I calculate high-index roots in my head while waiting for a poke bowl.
This was supposed to be the post analyzing the survey results.Then I thought: if I’m writing that, I may as well show examples of some basic Bayesian analysis, like using likelihood ratios. And if I’m doing analysis, I may as well give some more background on data science and also show how the results depend on assumptions. And if the results depend on assumptions, I may as well fit a full consequential model with continuous interdependent parameters and the appropriate prior.
Bottom line: I spent the week reading a textbook on data analysis and didn’t write anything. Instead, this short post is a sequel to Conned, part of an emerging series tentatively called “what it’s like being a crazy person who nitpicks random numbers he sees”.
So, a crazy person walks into a new poke restaurant. First, he notices that this restaurant, like the last 7 poke restaurants he went to, isn’t called Pokestop. This is puzzling, because the perfect name for a poke restaurant exists, and it’s Pokestop.
The crazy person flips the menu, and gets so caught up in the math that he somehow orders a grotesque monstrosity made of surimi (I learned that it’s just a fancy word for imitation crab sticks), mango, seaweed, and Hawaiian salt (I learned that it’s just a fancy word for salt).
As the astonished cook reaches for the salted mango, the crazy person starts doing mental math.
200,000 combinations and we have 6 categories, so the average number of items in each category must be the 6th root of 200,000, or the cube root of the square root of 200,000. The square root of every even power of 10 is easy, i.e. √10,000 = 100. We’ll break 200,000 into 10,000*20. 20 is between 16 and 25 so the square root of 20 is ~4.5. This means that √200,000 ≈ 100*4.5 = 450. OK, I need the cube root of 450. Do I remember any cubes? 103=1,000, that’s too much. 83=29=512, bingo! The sixth root of 200,000 is the cube root of 450 is just below 8, so there should be 7-8 combinations on (geometric) average in each category. (The actual answer turns out to be 7.65).
That’s how I do math quickly in my head. I remember a few basic facts (like powers of 2 up to 1,024) and a few basic rules (like ( a m) n = a mn). I can get an approximate answer in my head to almost any calculation including roots, logarithms and exponents faster than I can pull out my phone. I taught a workshop training my MBA classmates to do this before consulting interviews. One Chinese girl was so impressed by this workshop that she dated me for a month even though she’s a straight 10 and I’m a 6.5 if I get a good haircut.
Anyway, back to poke: 200,000 options is obviously way too low. The average number is close to 7 or 8, but several of the categories allow you to pick more than one item. For example, you can create 16 combinations of toppings by choosing to include or exclude any of the four toppings available. As for add-ins, being able to pick 6 out of 13 involves the combination function, and the combination function has factorials in it so you know it means business. By the time my bowl was done, I estimated that Koshe Poke are underselling themselves by at least two orders of magnitude. It turns out they’re off by a factor of 3,500:
710 million! You can try a different combination of poke each day without repeating yourself for almost 2 million years. Sometime around 1,509,464 AD, you’ll stumble upon a combination as horrible as surimi-mango-salt-seaweed and you’ll finally understand what it’s like to be me, a crazy person living in a world of crazy numbers.
Fighting the crusade against fake numbers, one utility van at a time.
Once in a while I’m asked “what makes you special?” It’s hard to give an honest answer other than “I’m not a snowflake, there’s nothing really unique about me”. Even my most esoteric pursuits form great tribes around them. The raison d’être of Putanumonit is that whatever peculiar idea I can write about, it will resonate with at least a thousand people somewhere in the world.
With that said, I probably have a pretty singular reaction to utility company vans.
Most people would pass by this truck and not think twice about it. Most wouldn’t even think once. I pass by this truck and think: 20% of household is like 20 mil, so 10 households per tree per year sounds completely made up and I’ll bet 5:1 that this number is off by at least a factor of 2 and ConEdison are lying because everyone is innumerate.
Then I get home and do some Googling:
There are 125 million households in the United States. Generously assuming that they all get electrical bills, 20% of them are 25 million households.
My own bill from ConEdison is 2 pages. If ConEdison cared about trees they’d use double sided printing, but let’s be generous again and assume 4 total pages of paper statement per household per month, including the envelope and the check.
A letter sized page is 8.5″ x 11″, or 216 mm x 279 mm, which comes out to 0.06 m2. Four pages have an area of 0.24 m2.
We needed the area calculation because paper weight is measured in GSM, or grams per square meter. Common printer paper weighs 74 GSM, so 0.24 square meters of that paper weigh 74 x 0.24 = 17.7 grams.
17.7 grams of paper per month * 12 monthly bills = 213 grams of paper per year per household that refuses to pay their bills online.
With 25 million households, that’s 5.3 million kg of paper per year.
Not “almost two million”, not even within an order of magnitude of two million. A mere 127,000 trees. For scale, that’s 0.25% of the 50 million trees a single country can plant in a day.
By the way, did I mention that I worked for a major paper manufacturer? American paper companies practically never log new forests. They mostly own the tree farms, which are basically small private forests, that supply the timber they need. Also, a fiber of paper can get recycled around 7 times before it becomes unusable, but often get recycled less because paper is so cheap that some recycling isn’t worth it on the margin.
If 100% of American households switched to unrecycled paper bills tomorrow, the paper industry would react by increasing the recycled paper content in products like paper towels and toilet tissue and recycling paper more times. They’ll also plant more trees in the tree farms, and supply will catch up to demand over a few years. If 100% of households switched away from paper, the tree farms (which in the process of growing into paper do nice things like capture CO2 ) would be replaced by something else, like parking lots.
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Good news: 2016 is coming to a close.
Bad news: “2016” is an arbitrary construct without causal agency. The decline of civilization is not the calendar’s fault, and it’s unlikely to get any better in 2017. Only one thing is guaranteed to get better in 2017 – this blog. Because you will make it better.
At the bottom of the post is a short, multiple choice, anonymous survey, designed to give me feedback on improving Putanumonit. I have very little information on what my readers like and dislike. When 1,000 people read my post and 5 of them leave comments, I have no clue what the other 995 thought of it. Please answer as many questions as you can whether you’re a dedicated reader or just discovered Putanumonit for the first time.
If you are an enthusiastic reader and want to be involved in Putanumonit beyond just seeing the finalized posts, you can check out In Cahoots with Putanumonit but please come back afterwards and fill out the survey. The more honest your responses are, the more you’ll like this blog in 2017.
2017 Reader Survey
Each question is a separate poll, so don’t forget to hit Vote after answering each one.
How much of Putanumonit have you read? I write about 4 posts a month, and 53 total so far.
