used to be notarized are just signed by the client or witness in pen under penalty of perjury, scanned, and emailed to the lawyer for filing. 

As a result, modern law firms are profoundly more top heavy than they used to be in most kinds of law practices, and lawyers no longer work "banker's hours."

Mass produced electric cars were reinvented in my children's lifetime. I have never owned a car that wasn't made by a Japanese or Korean car company since my children were born. We haven't had broadcast television service at any time in my children's lives. We ended our cable TV service before they started middle school. We discontinued our landline telephone service before my children were in high school. My wife was pregnant with my oldest child when the Euro came into being and about a dozen European national currencies ceased to exist. My children were alive when cryptocurrencies came into being and when same sex marriages were legalized. The Department of Homeland Security, the TSA, the "no fly list", security checkpoints with shoe removal, and limits on carrying liquids arose after my oldest child was born. The U.S. has been a party to low intensity "small" wars for essentially all of my children's lifetimes. The privately enforceable constitutional right to bear arms was first recognized in my children's lifetimes. Lockdown drills at school, in response to numerous mass school shootings, have replaced in my children's generation the duck and cover drills of the Cold War era.

My children don't really remember ever living without the Internet or cell phones. Some of my children's high school textbooks were delivered on electronic tablets and they had homework assignments in high school that included typing mathematical formulas using LaTex computer typesetting. COVID, of course, arose during my children's lifetime. We are still a couple of years away from the U.S. getting its first truly high speed rail line, long after they have become common in Europe and China.

This recitation of historical events reminiscent of Billy Joel's song, "We Didn't Start The Fire" and a few subsequent imitations of its structure, may be a bit excessive and familiar. But, in this post, my real point is that everyone alive today, and our parents, and our grandparents, and even a generation or two beyond them, have never known a time when science, technology, economics, international affairs, culture, and law weren't in periods of breakneck change. 

Austrian-born economist Joseph Schumpeter, who is most famous for his Marxist inspired characterization of dynamic capitalist economies in the long run as a process of "creative destruction", particularly in his 1942 book Capitalism, Socialism and Democracy, was one of my favorite economists in college. This was because he had a realistic description and astute understanding of the essential features of the big picture of the workings of modern capitalism, when other economists so frequently seemed to lose sight of the forest for the trees attempting to devise simple, theory driven mathematical models of the economy.

It is easy to fall into the trap of thinking about the present as if this is the way that the world has always been and always will be, and one of the most important lessons I learned as a history minor in college was just how untrue that assumption was over far shorter time frames than I ever would have guessed otherwise.

But, solving for an equilibrium in the social sciences that can't be reached in the very short term of a fewer minutes to a few decades, at most, is irrelevant and often counterproductive. 

Change, and not equilibrium, has been the long standing norm for all of living history and all of the oral history and recollections of the vast majority of living people alive today. 

Forcing yourself to almost always consider dynamic models in the social sciences and in predicting the future of technology, is far harder and far less certain than trying to solve for an equilibrium predicted by your theories based upon the present. But, at least doing so avoids the near certainty that any attempt to solve for the equilibrium for any significant period of time will be wrong.

16 March 2022

Somebody's Not Going To Have Any Difficulty Getting Into College

Glenn Bruda is truly brilliant young man whom I can relate to. I've known a few other math prodigies in his league, although his accomplishments are particularly impressive. 

If I were him, I'd be applying to schools like Cal Tech,  M.I.T., and Princeton, all of which would be thrilled to admit him, rather than the University of Florida. But that's his prerogative, I guess.
Glenn Bruda . . . a [17-year-old] senior at Buchholz High School in Gainesville. He . . .  concocted [what] turned out to be an entirely new calculus technique to solve integral equations. He cross checked it with mathematics professors at Santa Fe College and the University of Florida, who later encouraged him to submit his discovery for publication. On Jan. 30, 2022, it was published to Cornell University’s “arXiv”, an open-access archive for scholarly scientific articles. . . . Bruda titled his integration technique the “Maclaurin Integration” because it is derived from a formula named after Colin Maclaurin, a famous 18th century Scottish mathematician. He is now in the process of writing a second mathematical paper that will propose another original integration technique.

The Maclaurin Integration technique Bruda developed is designed to be “one of the most versatile integration techniques” because, with it, “there is essentially zero human labor involved in calculating integrals.”
Bruda keeps the notebook where he wrote his first original integral calculus technique as a source of motivation. There are visible water stains on the page from when he spilled his glass in excitement. (Photo courtesy of Jennifer Bruda)
Where most integration techniques can only be applied to around 10% to 40% of integral problems, Bruda’s technique applies to approximately 73% of integrals. That means it is almost two times more effective than most mainstream techniques.

