Tag Archives: randomness

Addressing sorting and inequalities with lotteries and luck

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Sociologist Dalton Conley suggests using lotteries to counter the inequalities in the United States due to Americans sorting people into different locations:

Photo by Dids on Pexels.com

As our society has become less random, it has become more unequal. Many people know that inequality has been rising steadily over time, but a less-remarked-on development is that there’s been a parallel geographic shift, with high- and low-income people moving into separate, ever more distinct communities. In 2019, the median household income in Washington, D.C., was $92,266. The corresponding figure for Mississippi was $45,792. Even locally, spatial differences are stark. New York City’s Fifteenth Congressional District, which covers the South Bronx, is the poorest in the nation, with a median income of thirty-one thousand dollars. The nation’s richest district, New York’s Twelfth, is just a mile or so to the south; it includes the Upper East Side and has a median income just shy of a hundred and twenty-five thousand dollars. Sorting occurs even in areas where people of multiple social classes overlap: people of different incomes often frequent different establishments on the same city block…

ut there’s another route to consider. What if, instead of paying taxes where we reside, and then reaping their benefits locally, we sprinkled taxation and revenues randomly—and therefore evenly—across the United States? What if, instead of paying a third of my taxes to New York City and State, I instead paid them to Pod No. 2,264—a group to which I was randomly assigned by a lottery the year I turned eighteen? What if, instead of camping out on the sidewalk the night before the school-enrollment date in hopes of getting my kids into a well-funded public school, I received a monthly check from Pod 2,264 that was meant to pay for my children’s schooling wherever I wanted to send them? In such a system, the retreat of affluent people from the places where they live doesn’t matter. In fact, it doesn’t matter where anybody lives. Nobody can escape contributing to the public sphere, no matter how far they move…

Some of us would lose in a more lottery-based society. But many of us would win. And we might end up being more compassionate toward one another; we’d be forced to acknowledge that much of our lot is the luck of the draw. We argue endlessly about the meaning of luck, even if we don’t always realize it. How much are we responsible for what happens in our lives? What’s the difference between luck and choice? How much should society try to help the unfortunate? Much psychological research shows that Americans who believe that luck plays a large role in our lives tend to be more liberal, supporting redistributive policies. Yet almost all of us seem to wish for a society in which luck plays no role, and in which everyone gets what they deserve, whether through their own actions or through mutual aid…

Despite this common goal, we tend to reach for lotteries only as a last resort, as President Nixon did when waging an unpopular war. We tell ourselves that we are successfully squeezing randomness out of life, by means of ever more refined algorithms and targeted social policies. But one lesson of our pod-based thought experiment is that we already live under the reign of lotteries—lotteries of birth, of location, of economic and social fate. We’ll never truly randomize America, but even entertaining the possibility can help us see that it can be useful to acknowledge randomness, and even to incorporate rolls of the dice into our collective life. What if, instead of trying to erase luck, we embraced it?

Since we do not control into which families, locations, and conditions we are born, there is some dimension of randomness from early ages. Some people have certain conditions, others have different conditions.

This also reminds me of the documentary Waiting for Superman. There, a lottery provides spots in a charter school for students and families who want opportunities. If I remember correctly, the message there is less about using a lottery to allocate scarce resources and more about suggesting that all children should be able to go to good schools.

How much would it take to get Americans to support such systems? Persistent in American ideology is the idea that people contribute greatly to their own outcomes. If people do not like the idea of random selections, would considering the possibilities of lotteries help people think about other ways of allocating resources or distributing opportunities?

Are NFL fans now better off with all the draft knowledge they can access?

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The NFL draft process has been drawn out even further this year and it leads to an interesting question: is a better-informed fan a more-in-control fan?

For many Americans, football fandom is a knowledge contest, an anxious dedication to information gathering that drives us to consume the NFL’s human-resources wing as entertainment. Last year, more than 7.9 million of us watched the draft and another 7.3 million viewed some portion of the scouting combine. This year, the draft moved from April to May, a transition attributed to a scheduling glitch: Radio City Music Hall, the draft’s venue in recent years, booked a Rockettes Easter special during the NFL’s big weekend. But it’s a favor, really: We need more time for recreational panic, more time for our 11-year-olds to prognosticate with radio hosts…

When Mayock started his work, most information about prospects was relegated to team officials and media members. But now, anyone could develop informed opinions about someone like Landry. Anyone who wants to can study six of his games and learn about his perceived value on mock draft sites. Walter Cherepinsky, the founder of one such site, tells me it gets 40 million visits per month. (One of his recent mocks has Landry going to the Carolina Panthers with the 92nd selection.) For the most committed students, there are draft guides such as Matt Waldman’s Rookie Scouting Portfolio, more than 1,200 pages about offensive prospects. Waldman writes that Landry blocks and runs routes like a reserve player, but he catches passes like an NFL star.