Many of my posts (but not all of them) fall into 3 broad categories:
What makes people who hold an extreme opinion think that they represent the majority?
[After 3,000 words on statistics, I deserve a condescending politics / culture war post. I have put these posts under the “hedgehog alert” category because if that’s not your cup of bitter acid rain, you should enjoy this hedgehog instead.]
My point was that it’s important to recognize when you’re holding an unpopular opinion and to change your tactics accordingly. Even if normatively you are right and everyone is wrong, instrumentally you should pursue your goals one way if 5% share your goals and worldview and another way if 80% do. For example, shaming others and calling them names (e.g. bigot or traitor) works (sometimes) if you’re part of the majority and doesn’t work if you’re part of the fringe.
Even if your entire social circle shares your views, you have to be cognizant of the amount of support your position has in the broad public. It’s not quite what outside view is, but it requires a similar mental process of stepping outside your immediate surroundings. Here are a couple of examples from my own life:
I’m an atheist, and many of my friends are atheist, but I realize that on a national scale atheists are a tiny minority (~4%). If I want to promote atheism, I should be able to tell the difference between ardent religious zealots and the median American who believes in God and goes to church every other week but isn’t a talking snake-ist. When I talk with the latter about atheism, I politely explain for example how an atheist can share the intuition that murder is wrong with a holy book. I don’t tell anyone who believes in a deity that they’re a deluded fanatic.
I’m a left-libertarian, and I engage intellectually with many left libertarians. For example, I think that regardless of how much welfare we have raising the minimum wage will hurt the poor because it dminishesthe employability of the 102 million adult Americans who don’t have a job and increases the prices they pay. I also think that regardless of where the minimum wage is, we should have more unconditional welfare to help the poor (whether food stamps or basic income). And yet, I’m aware that “abolish the minimum wage but raise taxes to implement basic income” is an extreme position. When I talk to liberals about the minimum wage or to conservatives about welfare I try to gently convince them with stats and numbers, I don’t call them heartless monsters who hate the poor.
On the other hand, homophobia has finally become a minority position and it’s not counterproductive to shame homophobes.
This seems like common sense to me – you fight differently when you’re outnumbered than when you’re dominating. I thought it would be obvious for example to Jamelle Bouie that calling the NY Times racist for encouraging dialogue with Trump voters is a minority opinion.
Consider Hillary Clinton’s words from the second presidential debate: “It is important for us as a policy not to say, as Donald has said, we’re going to ban people based on a religion.” […] Here Clinton establishes a minimum standard of liberal decency that few American Jews would be inclined to deny. […] Yet insofar as Israel is concerned, every liberal Zionist has not just tolerated the denial of this minimum liberal standard, but avowed this denial as core to their innermost convictions. Whereas liberalism depends on the idea that states must remain neutral on matters of religion and race, Zionism consists in the idea that the State of Israel is not Israeli, but Jewish.
Palestinians in fact do not demand a “right of return” to their pre-1967 homes, but to their pre-1948 homes. In other words, the issue isn’t the occupation, which many liberal Zionists agree is a crime, but Zionism itself. Opposition to the Palestinians’ “right of return” is a matter of consensus among left and right Zionists because also liberal Zionists insist that Israel has the right to ensure that Jews constitute the ethnic majority in their country.
The following years promise to present American Jewry with a decision that they have much preferred to avoid. Hold fast to their liberal tradition, as the only way to secure human, citizen and Jewish rights; or embrace the principles driving Zionism.
The article explicitly states that opposing the right of Palestinians to move to Israel proper (right of return) is beneath a minimum standard of liberal decency, and thus Zionism is incompatible with liberalism. I commented that regardless of your normative opinion on Zionism, the right of return, as a matter of fact, has very little support among Jews. The article itself agrees that this is a consensus. Israel has 4 million more Jewish citizens than Muslim citizens, allowing 5 million Palestinian refugees to immigrate will immediately end Jewish majority in Israel and the character of the country as we know it. Even if one thinks that it’s the moral thing to do, it’s a very unpopular opinion among Jews, on par with the percentage of Americans who would be in favor of allowing 300 million Muslim immigrants into the US.
I wrote that if you present Jews with the dilemma of accepting the right of return or not being a “liberal”, this sort of “liberalism” will not attract many Jews. This is the immediate response I got:
So far, nothing out of the ordinary. The argument I make requires separating normative claims and factual claims which is an unusual and difficult exercise. It’s predictable that at least one person will try to insult me out of the conversation instead of trying to address the argument itself.
Then came the first warning sign:
This absurd accusation that rationalists are sympathetic to Trump is from the friend who originally defended me. The meme that the sun is a hummingbird is based on zero evidence. The meme that rationalists like Trump is based on negative evidence.
Julia Galef, Rob Wiblin and other prominent Effective Altruists debated back in the spring whether donating to Clinton’s campaign may be better than saving kids from malaria. Yes, many rationalists admire Peter Thiel. They were all pretty confused when Thiel endorsed Trump.
Truth seeking, charity and concern for the future of humanity are anathema to Donald Trump. He’s the rationalist Antichrist. So how could anyone believe that rationalists are sympathetic to Trump?
I’m not sure what to do when people straight up tell me I’m lying. I assumed they’re just confused by the math, so I explained the math: let’s imagine again that we put all Americans on a single axis from least liberal (1st percentile) to most liberal as defined by current political affiliation (100th percentile). The 50th percentile American barely chose Trump over Clinton, and I imagine that I’m about as far to the left of the marginal Trump voter as I am to the right of a 90th percentile leftist. Thus, 70th percentile liberal.
But people were not in the mood to do math.
Hey, math is hard, I get it.
Why did these liberals react so venomously to the suggestion that I’m more liberal than the average American? Why do they think that rationalists, a group of strange but certainly left-of-center people, are enemies of liberalism?
My first hypothesis was that they’re trying to make their ideas unpopular on purpose, by insulting and bullying outsiders who try to engage with them. Collectively this makes “liberalism” lose, but individually they gain status by signalling the extremity of their faith in the true cause. I wondered if Mr. Bouie doesn’t mind that his tactics are counterproductive to fighting racism, I would wager that Slate‘s ratings are higher with Trump in office than they would have been had Clinton won.
I realized that this is too cynical. Organizations never solve the problem they were created to solve (as that would put the organization out of work), but it’s hard for people to be so explicitly hypocritical. It’s easier to convince others that you’re a fighter for liberalism / against racism if you actually believe this as well. I had to admit that these people really believed that they are helping the spread of liberalism as they see it.