Integration techniques are most common in Calculus II courses, which – despite not having graduated high school – Bruda claims as his favorite mathematics course to date. Bruda is a dual-enrolled student at Santa Fe College, where he is currently enrolled in courses like Differential Equations and Physics I with Calculus.. . . He’s now applying for the Davidson Fellows Scholarship, a prestigious scholarship for gifted high school students with rewards of $10,000, $25,000 and $50,000. The scholarship is awarded to students who create a “significant piece of work” at the graduate level. The Davidson Institute defines significant work as work “that experts in the field recognize as meaningful and has the potential to make a positive contribution to society.” . . . He is a Gainesville native who hopes to study mathematics at the University of Florida.

Bruda poses with his dog Leggo while wearing a graduation cap and gown. He graduates from Buchholz soon, and hopes to study mathematics at the University of Florida. (Photo courtesy of Jennifer Bruda)

15 September 2020

Is A Perfection Premium A Cognitive Bias?

A new paper suggests that a "perfection premium" is a real phenomena and is also a distorting cognitive bias. It isn't obvious that this is a correct assessment.

The paper and its abstract are as follows:
This research documents a perfection premium in evaluative judgments wherein individuals disproportionately reward perfection on an attribute compared to near-perfect values on the same attribute. For example, individuals consider a student who earns a perfect score of 36 on the American College Test to be more intelligent than a student who earns a near-perfect 35, and this difference in perceived intelligence is significantly greater than the difference between students whose scores are 35 versus 34. The authors also show that the perfection premium occurs because people spontaneously place perfect items into a separate mental category than other items. As a result of this categorization process, the perceived evaluative distance between perfect and near-perfect items is exaggerated. Four experiments provide evidence in favor of the perfection premium and support for the proposed underlying mechanism in both social cognition and decision-making contexts.

The trouble is that I'm not sure that a perfection premium is a cognitive bias. Most scoring systems, like ACT scores, have a domain of validity. They discriminate meaningfully in a normal distribution over a range of performance. Consider the ACT:


The top score included not just everyone who is one unit better in a normal distribution broken up into 36 units than the previous score (a 2.62 sigma above average result). It also includes everyone who would have a score more than 36 if the normal distribution were continued beyond the domain of applicability of the test.

If having a genius student in the student body who would score 42 on the ACT is its scoring range extended that far is more valuable to the institution than having a student who is merely very smart and would score 36 on the ACT even if its scoring extended higher. 

These are sometimes called "ceiling effects."

If a significant number of applicants with a perfect score receive a 36 only because the scoring range doesn't go any higher, it may be perfectly rational, and not a cognitive basis to have a "perfection premium". 

Also, the correct amount of the "perfection premium" depends upon the extent  to which the institution values having a small number of ultra-high performers (who may bring outsized recognition to the institution) relative to merely very high performers. There is no way to determine the correct premium for ultra-high performers in a vacuum.

A handful of people who would have scored much higher than 36 on the ACT if it were possible might very well bring outsized benefits to the institution in terms of awards, recognition, admissions to top grad schools that look good for the institution, much sought after organization leaders, faculty research assistants to mentor, or what have you. So a perfection premium may be appropriate.

I also question how real a "perfection premium" really is. Normally, admissions offices and hiring departments triage people into almost automatically deny, almost automatically admit/hire, and a middle ground of further deliberation. Everyone with a perfect or near perfect application goes into the almost automatically admit/hire and the threshold for decision making is almost never near the perfect threshold. If it was, the process would be reformed to be harder so it would be easier to distinguish between large numbers of seemingly perfect applicants.

24 January 2020

Mammograms Are Not Very Effective

The false positive rate for mammograms over a ten year period (61.3%) is very high relative to the number of cancer deaths prevented (0.1%) by having them as recommended for ten years.

Could the value of the cost and distress associated with this routine diagnostic procedure be redirected towards something that would save more lives? 


From here.

A new, less invasive and more effective breast cancer detection technology called thermography has been invented, but doesn't yet have widespread use.

Traditional PAP smears are also much less accurate and effective than more modern HPV tests.

21 November 2019

The Limits of Diversification


Diversification only reduces risk if the risks are accurately quantified and not correlated with each other.