While the adage tells us knowledge is power, though, it’s less clear how all of this information empowers draft-obsessed fans. That 11-year-old from the sports talk show wanted his team to select a receiver, but wanting that or having an argument in favor of it won’t make it so. What erudition of this sort provides is a sense of autonomy, in terms of identity, a guard against power abused. NFL insiders tend to whisper the same general stat: that one-third of the league’s general managers have no business overseeing personnel decisions—they’re either misguided in the way they evaluate players or they don’t bother to put in the requisite research. Draft savvy, then, lets fans separate their outcomes (the success of their favored college prospects) from those of their favorite teams (the players chosen by their teams and the team’s outcome on the field); fans can timestamp their opinions and later say, “I told you so.”

But does this kind of autonomy relieve fans’ helplessness, or does it make them feel more like pawns beholden to the real draft-day outcomes they want to control but can’t? Let’s say you’re sure, after months of research, your team should use its third-round pick on a quarterback, but the team instead drafts a punter—a punter—and the quarterback selected five slots later goes on to win a Super Bowl within two seasons. Besides a conniption, this could also give you a grudge to unleash on team executives, message board commenters, and media members who disagree with your football opinions.

The evidence seems clear: the draft is popular and the NFL can afford to drag it out when people keep watching. But, do people really enjoy it? More broadly in sports, if fans know even more about potential players (college, minor leagues, developmental leagues, overseas prospects, etc.), does this lead to feeling more in control?

Having more information is generally seen as a good thing in today’s world. The more input you can gather, the better. Yet, this doesn’t necessarily lead to better outcomes or more perceived control. (Read The Paradox of Choice for a good introduction.) I would argue that much of the appeal of sports is the unpredictably, the odd things that can happen on a playing surface at any point. All the information in the world can’t easily explain some of these events – and would we want it to or would we rather see unpredictable things happen in games?

The draft is a good example of this unpredictability and how we might perceive information as a way to limit this. Think about all of the mock drafts. All of the talking heads. Stretching out the draft even longer. Yet, there are still things that happen on draft day that are hard to predict, even for all the experts. (I’m particularly intrigued by recent mock drafts that incorporate more complicated draft-day trades.) Assessing the results of drafts can take years or even decades. Sports Illustrated had a recent story about the Tampa Bay Buccaneers making a disastrous pick in the 1980s that led to 10+ years of ineptitude – but this wasn’t visible for years.

All together, football players make choices, teams make choices, fans respond to all of this with more or less information, and it all collides in a “sports experience.” I suspect sports fans don’t really want to know everything (stronger predictive abilities would reduce the uncertainty about outcomes) even if they often want to immerse themselves in the sports experience. At some point, the return on having more and more sports knowledge likely decreases enjoyment though this curve could easily differ by person.

Selecting a 4 digit pin code is hardly random

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There are 10,000 possible pin codes that could be made with four digits (0-9) but what pins we select to use are hardly random:

What he found, he says, was a “staggering lack of imagination” when it comes to selecting passwords. Nearly 11% of the 3.4 million four-digit passwords he analyzed are 1234. The second most popular PIN in is 1111 (6% of passwords), followed by 0000 (2%). (Last year SplashData compiled a list of the most common numerical and word-based passwords and found that the “password” and “123456” topped the list.)

Berry says that a whopping 26.83% of all passwords could be guessed by attempting just 20 combinations of four-digit numbers (see first table). “It’s amazing how predictable people are,” he says…

Many of the commonly used passwords are, of course, dates: birthdays, anniversaries, the year you were born, etc. Indeed, using a year, starting with 19__ helps people remember their code, but it also increases its predictability, Berry says. His analysis shows that every single 19__ combination be found in the top 20% of the dataset…

Somewhat intriguing was #22 on the most common password list: 2580. It seems random, but if you look at a telephone keypad (or ATM keypad) you’ll see those numbers are straight down the middle — yet another sign we’re uncreative and lazy password makers…

The least-used PIN is 8068, Berry found, with just 25 occurrences in the 3.4 million set, which equates to 0.000744%. (See the second table for the least popular passwords.) Why this set of numbers? Berry guesses, “It’s not repeating pattern, it’s not a birthday, it’s not the year Columbus discovered America, it’s not 1776.” At a certain point, these numbers at the bottom of the list are all kind of “the lowest of the low, they’re all noise,” he says.

This is a great example of two things:

1. There are often patterns among supposedly “random” numbers.

2. Humans don’t particularly like to use “random” numbers but instead prefer numbers that are meaningful to them (which corresponds with them being able to remember their codes).

Would having a math PhD really help you win the lottery?