My second hypothesis is this:
Theory of inflated bubbles – When your ideological bubble becomes small and tight enough, you start thinking that almost everyone outside the bubble agrees with you. In your mind, your bubble has inflated to encompass the entire world.
I work hard to make holes in the bubbles I live in. I have neoreactionary friends, Marxist friends, anti-Semitic friends and apparently a friend who thinks that rationalists are villainous freaks. I engage all the time with people who strongly disagree with me, I know that they’re out there in great numbers.
But once you slide down the horseshoe into extremism and attack anyone who disagrees with you, the heretics to your worldview evaporate out of your bubble. If you live in a very liberal city (these three guys are from D.C., New York and Silicon Valley), consume very liberal media, and tell everyone who isn’t very liberal to choke on a dick, your entire world becomes exclusively made up of very liberal people. All perspective is lost. Availability bias and confirmation bias will then work tirelessly to convince you that those who disagree with you are an extremist fringe minority.
If you think that the NY Times or Bay Area rationalists are terribly bigoted, you will start thinking that the NY Times and the rationalists are part of the conservative minority even thought they’re both more liberal than the vast majority of the United States. No one can handle the cognitive dissonance of imagining that they live in a world that is 90% monster.
This is a self-reinforcing phenomenon: you think that those who disagree with you are a small minority and thus their views are extreme, and if their views are extreme they must be a small minority.
This explains why so many leftists blame this election on the alt-right (who are a tiny minority on the right that most Trump voters don’t care about) and rightists blamed Obama on groups like liberal university professors (who are a tiny minority on the left that most Obama voters don’t care about). They believe that anyone who voted against them is part of a small cult that somehow got lucky. How can merely losing an election convince anyone that they’re a minority when three of the fiercest biases a brain can employ work to convince them otherwise?
This is a half-baked hypothesis. I don’t know how likely it is to be true (that many extremists think the majority agrees with them) and how to precisely define the phenomenon. It’s not charitable and it’s not scientific and it’s very condescending. But, it really makes a lot of what I’ve been seeing since the election make a lot more sense.
The only question that remains is: what crazy ideas do I hold that I deludedly think most people agree with? I hope it’s not my faith that every human has the capacity for reason and kindness.
Protect yourself from p-hacking with precision, whether you’re doing drugs or gambling.
Of all the terrible vices known to man, I guess NFL gambling and alternative medicine aren’t very terrible. Making medicine that doesn’t work (if it worked, it wouldn’t be alternative) is also a tough way to make money. But if you’re able to squeeze a p-value of 0.05 for acupuncture out of a trial that clearly shows that acupuncture has zero effect, you can make money and get a PhD in medicine!
It’s also hard to make money off of gambling on the NFL. However, you can make money by selling NFL gambling advice. For example, before the Eagles played as 6 point underdogs on the turf in Seattle after a 208 yard rushing game, gambling guru Vince Akins declared:
The Eagles are 10-0 against the spread since Dec 18, 2005 as an underdog and on turf after they’ve had more than 150 yards rushing last game.
10-0! Betting against the spread is a 50-50 proposition, so 10-0 has a p-value of 1/(2^10) = 1/1024 = 0.0009. That’s enough statistical significance not just to bet your house on the Eagles, but also to get a PhD in social psychology.
No more! In this new installment of defense against the dark arts we will learn to quickly analyze multiplicity, notice conjunctions, and bet against the Eagles.
Hacking in Depth
[This part gets stats-heavy enough to earn this post the Math Class tag. If you want to skip the textbooky bits and get down to gambling tips, scroll down to “Reading the Fish”]
The easiest way to generate multiple hypotheses out of a single data set (that didn’t show what you wanted it to show) is to break the data into subgroups. You can break the population into many groups at once (Green Jelly Bean method), or in consecutive stages (Elderly Hispanic Woman method).
The latter method works like this: let’s say that you have a group of people (for example, Tajiks) who suffer from a medical condition (for example, descolada). Normally, exactly one half of sick people recover. You invented a miracle drug that takes that number all the way up to… 50%. That’s not good enough even for the British Journal of General Practice.
But then you notice that of the men who took the drug 49% recovered, and of the women, 51% did. And if you only look at women above age 60, by pure chance, that number is 55%. And maybe 13 of these older Tajik women, because Tajikistan didn’t build a wall, happened to be Hispanic. And of those, by accident of random distribution, 10 happened to recover. Hey, 10 out of 13 is a 77% success rate, and more importantly it gives a p-value of… 0.046! Eureka, your medical career is saved with the publication of “Miracle Drug Cures Descolada in Elderly Hispanic Women” and you get a book deal.
Hopefully my readers’ nose is sharp enough not to fall for 10/13 elderly Hispanic women. Your first guide should be the following simple rule:
But what if the drug did nothing detectable for most of the population, but cured 61 of 90 Hispanic women of all ages. That’s more than two thirds, the sample size of 90 isn’t tiny, and it comes out to a p-value of 0.0005, is that good enough?
Let’s do the math.
First, some theory. P-values are generally a terrible tool. Testing with a p-value threshold of 0.05 should mean that you accept a false result by accident only 5% of the time, yet even in theory using a 5% p-value makes a fool of you over 30% of the time. P-values do one cool thing, however: they transform any distribution into a uniform distribution. For example, most samples from a normal distribution will lie close to the mean, but their p-values will be spread evenly (uniformly) across the range between 0 and 1.
Uniform distributions are easy to deal with. For example, if we take N samples from a uniform distribution and arrange them by order, they will fall on average on 1/N+1, 2/N+1, .. N/N+1. If you test four hypotheses (e.g. that four kinds of jelly beans cause acne) and their p-values fall roughly on 1/(4+1) = 0.2, 0.4, 0.6, 0.8 you know that they’re all indistinguishable from the null hypothesis as a group.
Usually you would only see the p-value of the best hypothesis reported, i.e. “Wonder drug cures descolada in elderly Hispanic women with p=0.0005”. The first step towards sanity is to apply the Bonferroni rule:
Bonferroni Rule – A p-value of α for a single hypothesis is worth about as much as a p-value of α/N for the best of N hypotheses.
The Bonferroni correction is usually given as an upper bound, namely that if you use an α/N p-value threshold for N hypotheses you will accept a null hypothesis as true no more often than if you use an α threshold for a single hypothesis. It actually works well as an approximation too, allowing us to replace no more often with about as often. I haven’t seen this math spelled out in the first 5 google hits, so I’ll have to do it myself.
h1,…,hN are N p-values for N independent tests of null hypotheses. h1,…,hN are all uniformly distributed between 0 and 1.
