Bayes and What He Hath Wrought

Thomas Bayes was an 18th century British statistician, philosopher and Presbyterian minister. He’s known today because he formulated Bayes’ Theorem, which has since given rise to Bayseian probability, Bayseian inference, Bayseian epistemology, Bayesian efficiency and Bayseian networks, among other things.

The reason I bring this up is that philosophers, especially the ones who concentrate on logic and the theory of knowledge, often mention something Bayseian, usually in glowing terms. It’s been a source of consternation for me. I’ve tried to understand what the big deal is, but pretty much failed. All I’ve really gotten out of these efforts is the idea that if you’re trying to figure out a probability, it helps to pay attention to new evidence. Duh.

Today, however, the (Roughly) Daily blog linked to an article by geneticist Johnjoe McFadden called “Why Simplicity Works”. In it, he offers a simple explanation of Bayes’ Theorem, which for some reason I found especially helpful. Here goes:

Just why do simpler laws work so well? The statistical approach known as Bayesian inference, after the English statistician Thomas Bayes (1702-61), can help explain simplicity’s power.

Bayesian inference allows us to update our degree of belief in an explanation, theory or model based on its ability to predict data. To grasp this, imagine you have a friend who has two dice. The first is a simple six-sided cube, and the second is more complex, with 60 sides that can throw 60 different numbers. [All things being equal, the odds that she’ll throw either one of the dice at this point are 50/50].

Suppose your friend throws one of the dice in secret and calls out a number, say 5. She asks you to guess which dice was thrown. Like astronomical data that either the geocentric or heliocentric system could account for, the number 5 could have been thrown by either dice. Are they equally likely?

Bayesian inference says no, because it weights alternative models – the six- vs the 60-sided dice – according to the likelihood that they would have generated the data. There is a one-in-six chance of a six-sided dice throwing a 5, whereas only a one-in-60 chance of the 60-sided dice throwing a 5. Comparing likelihoods, then, the six-sided dice is 10 times more likely to be the source of the data than the 60-sided dice.

Simple scientific laws are preferred, then, because, if they fit or fully explain the data, they’re more likely to be the source of it.

Hence, in this case, before your friend rolls one of the dice, there is the same probability that she’ll roll either one. With the new evidence — that she rolled a 5 — the probability changes. To Professor McFadden’s point, the simplest explanation for why she rolled a 5 is that she used the dice with only 6 sides (she didn’t roll 1, 2,3, 4 or 6), not the dice with 60 sides (she didn’t roll 1, 2, 3, 4, 6, 7, 8, 9, 10, . . . 58, 59 or 60).

Now it’s easier to understand explanations like this one from the Stanford Encyclopedia of Philosophy:

Bayes’ Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes’ Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist positions. Indeed, the Theorem’s central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. . . .

To illustrate, suppose J. Doe is a randomly chosen American who was alive on January 1, 2000. According to the United States Center for Disease Control, roughly 2.4 million of the 275 million Americans alive on that date died during the 2000 calendar year. Among the approximately 16.6 million senior citizens (age 75 or greater) about 1.36 million died. The unconditional probability of the hypothesis that our J. Doe died during 2000, H, is just the population-wide mortality rate P(H) = 2.4M/275M = 0.00873. To find the probability of J. Doe’s death conditional on the information, E, that he or she was a senior citizen, we divide the probability that he or she was a senior who died, P(H & E) = 1.36M/275M = 0.00495, by the probability that he or she was a senior citizen, P(E) = 16.6M/275M = 0.06036. Thus, the probability of J. Doe’s death given that he or she was a senior is PE(H) = P(H & E)/P(E) = 0.00495/0.06036 = 0.082. Notice how the size of the total population factors out of this equation, so that PE(H) is just the proportion of seniors who died. One should contrast this quantity, which gives the mortality rate among senior citizens, with the “inverse” probability of E conditional on H, PH(E) = P(H & E)/P(H) = 0.00495/0.00873 = 0.57, which is the proportion of deaths in the total population that occurred among seniors.