13 December 2018

Using Statistics To Estimate Atrocity Size From Incomplete Lists Of Victims

If you have multiple incomplete lists of victims of an event, you can use the extent to which the lists overlap or not to accurately estimate the total number of victims, including those who were omitted from all of the lists.

15 October 2018

The Trouble With The Science Of Healthy Living

We got every possible vaccination for our children. I get a flu shot every year. I almost always favor allopathic medicine (the kind M.D.'s practice) over the various "holistic" alternatives (e.g. over osteopathic medicine, herbal remedies, faith healing, homeopathy, chiropractic, acupuncture, etc.).

Bad, Evidence Based Nutrition Advice

But, some of the biggest, supposedly evidence based health recommendations of my lifetime have turned out to be unsupported as past evidence was critically reviewed and new evidence was gathered.

* The recommendation of a low fat diet has been almost universally discarded in the weight loss field in favor of diets that are low carb and high in green vegetables, mostly because few people can keep to a low fat diet and loss weight on a sustained basis, while many people can lose weight on a diet that focuses on lower carbs and relatively more proteins. The recommendation was based on low protein, high carb (on a percentage basis) diets in places like Japan during periods of dietary scarcity and accompanied by more physical activity, that didn't translate well to Americans.
Several recent systemic reviews show that high-fat diets produce greater weight loss than low-fat diets, when both groups in the trials are given equivalent support. 
Most importantly, reducing fat intake did not lower rates of cardiovascular disease in two major clinical trials, Look Ahead and Women's Health Initiative, whereas increasing fat intake in the Predimed Mediterranean diet study did. Consistent with these findings, a study this year found that people consuming a high-fat diet had 16% lower rates of premature death than those consuming a low-fat diet (although the type of fats played a significant role in determining risk). 
Responding to new evidence, the 2015 USDA Dietary Guidelines lifted the limit on dietary fat, unofficially ending the low-fat diet era.
* The recommendation of a low salt diet has been largely discredited.

* The recommendation of moderate alcohol consumption with a very large effect size (a reduction in cardiovascular disease by something on the order of 50%), accompanied by anecdotal evidence from France (where wine consumption is high and cardiovascular disease rates seem low relative to a very rich diet) and from many people who lived very long lives with moderate alcohol consumption as a habit. 

But, it turns out that the data was skewed by the fact that in American society a lot of people who consumer no alcohol at all do so due to a prior history of alcohol abuse that they are responding to, or because they take drugs for other health problems that don't interact well with alcohol. This is the so called "sick quitter" problem. New research shows essentially that no alcohol consumption is optimal from a health perspective.

* Low does aspirin regimes also had a very large effect size (a reduction in cardiovascular disease and some cancers by something on the other of 50% in a manner potentially cumulative with moderate alcohol consumption), but while this does have a powerful effect in people who are actually diagnosed with a cardiovascular disease, it is harmful in older people who have not been diagnosed with cardiovascular disease.
For decades, a daily dose of aspirin has been widely considered a way to protect healthy people from cardiovascular disease and even cancer. But a large international study finds that even at low doses, long-term use of aspirin may be harmful — without providing any benefit — for older people who have not already had a heart attack or stroke. 
The new research reinforces the results of a study published in late August, which found that daily low-dose aspirin was too risky to be prescribed to patients at moderate risk of heart disease. In the August study and the new one, researchers found a significant risk of internal gastric bleeding caused by the medication, which thins the blood. Older patients experienced no health benefits from taking aspirin, according to the new report, published Sunday in the New England Journal of Medicine.
Individually, these results revisions make sense. But, the initial discredited results screwed up the lives of tens of millions of people at a time over half a century or so, and seriously tarnishes the credibility of evidence based health recommendations in the process.

Finally, there is no serious doubt that sugary drinks like sodas make obesity more likely. New studies have found that diet sodas are correlated with health risks almost as great as sugary sodas. But, those studies have almost identical flaws to the moderate alcohol consumption studies. Most people drink diet sodas because they are obese after a history of drinking sugary sodas. Obesity is bad for your health. And, lots of people who drink diet sodas nonetheless fail to lose substantial weight.

The Bigger Issue

The big picture issue is that a cultural mix of diet, exercise and patterns of daily life that persisted, sometimes for centuries, has been thrown out of whack by new conditions that most people have encountered in the modern developed world and the United States, in particular.