The chance that one of the N p-values falls below α/N = P(min(h1,…,hN) < α/N) = 1 – (1 – α/N)N ≈ 1 – e-α ≈ 1 – (1-α) = α = the chance that single p-value falls below α. The last bit of math there depends on a linear approximation of ex =1+x when x is close to 0.
The Bonferroni Rule applies directly when the tests are independent, but that is not the case with the Elderly Hispanic Woman method. The “cure” rate of white men is correlated positively with the rate for all white people (a broader category) and with young white men (a narrower subgroup). Is the rule still good for EHW hacking? I programmed my own simulated unscrupulous researcher to find out, here’s the code on GitHub.
My simulation included Tajiks of three age groups (young, adult, old), two genders (the Tajiks are lagging behind on respecting genderqueers) and four races (but they’re great with racial diversity). Each of the 2*3*4=24 subgroups has 500 Tajiks in it, for a total population of 12,000. Descolada has a 50% mortality rate, so 6,000 / 12,000 cured is the average “null” result we would expect if the drug didn’t work at all. For the entire population, we would get p=0.05 if only 90 extra people were cured (6,090/12,000) for a success rate of 50.75%. A meager success rate of 51.5% takes the p-value all the way down to 0.0005.
Rule of large sample sizes – With a large sample size, statistical significance doesn’t equal actual significance. With a large enough sample you can get tiny p-values with miniscule effect sizes.
Corollary – If p-values are useless for small sample sizes, and they’re useless for large sample sizes, maybe WE SHOULD STOP USING FUCKING P-VALUES FOR HYPOTHESIS TESTING. Just compare the measured effect size to the predicted effect size, and use Bayes’ rule to update the likelihood of your prediction being correct.
P-values aren’t very useful in getting close to the truth, but they’re everywhere, they’re easy to work with and they’re moderately useful for getting away from bullshit. Since the latter is our goal in this essay we’ll stick with looking at p-values for now.
Back to Tajikistan. I simulated the entire population 1,000 times for each of three drugs: a useless one with a 50% success rate (null drug), a statistically significant one with 50.75% (good drug) and a doubly significant drug with 51.5% (awesome drug). Yes, our standards for awesomeness in medicine aren’t very high. I looked at the p-value of each possible sub-group of the population to pick the best one, that’s the p-hacking part.
Below is a sample of the output:
13 hispanic 1 0.122530416511473
14 female hispanic 2 0.180797304026783
15 young hispanic 2 0.25172233581543
16 young female hispanic 3 0.171875
17 white 1 0.0462304905364621
18 female white 2 0.572232224047184
19 young white 2 0.25172233581543
20 young female white 3 0.9453125
21 adult 1 0.368777154492162
22 female adult 2 0.785204746078306
23 asian 1 0.953769509463538
24 female asian 2 0.819202695973217
The second integer is the number of categories applied to the sub-group (so “asian” = 1, “asian adult female” = 3). It’s the “depth” of the hacking. In our case there are 60 groups to choose from: 1 with depth 0 (the entire population), 9 with depth 1, 26 with depth 2, 24 with depth 3. Since we’re testing the 60 groups as 60 separate hypotheses, by the Bonferroni Rule the 0.05 p-value should be replaced with 0.05 / 60 categories = 0.00083.
In each of the 1,000 simulations, I picked the group with the smallest p-value and plotted it along with the “hacking depth” that achieved it. The vertical lines are at p=0.05 p=0.00083. The horizontal axis the hacked p-value on a log scale and the vertical how many of the 1,000 simulations landed below it:
For the null drug, p-hacking achieves a “publishable” p-value of
If your goal is to do actual science (as opposed to getting published in Science), you want to be comparing the evidence for competing hypotheses, not just looking if the null hypothesis is rejected. The null hypothesis is that we have a 50% null drug, and the competing hypothesis are the good and awesome drugs at 50.75% and 51.5% success rates, respectively.
Without p-hacking, the null drug will hit below p=0.05 5% of the time (duh), the good drug will get there 50% of the time, and the awesome drug 95% of the time. To a Bayesian, getting a p-value below 0.05 is a very strong signal that we have a useful drug on our hands: 50%:5% = 10:1 likelihood ratio that it’s the good drug and 95%:5% = 19:1 that it’s the awesome drug. If ahead of time we thought that each of the cases is equally likely (1:1:1) ratio, our ratios would now be 1:10:19, this means that the probability that the drug is the null one went from 1/3 to 1/(1+10+19) = 1/30. The null drug is 10 times less likely.
With p-hacking, however, the good and the awesome drugs don’t do so well. We’re now looking how often each drug falls below the Bonferroni Rule line of p=0.00083. Instead of 50% and 95% of the time, the good and awesome drugs get there 23% and 72% of the time. If we started from 1:1:1 odds, the new odds are roughly 1:5:15, and the probability that the drug is the null one is 1/21 instead of 1/30. The null drug is only 7 times less likely.
Rule of hacking skepticism – Even though a frequentist is happy with a corrected p-value, a Bayesian knows better. P-hacking helps a bad (null) drug more than it does a good one (which is significant without hacking). Thus, hitting even a corrected p-value threshold is weaker evidence against the null hypothesis.
You can see it in the chart above: for every given p-value (vertical line) the better drugs have more green points in its vicinity (indicating less depth of hacking) and the bad drug has more red because it has to dig down to a narrow subgroup to luck into significance.
Just for fun, I ran another simulation in which instead of holding the success probability for each patient constant, I fixed the total proportion of cures for each drug. So in the rightmost line (null drug) exactly 6,000 of the 12,000 were cured, for the good drug exactly 6,090 and for the awesome drug 6,180.
We can see more separation in this case – since the awesome drug is at p=0.0005 for the entire group, hacking can not make it any worse (that’s where the tall green line is). Because for each drug the total cures are fixed, if one subgroup has more successes the other one by necessity have less. This mitigates the effects of p-hacking somewhat, but the null drug still gets to very low p-values some of the time.
Reading the Fish
So what does this all mean? Let’s use the rules we came up with to create a quick manual for interpreting fishy statistics.
Check the power – If the result is based has a tiny sample size (especially with a noisy measure) disregard it and send an angry email to the author.
Count the categories – If the result presented is for a subgroup of the total population tested (i.e. only green beans, only señoritas) you should count N – the total number of subgroups that could have been reported. Jelly beans come in 50 flavors, gender/age/race combine in 60 subgroups, etc.
Apply the correction – divide the original threshold p-value by the N you calculate above. If the result is in that range, it’s statistically significant.