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A journalist suggests that one woman who won four multi-million dollar lottery payouts was able to do so because she had a mathematics PhD:

First, [Joan Ginther] won $5.4 million, then a decade later, she won $2 million, then two years later $3 million and finally, in the spring of 2008, she hit a $10 million jackpot.

The odds of this has been calculated at one in eighteen septillion and luck like this could only come once every quadrillion years.

Harper’s reporter Nathanial Rich recently wrote an article about Ms Ginther, which questioned the validity of this ‘luck’ with which she attributes her multiple lottery wins to.

First, he points out, Ms Ginther is a former math professor with a PhD from Stanford University specialising in statistics.

A professor at the Institute for the Study of Gambling & Commercial Gaming at the University of Nevada, Reno, told Mr Rich: ‘When something this unlikely happens in a casino, you arrest ‘em first and ask questions later.’…

Three of her wins, all in two-year intervals, were by scratch-off tickets bought at the same mini mart in the town of Bishop.

Mr Rich proceeds to detail the myriad ways in which Ms Ginther could have gamed the system – including the fact that she may have figured out the algorithm that determines where a winner is placed in each run of scratch-off tickets.

He believes that after Ms Ginther figured out the algorithm, it wouldn’t be too difficult to then determine where the tickets would be shipped, as the shipping schedule is apparently fixed, and there were a few sources she could have found it out from.

At first glance, the story does seem unlikely: four wins and three from scratch-off tickets from the same retail location. But here are three reasons to doubt the claim that this woman beat the system:

1. If lottery algorithms could be figured out by the public, wouldn’t other people have figured this out as well? A math PhD sounds problematic but other smart people could figure this out if it could be figured out. Additionally, couldn’t this woman win more than 4 times if she had it all figured out?

2. Just because someone won the lottery four times does not mean that something underhanded happened. Just because some events are “random,” like winning the lottery or being struck by lightning, does not mean that people can’t win multiple times. Aren’t there plenty of other multiple lottery winners?

3. The quote from the professor is interesting: be suspicious first and then figure out what is happening. This is the view from the business end. If someone is gambling and consistently winning your money, you might respond. For example, this book about card-counting MIT students is fascinating (much better than the movie based on the book) not only for how the students figured out how to count cards but also because of the response of the casinos. (My favorite part – and I think I am remembering this correctly: the students leave Las Vegas because they are raising suspicions with their winnings. But they eventually find that their names and photos have been sent to casinos around the country. It gets to the point where they are escorted out of a casino just moments after entering.) But it sounds like the Texas Lottery Commission doesn’t think anything is wrong. Shouldn’t they be the ones who care the most?

If you read the original story, Ginther’s buying habits do sound strange. But I still think this reporter needs to find some more evidence before Ginther could be accused with certainty.

Discovering fake randomness

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In the midst of a story involving fake data generated for DailyKos by the polling firm, Research 2000, TechDirt summarizes how exactly it was discovered that Research 2000 was faking the data. Several statisticians approached Kos after seeing some irregularities in cross-tab (table) data. The summary and the original analysis on DailyKos are fascinating: even truly random data follows certain parameters. One takeaway: faking random data is a lot harder than it looks. Another takeaway (for me at least): statistics can be both useful and enjoyable.

The three issues as summarized on DailyKos:

Issue one: astronomically low odds that both male and female figures would both be even or odd numbers.

In one respect, however, the numbers for M and F do not differ: if one is even, so is the other, and likewise for odd. Given that the M and F results usually differ, knowing that say 43% of M were favorable (Fav) to Obama gives essentially no clue as to whether say 59% or say 60% of F would be. Thus knowing whether M Fav is even or odd tells us essentially nothing about whether F Fav would be even or odd.

Issue two: the margin between favorability and unfavorability ratings did not display enough variance. If the polls were truly working with random samples, there would be broader range of values.

What little variation there was in the difference of those cross-tab margins seemed to happen slowly over many weeks, not like the week-to-week random jitter expected for real statistics.

Issue three: the changes in favorability ratings from week to week were too random. In most polls like this that track week to week, the most common result is no change. Research 2000 results had too many changes from week to week – often small changes, a percent either way.

For each individual issue, the odds are quite low that each would arise with truly random data. Put all three together happening with the same data and the odds are even lower.

Besides issues regarding integrity of data collection (and it becomes clearer why many people harbor a distrust toward polls and statistics), this is a great example of statistical detective work. Too often, many of us see numbers and quickly trust them (or distrust them). In reality, it takes just a little work to dig deeper into figures to discover what exactly is being measured and how it is being measured. The “what” and “how” matter tremendously as they can radically alter the interpretation of the data. Citizens and journalists need some of these abilities to decipher all the numbers we encounter on a daily basis.