New agricultural methods, international trade, and affluence have made foods that were previously very scarce, like refined sugars and simple carbohydrates and red meats, easy and cheap for everyone to obtain, while technologies from widespread personal automobile ownership to computers and agricultural and factory automation, with changed urban planning patterns driven by these technologies, has also produced dramatically mode sedentary lives.

Try as we might, our patterns of diet, exercise, sleep and all other aspects of daily living have fallen into disequilibrium in this period of dramatic economic and technological change. But, try as we might to seek scientific guidance and to change our lifestyles (and food and tobacco consumption statistics for the U.S. show genuine significant mass responses to the latest public health recommendations of all kinds with a decade or two lag in most cases), we still haven't struck a comprehensive balance that can become a new tradition that is part of a new globalist, modern culture.

As a result, a lot people people are overweight and a lot more people are obese and morbidly obese with associated health problems like type two diabetes, cardiovascular risks, cancer and more.

In a couple of generations, we will probably as a society, strike a new balance of daily life traditions of eating and activity and other practices that make us all healthy, but we aren't there yet, although the latest rounds of reassessed evidence bring us closer than we were fifty years ago.

Of course, it may take longer, because the situation is still in flux.

New foods (like pea based meat substitutes and lab grown meats) are being created. New lifestyles (like intermittent fasting) are developing.

Considerations like the water demands of different kinds of foods, the environmental issues associated with petroleum based fertilizers and pesticides, and with toxic pesticides, the potential issues (thus far, with worries not realized) of genetically modified (GMO) foods, and the efficiency with which different foods convert energy and other resources into food, may put economic pressures on different mixes of foods that aren't yet present. World populations are growing, although they are leveling off as countries develop. Climate change and rising fossil fuel prices in the long run could also be relevant.

18 April 2018

Bayesian Statistical Reasoning and Race In The Criminal Justice System

Bayesian Reasoning Is Discouraged In Guilt-Innocence Trials.

The legal system, especially the criminal justice system, in the United States aspires mightily to avoid Bayesian statistical reasoning, in which your end analysis of probabilities is influenced by your "priors" - i.e. your expectation of what the probabilities will be going forward based upon past experience.

For example, one of the reasons that most criminal trials are jury trials is that the jury is not told (at least if the defendant refuses to testify, which he has a right to do without an adverse inference under the 5th Amendment) about a defendant's prior criminal record. 

Defendants routinely decline to testify because this opens the door to admission of evidence of their prior criminal records. 

But, empirical evidence suggests that even though juries are strongly admonished to ignore a defendant's failure to testify when rendering their verdict, that juries do, in fact, penalize defendant's for failing to testify to approximately the same degree that they penalize defendants with a prior criminal history for testifying when that is revealed to them. 

Our willingness to admit Bayesian prior establishing evidence of witness credibility undermines our efforts to suppress Bayesian prior establishing evidence that someone has a propensity to commit a crime.

The British resolve this conundrum by allowing criminal defendants to testify without being under oath and without revealing their criminal histories, and not creating strong incentives for defendants to suppress this testimony probably does more to enhance the accuracy of fact finding in criminal trials than to undermine it. The mere fact that someone has a huge self-interest in providing self-serving testimony when one is a criminal defendant is more than sufficient to cause juries to consider that evidence skeptically, especially when the offense charged is a serious one, even without knowing that a defendant may have a significant criminal history.

Also, while it may create an unfair snowball effect for a jury to know that a defendant has a criminal history, increasing the probability of a wrongful conviction in the instance case where one would not have been made if the jury had not known that fact, criminal defense attorneys, if they are clever, can present evidence that strongly implies a lack of a criminal history without openly saying so. They can call their criminal defendant client to the stand to testify. They can try to sprinkle in references in passing to activities that someone with a criminal history couldn't have engaged in (like notarizing a document or practicing in some other licensed profession), they can solicit testimony about things like a long, continuous employment history that would be inconsistent with having served time in prison, and they can ask questions like "do you know how a drug test works?" that answered in the negative, indicates a lack of a criminal record. So, suppressing the truth can work.

And, given that the majority of participants in the criminal justice system are recidivists, and that juries presume as much, perhaps defendants with no criminal history ought to be entitled to disavow that presumption by telling the jury that fact. If people are inherently Bayesian in how they evaluate probabilities, and that is was a trier of fact in a criminal trial is charged with doing, than an absence of evidence to the contrary of a widely held Bayesian prior of the jury is substantively prejudicial.