Stay skeptical – Remember that a p-hacked result isn’t as good of a signal even with correction, and that statistical significance doesn’t imply actual significance. Even an infinitesimal p-value doesn’t imply with certainty that the result is meaningful, per the Rule of Psi.
For example, if I think that at least 1 in 1,000 psychology studies have a fatal experimental flaw or are just completely fabricated, I would give any p-value below 1/1,000 about as much weight as 1/1,000. So there’s a 1.2*10^-10 chance that the parapsychology meta-analysis mentioned above was perfect and got a false positive result by chance, but at least 1 in 1,000 chance that one of the studies in it was bogus enough to make the result invalid.
Let’s apply our manual to the Eagles game:
The Eagles are 10-0 against the spread since Dec 18, 2005 as an underdog and on turf after they’ve had more than 150 yards rushing last game.
First of all, if someone tells you about a 10-0 streak you can assume that the actual streak is 10-1. If the Eagles had won the 11th game going back, the author would have surely said that the streak was 11-0!
The sample size of 11 is really small, but on the other hand in this specific case the error of the measure is 0 – we know perfectly well if the Eagles won or lost against the spread. This doesn’t happen in real life research, but when the error is 0 the experimental power is perfect and a small sample size doesn’t bother us.
What bother us is the insane number of possible variables the author could have mentioned. Instead of [Eagles / underdog / turf / after 150 yards rushing], the game could be described as [Seattle / at home / after road win / against team below average in passing] or [NFC East team / traveling west / against a team with a winning record] or [Team coming off home win / afternoon time slot / clear weather / opponent ranked top-5 in defense]. It’s hard to even count the possibilities, we can try putting them in separate bins and multiplying:
Descriptors of home team – division, geography, record, result of previous game, passing/rushing/turnovers in previous game, any of the many season stats and rankings – at least 20
Descriptors of road team – at least 20
Game circumstances – weather, time slot, week of season, field condition, spread, travel, matchup history etc. – at least 10.
Even if you pick just 1 descriptor in each category, this allows you to “test” more than 20*20*10 = 4,000 hypotheses. What does it mean for the Eagles? A 10-1 streak has a p-value of 0.0107, about 1/93. But we had 4,000 potential hypotheses! 1/93 is terrible compared to the p=1/4,000 we would have expected to see by chance alone.
Of course, this means that the gambling guru didn’t even bother testing all the options, he did just enough fishing to get a publishable number and published it. But with so much potential hacking, 10-1 is as much evidence against the Eagles as it is in their favor. The Eagles, a 6 point underdog, got their asses kicked by 11 points in Seattle.
You can apply the category-counting method whenever the data you’re seeing seems a bit too selected. The ad above tells you that Trinity is highly ranked in “faculties combining research and instruction”. This narrow phrasing should immediately make you think of the dozens of other specialized categories in which Trinity College isn’t ranked anywhere near the top. A college ranked #1 overall is a great college. A college ranked #1 in an overly specific category within an overly specific region is great at fishing.
To No And
It’s bad enough when people don’t notice that they’re being bamboozled by hacking, but digging deep to dredge up a narrow (and meaningless) result can sound more persuasive than a general result. Here’s an absolutely delightful example, from Bill Simmons’ NFL gambling podcast:
Joe House: I’m taking Denver. There’s one angle that I like. I like an angle.
Bill: I’m waiting.
Joe House: Defending Super Bowl champions, like the Denver Broncos, 24-2 against the spread since 1981 if they are on the road after a loss and matched up against a team that the previous week won both straight up and against the spread and the Super Bowl champion is not getting 7 or more points. This all applies to the Denver Broncos here, a wonderful nugget from my friend Big Al McMordie.
Bill: *sigh* Oh my God.
I’ve lost count of how many categories it took House to get to a 24-2 (clearly 24-3 in reality) statistic. What’s impressive is how House sounds more excited with each “and” he adds to the description of the matchup. To me, each new category decreases the likelihood that the result is meaningful by multiplying the number of prior possibilities. To House, it seems like Denver fitting in such an overly specific description is a coincidence that further reinforces the result.
The conjunction fallacy is when humans rate the probability P(A&B) higher than the probability P(B), even though it is a theorem that P(A&B) <= P(B). For example, in one experiment in 1981, 68% of the subjects ranked it more likely that "Reagan will provide federal support for unwed mothers and cut federal support to local governments" than that "Reagan will provide federal support for unwed mothers." […]
Which is to say: Adding detail can make a scenario SOUND MORE PLAUSIBLE, even though the event necessarily BECOMES LESS PROBABLE. […]
In the 1982 experiment where professional forecasters assigned systematically higher probabilities to “Russia invades Poland, followed by suspension of diplomatic relations between USA and USSR” versus “Suspension of diplomatic relations between USA and USSR”, each experimental group was only presented with one proposition. […]
What could the forecasters have done to avoid the conjunction fallacy, without seeing the direct comparison, or even knowing that anyone was going to test them on the conjunction fallacy? It seems to me, that they would need to notice the word “and”. They would need to be wary of it – not just wary, but leap back from it. Even without knowing that researchers were afterward going to test them on the conjunction fallacy particularly. They would need to notice the conjunction of two entire details, and be shocked by the audacity of anyone asking them to endorse such an insanely complicated prediction.
Is someone selling you a drug that works only when the patient is old and a woman and Hispanic? A football team that is an underdog and on turf and good at rushing? One “and” is a warning sign, two “ands” is a billboards spelling BULLSHIT in flashing red lights. How about 11 “ands”?
11 “ands” is a level of bullshit that can only be found in one stinky stall of the washrooms of science, the gift that keeps on giving, the old faithful: power posing. After power posing decisively failed to replicate in an experiment with 5 times the original sample size, the authors of the original study listed 11 ways in which the experimental setup of the replication differed from the original (Table 2 here). These differences include: time in poses (6 minutes in replication vs. 2 minutes in the original), country (Switzerland vs. US), filler task (word vs. faces) and 8 more. The authors claim that any one of the differences could account for the failure of replication.
What’s wrong with this argument? Let’s consider what it would mean for the argument to be true. If it’s true that any of the 11 changes to the original setup could destroy the power posing effect, it means that the power posing effect only exists in that very specific setup. I.e. power posing only works when the pose is held for 2 minutes and only for Americans and only after a verbal task and 8 more ands. If power posing requires so many conjunctions, it was less probable to start with than the chance of Amy Cuddy admitting that power posing isn’t real.
Answering the weirdest search queries that have brought readers to Putanumonit.