Exactly.

We Can’t Afford To Be Discouraged

Every so often I step back from the day’s transitory events and consider that a president of the United States recently tried to overturn the results of an election so he could stay in office. With the help of various public officials and propagandists, he has been able to convince millions of Americans that changing the results of the election, i.e. insurrection, was justified. A year later, few Republican politicians refuse to admit he lost.

Furthermore, all around the country, the former president’s supporters are trying to make it harder to vote and easier to change the results of future elections, including an election in which he may again be a candidate.

Support for the Republican Party should have collapsed by now. It hasn’t.

Meanwhile, in Washington, two senators who claim to be Democrats are delaying the implementation of President Biden’s agenda, even though it’s the agenda Biden ran on in 2020. In fact, these two senators refuse to modify the current version of a Senate rule in order to protect the voting rights under assault by members of the other party.

Some voters who ordinarily support Democrats, or might be inclined to do so given the present state of the Republican Party, are discouraged. It’s feared that these voters might not turn out in sufficient numbers in upcoming elections.

The irony is that the situation in Congress and Republican-led statehouses should lead more people to vote and support Democratic candidates. Insuring that the House of Representatives remains in Democratic hands after the 2022 election is crucial. Insuring that there are at least 50 Democrats in the Senate willing to support the president’s agenda and protect voting rights is also crucial. Insuring that more Democrats win local elections is crucial too.

It isn’t fearmongering to point out that America’s political system is on very shaky ground. Majority rule is under attack by right-wing authoritarians. Time is running out to seriously address the climate crisis. This is no time to be discouraged and stop fighting for a better America and a better world.

Nothing New, But It Bears Repeating

From Maureen Dowd of The New York Times:

Ordinarily staid and silent Supreme Court justices have become whirling dervishes of late, spinning madly to rebut the idea that Americans are beginning to regard the court as a dangerous cabal of partisan hacks.

They need not fret and wring their hands. No one is beginning to think that.

Many of us have thought that for a long time.

Supremes are often Shakespeare fans, so of course they are familiar with the phrase “doth protest too much, methinks.”

The once august court’s approval ratings on fairness were already falling two decades ago. The bloom came off the robe in 2000, when the court threw the game on Bush v. Gore, voting 5 to 4 to stop the Florida recount and anoint a Republican president.

If we conjure an alternative-history look at America, consider all the things that the Supreme Court brought down on our heads by pre-emptively purloining that victory for George W. Bush: two interminable and inexplicable wars, costing so many lives and so many trillions; a descent into torture; the villainous Dick Cheney.

As some on Twitter noted, our 20 years of quicksand in Afghanistan was capped Friday with this headline: “Son of Afghanistan’s Former Defense Minister Buys $20.9 Million Beverly Hills Mansion.”

Al Gore, mocked as “Ozone Man” by Bush senior, certainly would have tried to head off the biblical floods and fires engulfing our country.

The right-wing justices may as well embrace their reputation for hackery. Because in this blockbuster year, when the conservative court begins debating abortion and the Second Amendment, one thing is certain: They are going to make rulings that will drive people crazy, rulings that will be out of sync with what most Americans believe.

So please, conservative cabal, don’t pretend you’re not doing this out of ideology.

And please, Justice Breyer, skedaddle. You’re playing a dangerous game. You need to get out of there because it looks as if the midterms are going to be bad, and if the Democrats lose the Senate majority, there’s no guarantee that Mitch McConnell will let any Biden nominee onto the court, even with two years left on the president’s term. Do you want the court to be 7 to 2?

Listen to those Democrats who are warning that staying would be irresponsible and egotistical. Don’t make the colossal mistake that Ruth Bader Ginsburg did, ignoring entreaties from top Democrats and hints from the Obama White House to leave in a timely way and hanging on so long that the worst possible outcome happened: That remarkable feminist’s seat went to the ferociously anti-abortion Lady Handmaid’s Tale . . . 

And please, America, can we have term limits? Justices should not be on the court for 30 years, or into their late 80s.