Also, while a judge in a rare criminal bench trial will usually know a defendant's criminal history even though the judge is supposed to ignore it when rendering a guilt or innocence verdict, it is unlikely that they actually do so, and certainly, prosecutors negotiating plea bargains which is the source of the lion's share of criminal convictions do not ignore a defendant's criminal history.

So, while the criminal justice system gives the appearance of not considering a defendant's prior criminal history in an effort to make the process seem more legitimate, in practice, the signaling of guilt caused by a failure to testify and other cues inevitably influences juries just as strongly, and undermines one of the foundational premises of the exclusion of Bayesian prior propensity evidence from juries.

The theory is that we want to avoid a "snowball effect" in which past arrests (whether or not resulting in convictions) and past convictions, increase the probability that someone will be wrongfully convicted going forward.

Similarly, we exclude "propensity" evidence at trial, unless that evidence is so particularized and compelling that the modus operandi it demonstrates has become an identifying trademark linking a crime to a defendant.

On the other hand, this disdain for Bayesian priors in the criminal justice system evaporates once we depart the trial that determines guilt or innocence on the merits. 

Also, practices in the guilt or innocence trial phase designed to suppress criminal investigation practices based upon inappropriate Bayesian priors, such as the Fourth Amendment exclusionary rule, which acquits people known to be guilty or makes their acquittal or favorable plea bargain more likely, undermines the legitimacy of the formal guilt-innocence phase of the trial in the eyes of law enforcement and victims, which can cause law enforcement and victims to feel morally justified in engaging in retaliatory cheating through false testimony in affidavits, hearings and trials, when the believe that a defendant is guilty but present the evidence which is the actual basis of their beliefs to a judge or jury.

Bayesian Reasoning In Criminal Investigations

Police routinely focus on the "usual suspects" with prior criminal records when investigating crimes, because the usual suspects are usually the people who are guilty.

Knowledge of an individual's prior criminal history can either mean that a suspect has no legally enforceable right to privacy because he is on probation or parole, or can be used by law enforcement and prosecuting attorneys as one part of demonstration of probable cause for a search, a seizure, a wiretap, an arrest, an indictment for a felony, or a use of force, or as part of demonstration of reasonable suspicion for a "Terry stop," tested in a preliminary hearing, a grand jury presentation, or in defending a civil rights lawsuit.

Police are legally prohibited from resorting to Bayesian priors based upon race in making decisions with a probable cause or reasonable suspicion threshold, unless, of course, a witness or the electronic or photographic equivalent or DNA evidence establishes or at least strongly suggests a suspect's race. But, of course, there is pervasive evidence that police do so anyway in almost all matters in which they are vested with discretion.

Police are also permitted to consider, and routinely do consider, arrest records of people who are not convicted based upon arrests in their investigative work. And, it is often through this portal that impermissible racial bias leading to Terry stops and arrests of minority individuals (especially young minority men) who are not guilty of the offense for which they are being arrested on suspicion of, without probable cause, are laundered into arrest records that police are allowed to legally consider, and custodial searches that reveal evidence of crimes such as drug possession or driving with a suspended license, that would never have been discovered but for the wrongful stop.

The Fourth Amendment exclusionary rule seeks to limit the extent to which effectively random searches and arrested based solely upon racial priors turn into convictions, but police frequently treat arrest records which are the result of police discretionary decision making, as more credible than convictions, which are influenced by plea bargaining between prosecutors and criminal defenses lawyers for all sorts of reasons (the lion's share of convictions are a result of guilty pleas rather than trials). So, the snowball effects that the system tried to avoid at trial absolutely emerge in the pre-trial investigation portion of the criminal justice process.

Because racism is fundamentally somewhat flawed Bayesian reasoning, rather than mere ignorance, both white and minority police officers often employ it.

But, this is problematic in multiple respects. 

One is that it lead to snowball effects that create pervasive, lasting, inappropriate bias that can turn people who weren't on the prison track into criminals, when they weren't criminal at first.

Another is that if police perceive that young black and Hispanic men are criminals, in general, even if they haven't been caught yet, they are less likely to be morally troubled when those young men are wrongfully arrested, searched or convicted of crimes which they didn't commit, because the police feel that those young men had it coming to them for crimes for which the young men were not caught. And, police have to be self-policing, and are less likely to take self-policing action when they believe that no moral harm has occurred, even if rules were technically violated.