Hey, reader, how did you get here? Are you subscribed to Putanumonit? Clicked on a tweet or a status or a post? Followed a trail from SlateStarCodex or LessWrong? Either way, you probably know what to expect here. And, you deserve what’s coming to you.
But some people took a more interesting path to this blog. According to WordPress Stats, back in January someone googled ‘nextpart and hack’ and the 7th page of the results took them to my post on water charities. Others arrived on Putanumonit after googling ‘gern’, ‘sci-put’, ‘utrgv “wewillfail”‘ and ‘ya fat njie’. I have no clue what any of these people were looking for , but I doubt they found it on Putanumonit. And if there’s anything I really hate is leaving a client unsatisfied.
I decided to go through the list of search terms that brought people to the blog, and help them out with their unanswered queries. At the end, I’ll share my absolute favorite link to Putanumonit, one that by itself would have made the hundreds of hours I spend on this site worthwhile.
There but for the grace of Google go I
Original search terms in blockquotes.
messi before growth hormones
messi b4 when messi was a dwarf
He was actually a hobbit.
That’s what my LinkedIn profile says.
“intelligent life economist”
That’s what my Tinder profile says.
second option to keep 3galloping horse in tge living room of narth facing house
I don’t know what the first option was, but I would go with that one.
tribalism in the old testament
How about Samuel 15:3 – “Now go, attack the Amalekites and totally destroy all that belongs to them. Do not spare them; put to death men and women, children and infants, cattle and sheep, camels and donkeys.”
March 2016: is an ugly guy doomed as a pua
June 2016: dry spell pua
I guess you got your answer. Maybe you should try a more considerate and respectful approach to dating?
August 2016: a dramatic poem u’r intelligent girl
August 2016: pua date wait next week
There ya go!
penny’s size bell curve
Does the guy you see once a week know that you consider yourself “85% single”?
I imagine you get completely different results if you change the “i” in “shifted” to an “a”.
if you vote for the lesser of two evils you are still voting for evil and you will be judged for it. you should always vote for the best possible candidate, whether they have a chance of winning or not, and then, even if the worst possible candidate wins, the lord will bless our country more because more people were willing to stand up for what is right.
This explains most of Hellection 2016.
your beloved is dating
She’s probably dating the guy writing dramatic poetry about her intelligence.
Source of pride
There’s a subreddit called r/getdisciplined with a variety of tips to beat procrastination and such. You’d think the only relevant tip would be “get off Reddit and get back to work, you lazy bum”, but apparently there’s more to it. A couple of weeks ago, someone posted a collection of tips that included power posing. This led to the following exchange, which I have printed out and framed on my wall:
Let me spell out what happened. The first link is famous psychologist Dana Carney, the lead investigator in the original power posing study, disowning the totality of power posing research and listing a dozen methodological errors contributing to the original false result. This is dismissed by the reader as mere “opinion”.
The second link is my grumbling about Amy Cuddy. This is accepted by the forum as ironclad factual evidence settling the dispute on power posing forever.
Trump most dangerous failing is that he sees every human interaction as a zero sum game, a contest with winners and losers. Trump has made a lot of his money by exploiting others, his gains were someone else’s loss. He operates as if he can’t imagine things being any other way. And yet: our society and our economy are based on cooperation and dealings with mutual benefit. As long as spiteful deities don’t interfere, every time humans have tried cooperating with each on larger scales the results have been overwhelmingly positive.
We don’t win anymore. We don’t beat China in trade. […] I beat China all the time. All the time.
But this isn’t an essay about trade (so save your nitpicking about labor market theories). And this isn’t an essay about Trump (although he shall again prove unavoidable). This is an essay about cooperation versus polarization.
If Trump doesn’t start a nuclear war, the greatest damage he will do is to the norms that allow us to cooperate, globally and domestically, for the next four years. But polarization destroys these norms forever. Those who would sacrifice the norms of compromise, respect and democracy itself in order to fight Trump are doing the Devil’s work for him.
Content note: politics, culture wars, and everything that is wrong with human society. If you don’t want to read about everything that is wrong with human society, please enjoy this photo of my own hedgehog looking very fluffy af and come back next week.
Everything that is wrong with human society
…mostly comes in two flavors: coercion and failures of coordination. Coercion is the bad things we can’t avoid: wars, slavery, exploitation. Coordination failures are the good things we can’t achieve: win-win free trade, nuclear disarmament, climate change control, eliminating poverty, universal love.
Coercion is a bigger threat to weak societies subjugated strong adversaries: a peasant village under the thumb of a despot, a European town in the path of the Mongol horde, an African community raided by slavers. Coordination failures are a bigger threat to strong societies being devoured from the inside. That’s us.
When people appoint governments to solve their problems, the government ideally tries to solve the most coordination failures using the least coercion. For example, a basic coordination problem is having everyone in a society agree to abide by a certain set of rules regarding violence and property. Governments solve this through coercive institutions like courts, jails and the police. There is a balance to be struck – the Soviet Union had lower crime rates than the USA, but most people wouldn’t be willing to accept secret police and gulags just to have less car theft.
But the government doesn’t really decide how to solve coordination problems. More often, it just implements the solutions people already live by, and codifies the social norms that naturally evolved among its citizens. For example, public acceptance of gay unions in the United States has been shifting for decades, and The Supreme Court legalized gay marriage many years after it became the plurality opinion. Politicians have their own incentives, they will not promote honesty, kindness and tolerance beyond what people already live by. Governments are often slower to react to changing norms than even corporation are.
Point is: it is up to us to live by the norms that we want our government to have.
Social norms are themselves a coordination problem: we would all prefer to live in a society in which everyone (including us) is always honest, kind and tolerant. Yet, we often have much to gain from occasionally being dishonest, selfish and intolerant. The harm that these behaviors do to social norms is often ignored when a personal struggle is more pressing.
And yet, social norms are the only way to achieve cooperation without coercion. In most interactions it is rational to cooperate if you expect your opponent to do the same, but only then. This means that the social norms that promote cooperation are the most valuable thing we have, they are the ones that allow us to even start addressing other problems. And this means that nothing is more harmful than the norms that promote polarization and hamper cooperation.
We may imagine that polarization is at its worst today in the era of social media, outrage clickbait and demagoguery. It’s not: polarization is the result of human weakness, and humans were humans long before Facebook. My favorite quote about political polarization predates the United States itself by two decades:
In a nation distracted by faction, there are, no doubt, always a few, though commonly but a very few, who preserve their judgment untainted by the general contagion. They seldom amount to more than, here and there, a solitary individual, without any influence, excluded, by his own candour, from the confidence of either party, and who, though he may be one of the wisest, is necessarily, upon that very account, one of the most insignificant men in the society. All such people are held in contempt and derision, frequently in detestation, by the furious zealots of both parties.