Chief Justice John Roberts, who did not want the court to be seen as too extreme, has lost control because there are five more rabid conservatives running over him.

D____ T____’s ability to get three conservatives [Correction: reactionaries] on the court, thanks to McConnell, will turn out to be the most consequential part of his miserable presidency. And the minority leader is about to get his reward in the form of a bunch of conservative rulings.

The beauty of it for McConnell is that the court is going to do his dirty work for him. Republicans don’t want to vote to roll back abortion rights because they know it’s not popular and they don’t want their fingerprints on it. They’d prefer the court do it.

Linda Greenhouse, who has a book coming out called “Justice on the Brink,” had a piece in The Times summing up why it is brutal for our democracy to have institutions so out of step with majority views in the country: “Three polls within the past month show that fewer than a third of Americans want to see the court overturn Roe v. Wade. Yet it appears that only a third of the justices can be counted on to preserve the right to abortion as defined by the court’s current precedents.” So unlucky women in red states are going back to back-alley days?

. . . Ignore the charade of the parade of justices protesting that they are pure and neutral. Nobody’s buying it. We all know it’s a disaster if the country’s going one way and the court’s going the other. . . . 

How Being a Right-Wing Creep Can Give Meaning to Your Life

Earlier today, I posted a Twitter thread by David Roberts regarding the so-called “War on Christmas”. He provided context with an excerpt from a New York Times article by Thomas Edsall that discusses some relevant research:

In their September 2021 paper “Exposure to Authoritarian Values Leads to Lower Positive Affect, Higher Negative Affect, and Higher Meaning in Life,” seven scholars . . . write:

Right-wing authoritarianism played a significant role in the 2016 U.S. presidential election. In subsequent years, there have been numerous “alt-right” demonstrations in the U.S., including the 2017 Unite the Right rally in Charlottesville that culminated in a fatal car attack, and the 2021 Capitol Insurrection. In the U.S., between 2016 and 2017 the number of attacks by right-wing organizations quadrupled, . . . constituting 66 percent of all attacks and plots in the U.S. in 2019 and over 90 percent in 2020.

How does authoritarianism relate to immigration? [Jake Womick, one of the co-authors] provided some insight in an email:

Social dominance orientation is a variable that refers to the preference for society to be structured by group-based hierarchies. It’s comprised of two components: group-based dominance and anti-egalitarianism. Group-based dominance refers to the preference for these hierarchies and the use of force/aggression to maintain them. Anti-egalitarianism refers to maintaining these sorts of hierarchies through other means, such as through systems, legislation, etc.

Womick notes that his own study of the 2016 primaries showed that T____ voters were unique compared to supporters of other Republicans in the strength of their

group-based dominance. I think group-based dominance as the distinguishing factor of this group is highly consistent with what happened at the Capitol. These individuals likely felt that the T____ administration was serving to maintain group-based hierarchies in society from which they felt they benefited. They may have perceived the 2020 election outcome as a threat to that structure. As a result, they turned to aggression in an attempt to affect our political structures in service of the maintenance of those group-based hierarchies.

In their paper, Womick and his co-authors ask:

What explains the appeal of authoritarian values? What problem do these values solve for the people who embrace them? The presentation of authoritarian values must have a positive influence on something that is valuable to people.

Their answer is twofold:

Authoritarian messages influence people on two separable levels, the affective level, lowering positive and enhancing negative affect, and the existential level, enhancing meaning in life.

They describe negative affect as “feeling sad, worried or enraged.” Definitions of “meaning in life,” they write,

include at least three components: significance, the feeling that one’s life and contributions matter to society; purpose, having one’s life driven by the pursuit of valued goals; and coherence or comprehensibility, the perception that one’s life makes sense.