Perhaps most importantly, acting on racial Bayesian priors, even if those priors have a real factual basis because people fitting a demographic profile are significantly more likely to commit crimes in a particular context than people who do not, the cost that those racial Bayesian priors impose on law abiding people who happen to be of the same race are crushing.

"Driving while black" in a predominantly white neighborhood prompts police calls and stops made without reasonable suspicion or probable cause with great frequency. 

Innocent unarmed individuals holding cell phones are shot in their backyards because police assumed that the cell phone was a gun. 

Law abiding minority individuals learn to distrust police, and lose the full benefits of protection from the criminal justice system, because police don't get the information that would give rise to legitimate probable cause from the community and because they refrain from calling the police for assistance when there is a great risk that they or loved ones will be the victims of police misconduct if they do.

Basically law abiding minorities don't get the benefit of the doubt and leniency from law enforcement that causes many stops of whites to result in a warning, and for dubious offenses that almost never result in criminal charges like driving with a defective headlight, jaywalking, driving just a few miles an hour above the speed limit, possession of small amounts of marijuana, open contain law violations, and the like, to be enforced to the full extent of the law against them.

This mistreatment of law abiding minorities, even if motivated by reality based Bayesian priors, undermines the legitimacy of law enforcement for whole communities, stigmatizes people who shouldn't have criminal records in ways that make it harder for them to function legitimately, and undermines the incentives the criminal justice system is supposed to create to encourage people to follow the law.

Bayesian Reasoning In Sentencing

Similarly, once a defendant has been convicted, Bayesian priors are routinely used to determine an appropriate sentence for a defendant, through formal sentence enhancers for recidivist defendants, through formal consideration as part of sentencing guidelines in the federal system and in some states such as Florida, and through informal evaluation of a pre-sentencing report by a judge who has discretion to choose from a range of permissible sentences for an offense. The Bayesian priors are not restricted to prior criminal records either. 

While judges (and juries imposing death sentences) are legally forbidden from using race as a prior in making sentencing decisions (although overwhelming statistical evidence demonstrates that this is done pervasively), they are permitted to consider a defendant's education, marital status, employment status, community ties, motive for the crime, age, substance abuse issues, mental health and more. Gender is routinely considered as well, whether or not this is legally proper. Judges are also permitted to consider gut level perceptions of the individual defendant from a sentencing hearing and that perception inevitably is influenced by race and cultural differences between (or similarities with) the judge and the defendant. Judges are more lenient when they can empathize with a convicted defendant and the more similar a convicted defendant is in culture and life experiences to a judge, the more a judge will empathize with the defendant.

Similarly, Bayesian reasoning is pretty much mandated in parole hearings in states that have indeterminate sentences, to determine that likelihood that a convicted criminal will reoffend upon release.

One important reform in sentencing is to use empirically validated risk assessment tools to overcome the individual and less accurate Bayesian priors of individual judges acting in a non-systemic manner based upon gut instincts. But, while these tools can be more accurate than judges acting based upon interpersonal interactions in a brief sentencing hearing, there is still room for hidden basis based upon which factors are and are not considered by the risk assessment tool, based upon how the information used as inputs by the tool is collected, and there is likely room for misuse or gamesmanship of the tool because it is a black box whose implicit reasoning is often not disclosed or not easily understood.

Analysis

Would we be better off to acknowledge that reasoning based upon Bayesian priors in the criminal justice system is inevitable, in order to better regulate it?

Perhaps providing juries, judges and police with more information that would make their Bayesian priors more accurate would be a more fruitful approach than our current one. 

But, because Bayesian priors based on race and other impermissible factors can simultaneously make decision making more accurate overall, and make life oppressively unfair to generally law abiding people who share those identifiers, criteria that evaluate the cost of false positives and false negatives equally are inherently flawed as well. Simply causing priorities other than mere raw accuracy to be more widely acknowledged, for example, in creating risk assessment tools and devising rules in the criminal justice system and in civil rights laws, might go a long way towards improving our policy decisions in those matters.

Rather the maintaining the pretense that we can ignore some facts to improve accuracy, which is true less often than we pretend it to be, we might be better off acknowledging that some facts that are ignored could improve accuracy and that we will continue to do so because preventing false positives is more important that preventing false negatives. A person with a propensity to commit crimes who is acquitted will usually offend again and be caught and punished the next time (and if he doesn't the reform arising from the acquittal is itself a benefit to society). But, a person who is generally law abiding who is wrongfully convicted may suffer so much harm that they are dragged down into life of crime as a consequence of the wrongful conviction.