Of all the corrupters of moral sentiments, therefore, faction and fanaticism have always been by far the greatest.
The horsehoe theory holds that extremists on either side of a political/cultural divide share more similarities with each other than they do with centrists. It doesn’t apply to every single debate, but I noted the horseshoeness of the “gender wars” here and alluded to the similarities between the political extremes of left and right in my pre-election essay.
From the top of the horseshoe, society looks like a complex network of compromises and trade offs. On crime and terror, a compromise between liberty and security. On multiculturalism, a compromise between diversity and social cohesion. On trade, a compromise between growing the global pie and fairly dividing the domestic pie. On Nice Guys, a compromise between everyone’s personal desires to be safe, be respected and get laid.
This doesn’t mean that the horseshoe is always perfectly balanced – the moderate reasonable position on a topic depends on moderation and reason, not on its distance from the fanatics. The virtues of racial equality don’t depend on the number of white or black supremacists and their opinions.
From the ends of the horseshoe, the world looks completely different:
A single sacred valuedefines the worth of every person and action, and cannot be traded off for anything.
Zero sum game: any action that hurts the enemy is good, anything that helps the enemy is bad, regardless of other consequences.
The outgroup is seen as a homogenous glob of menace, with no nuance or differentiation.
The enemy is easily comprehended, seen clearly across the narrow gap. The enemy’s tactics (conformity for the in-group, condemnation for the rest) and the enemy’s worldview (same sacred value, just with a flipped polarity) are very familiar.
The moderate centrists are utterly incomprehensible, hidden from view by the horseshoe curve of almost-sympathizers. To extremists of either end, the centrists are despised as traitors. “All such people are held in contempt and derision, frequently in detestation, by the furious zealots of both parties.”
At the very bottom of the horseshoe, where cooperation is unimaginable and win-win games turn into mutually assured destruction, sits Moloch and devours the souls of his zealots.
I called the top of the horseshoe “normalizers”, I don’t mean that in the sense used commonly since the election just yet. We’ll talk about that “normalization” later. For now, it means – pulling people towards normalcy, and away from the eternal war and the soul-devouring demon. Most people try to nudge each other left and right on the horseshoe, but my goal is to pull everyone up.
Speaking of, how do smart people even find themselves slipping down towards the nasty edges of the horseshoe? The answer is bubbles and evaporation.
Everyone has heard a million times by now that we live in echo-chamber bubbles that protect us from beliefs we disagree with. Yet people don’t appreciate that two of the most powerful forces in the universe conspire to keep us bubbled up: confirmation bias and the algorithm. The latter latches on to your slightest deviation from equanimity by feeding you content that nudges you ever so slightly further in that direction. The former keeps you blind to the fact that anything nefarious is happening at all. In combination, they make the slope very slippery.
Bubbles keep us from hearing those we disagree with, evaporative coolingkeeps them from hearing us. When a social group begins to drift towards an extreme position, the sanest people are first to leave and the fanatics remain. The crazier the position becomes, the more devoted to it the remaining members are: anyone capable of doubt has long ago departed.
But I’m not picking on Slate because they disclose their voting patterns, I think this is commendable. And I’m not picking on them because they’re the worst, if you’ve noticed I already linked to a Slate article positively in this essay. I’m talking about Slate because its senior political editor, Jamelle Bouie, just wrote an article forged straight in Moloch’s furnace: There’s No Such Thing as a Good Trump Voter.
There’s no such thing as a good hate article
Let’s run through the checklist.
A single sacred value – as Jonathan Haidt explains: “The new sacred values on the left are about anti-racism and fighting discrimination”. Bouie doesn’t entertain the notion that people could have voted for Trump because they care about terror, or abortion, or taxes, or they just think that Hillary Clinton is a horrible and corrupt person. To him, all voting is single-issue voting on racism: “People voted for a racist who promised racist outcomes. They don’t deserve your empathy.”
Eternal conflict – Bouie sees everything as part of a perennial struggle against racism. Journalists who urge empathy for Trump voters in 2016 are compared to when “Between 1882 and 1964, nearly 3,500 black Americans were lynched. At the peak of this era, from 1890 to 1910, hundreds were killed in huge public spectacles of violence. And the people who watched these events, who brought their families to gawk and smile, were the very model of decent, law-abiding Americana.”
Zero sum – Can empathizing with Trump supporters actually increase tolerance and improve outcome for blacks? It doesn’t matter, any aid to the enemy is condemned as sin: “To insist Trump’s backers are good people is to treat their inner lives with more weight than the actual lives on the line under a Trump administration. At best, it’s myopic and solipsistic. At worst, it’s morally grotesque.”
Homogenous outgroup – “Trump’s 59 million votes… Meanwhile, more than 300 incidents of harassment or intimidation have been reported in the aftermath of Trump’s election, according to the Southern Poverty Law Center.” To me, it sounds like 58,999,700 people voted for Trump and did not proceed to harass minorities the next day. To Bouie, all 59 million share the collective guilt.
The enemy’s tactics are familiar – Two paragraphs after condemning 59 million people for the actions of 300, Bouie writes: “[Trump’s] campaign indulged in hateful rhetoric against Hispanics and condemned Muslim Americans with the collective guilt of anyone who would commit terror.” You see, according to Bouie there’s nothing wrong per se with employing the tactic of collective condemnation. It’s only a problem if you condemn the wrong collective.
The moderates are incomprehensible – Who are these terrible racists who are compared to the people who cheered at lynchings? Who are these right-wing extremists that Bouie calls “morally grotesque”? The New York Times and the Washington Post. Reminder: these are the two media companies that Trump has personally threatened to sue while remarking of the former: “They don’t write good. They have people over there, like Maggie Haberman and others, they don’t — they don’t write good. They don’t know how to write good.”
When you decide that even your enemies’ enemies are your bitter enemies, maybe you should consider making fewer enemies.
Intermission: why does everyone hate me?
I admit that it’s somewhat self-indulgent to position myself in Smith’s quote and assume that I’m “held in contempt and derision” because I’m the honest voice of calm reason. But I have a sneaking suspicion of reversed causality here. I mentioned some of the thinkers who inspired me: Haidt, Kling, Harris, Alexander, Yudkowsky. I noticed that we have one more thing in common besides fighting polarization and promoting rationality – we’re all (ethnically) Jewish.
For all our talents, Jews’ most remarkable ability is ending up equally hated by both sides of a polarized conflict. Naturally, whenever Sunni fight Shia they accuse each other of conspiring with Jews; so do Russia and Ukraine. In American culture wars, the SJ left hates Jews because they’re the rich and powerful oppressors. The alt-right accuses Jews of sacrificing babies to Moloch, which is very confusing to the Jews who try to use Moloch as a metaphor for cooperation failure.
Personally, I couldn’t find a home at the horseshoe’s tips even if I tried. I’m the worst kind of Jew you can imagine: an Israeli cosmopolitan liberal with an MBA. According to Malcolm X, this makes me an agent of the Zionist-capitalist conspiracy. According to the alt-right, this makes me an agent of the Zionist-capitalist conspiracy. The good news is that I’m bridging the gap between extremists just by existing. The bad news is that I’m only pushing this propaganda of tolerance and cooperation to further my Zionist-capitalist plot of global peace and prosperity (peace and prosperity increase stock prices).
I’m a bit worried that what led me to the center of the horseshoe isn’t cool rationality, but the fact that I was held in contempt and derision to start with. This shall be the new motto of the centrist moderates: “Does everyone hate you? You should try using reason, you have nothing to lose!”
Climbing the horseshoe
Ok, so you want to avoid being at the bottom of the horseshoe where everyone is your enemy and you’re destroying the social norms of cooperation that humanity depends on. How do you ascend to a more judicious position on the horseshoe?
Option 1 – convert to Judaism.
Option 2 – follow this simple, four-step plan:
Find some you disagree with, but don’t hate.
Figure out what they know that you don’t, and vice versa.
Figure out what goals and values they hold that you don’t, and vice versa.
Offer a compromise.
Let’s see if it works.
“Dear Mr. Bouie,
I have read your many articles regarding Trump supporters. I disagree with their content both factually and instrumentally. I don’t think they present the entire truth about racism in the United States, nor offer an effective way to fight it. But I admire your motivation in writing them, and I want to cooperate with you in our fight against racism.
There is no question that you know more than most about racism in the United States. From your writing I learned both about the historical cycles of racial integration and backlash, and about the present experience of being black in America. I don’t know much about either the past or the present of racism, all I know are bell curves.
Your article treats “attitudes about racism” as the only variable that mattered in the election, so that will be the bell curve’s axis. I will grant your implicit assumption that every Trump voter is more racist than every Clinton voter if you’ll grant me the mathematical assumptions needed for a Gaussian transformation. I want to “normalize” the racism of Trump’s voters, if you will.
If half the country voted for Trump, the median Trump voter is at the 75th percentile of racism. That’s 0.67 standard deviations more racist than the median American, and 1.33 SDs more racist than the median Clinton voter (and people like the New York Times). On the other hand, there are 6,000 registered KKK members out of 242 million American adults, that more than 4 SDs out on the racism axis. Even if we assume 100,000 white supremacists, a very pessimistic estimate, they occupy the area on the curve beyond 3.3 SDs. That’s twice as far from the median Trump voter as the latter is from the median Clinton voter.
Your main goal in opposing Donald Trump, Mr. Bouie, is fighting racism. I actually consider other issues more important. Yes, some Trump endorsers wonder if Jews are human (we’re actually dancer), but I am still more worried about nuclear war, the erosion of governance institutions and threats to global economic freedom. I know, I’m a weirdo. But for now, let’s put all that aside and concentrate solely on your goal: fighting racism.
Trump is especially worrying in regards to racism because he’ll be the first president to include the always-present minority of white supremacists in the government coalition. To combat that, we need to build an overwhelming anti-racist coalition. We can’t risk having just 51% of people on our side, we need at least three-quarters of the country. That means we need the “orange quarter” on my chart, the 25% of Americans who voted for Trump but are less racist than the median Trump voter.
Who are they? One of them is my old Jewish colleague who voted for Trump because of tax policy. One of them is my gay black friend who voted for Trump because he worries about illegal immigrants. Millions of them are the older rural whites in Pennsylvania and Michigan who swung the election Trump’s way. The same people whose great grandparentsbled for the Union to end slavery a century and a half ago.
We need to compromise with these people because we need them. We need to tell them: ‘We don’t care as much about taxes and immigration and revitalizing the rural Midwest, and you don’t care as much about white supremacists, but we’ll help you out on all of the above if you help us kick the idiots shouting “Heil Trump” far outside the Overton window (and maybe out a physical window as well). Besides,what’s more embarrassing than pasty white dudes calling themselves “Children of the sun“? Are those the friends you want?‘
These “orange voters” don’t really care what the New York Times thinks of them, let alone what Slate does. If Breitbart accused you of being politically correct, you would wear that as a badge of honor. All we’re doing by calling everyone “racist” is redefining “racist” to mean “people who disagrees with Slate on anything”, the same way “politically correct” now means “people who disagree with Breitbart on anything”.
Look, we need these orange Trump supporters in our coalition to fight racism and we are tellingthem that internment camps are something on their agenda. Actually, forget the supporters. Trump himself has only one agenda: “winning”. Let’s not tell him that his policy is locking Muslims up.
Now let’s get to the N-word: normalization. You’re saying that this isn’t just another normal election, that this isn’t politics as usual. Look at that orange person in the middle of the bell curve, the 270th elector. He (or she) is the normal one. To them, it was a normal election, and they voted for Trump. We don’t get to decide what’s “normal” in America, America decided what’s normal on November 8th.
This doesn’t mean that what’s “normal” isn’t wrong, just that treating normal people as if they were evil mutants isn’t the way to make them right. I believe that “normal” is wrong on many things, like altruism, welfare, and football coaching. I try to persuade people to my position with friendly arguments, not by calling them names. We don’t decide whether to normalize the orange voters or not, they are normal. We decide if we’re going to polarizeand radicalizethese people, or if we work with them to achieve our goals.
And yes, if a bunch of people who aren’t evil mutants voted for someone, that should give us some evidence that this person also isn’t an evil mutant. This isn’t a political point, just a Bayesian one.
You know what this is reminiscent of? Obama’s refusal to associate jihadi terrorism with Islam to avoid radicalizing Muslims. We both agree that Obama is pretty smart, so let’s make a deal. We’ll both reach out to people close to us on the political horseshoe and ask them to adopt the anti-radicalization logic. You’ll tell the New York Times not to call Trump voters racist, and I’ll tell Sam Harris not to call terrorists Islamic. He’ll listen to me, we’re both in the Zionist-capitalist club together. Let’s build our coalition at the top of the horseshoe and at the middle of the bell curve.
Because when Jews and blacks cooperate, beautiful things happen.