In a separate paper, “The Existential Function of Right-Wing Authoritarianism,” [political scientists] provide more detail:

It may seem ironic that authoritarianism, a belief system that entails sacrifice of personal freedom to a strong leader, would influence the experience of meaning in life through its promotion of feelings of personal significance. Yet right-wing authoritarianism does provide a person with a place in the world, as a loyal follower of a strong leader. In addition, compared to purpose and coherence, knowing with great certainty that one’s life has mattered in a lasting way may be challenging. Handing this challenge over to a strong leader and investment in societal conventions might allow a person to gain a sense of symbolic or vicarious significance.

From another vantage point, Womick and his co-authors continue,

perceptions of insignificance may lead individuals to endorse relatively extreme beliefs, such as authoritarianism, and to follow authoritarian leaders as a way to gain a sense that their lives and their contributions matter.

In the authors’ view, right-wing authoritarianism,

despite its negative social implications, serves an existential meaning function. This existential function is primarily about facilitating the sense that one’s life matters. This existential buffering function is primarily about allowing individuals to maintain a sense that they matter during difficult experiences.

In his email, Womick expanded on his work: “The idea is that perceptions of insignificance can drive a process of seeking out groups, endorsing their ideologies and engaging in behaviors consistent with these.”

These ideologies, Womick continued,

should eventually promote a sense of significance (as insignificance is what drove the person to endorse the ideology in the first place). Endorsing right-wing authoritarianism relates to higher meaning in life, and exposing people to authoritarian values causally enhances meaning. 

Understanding the Non-Existent War on Christmas

David Roberts writes a newsletter about “the technology, politics and policy of decarbonization”. He also writes a lot on Twitter. A few days ago, he wrote about the meaning of the “War on Christmas”:

I’ve always thought it’s worth examining the WoC more closely, not because it’s particularly important, but almost the opposite: because it’s so obviously silly & the stakes are so low, it’s easier to see the underlying dynamics clearly, without strong priors getting in the way.

To review: once upon a time, pretty much all US stores & public facilities put up Christmas decorations & had clerks & employees say “Merry Christmas!” around the holiday season. It was a reflection of the total dominance of white Christian culture in the US.

Over time, demographics & opinions shifted, at least in some quarters. It became clear that centering Christmas excludes Jews, Muslims, atheists . . . all the many US subcultures that don’t celebrate Xmas. Some businesses/institutions became leery of alienating customers/patrons.

Some places replaced Xmas decorations & “Merry Xmas!” with more generic *holiday* decorations & “Happy holidays!” The idea was that the more generic approach would welcome Christians but *also* welcome other cultures — welcoming all, alienating none. What’s the problem?

Anyway, RW media got hold of this & spun it into a “War On Christmas,” telling listeners & viewers that it was the first step to eliminating Christmas altogether & part of a larger war on Christianity. . . . 

Why is this interesting? Because it makes the conceptual structure of the US culture war extremely clear. Most culture war struggles share this structure.

First thing to say: generic “holiday” celebrations & greetings do not hurt or diminish Christians or Christmas.

That’s crucial. Nobody’s targeting or trying to diminish Christmas. Everyone who celebrates it can continue doing so.

What generic-holiday does is *decenter* Christmas. It renders Christmas just one holiday celebration among others, Christianity just one culture among others.

In trying to accommodate everyone, generic-holiday implicitly says that Christians are not *special*. They are one group living among other groups, as equals, all of which are free to live their cultures as they see fit, none of which have a right to dominate or exclude others.

And that, of course, is precisely the problem for the reactionaries on the right. For them, on a deep level, being dominant — having your culture, your folkways, your needs, your feelings centered — is *part of* the culture. Without domination, the culture is nothing.

That’s why so much of the War On Christmas rhetoric is about how Christmas is being “destroyed” by this, or how Christianity will be “wiped out.” If they lose being centered, lose being dominant, then in a very real way they *do* lose a culture premised on hegemony.

“To those accustomed to domination, equality feels like oppression.” There’s a reason versions of this cliché are everywhere these days — we’re seeing it play out in arena after arena. To reactionaries, being told their culture is one among equals feels like erasure.

Silly as it is, the War On Christmas clearly exposes the fundamental struggle unfolding in the US.

To some of us, the essence of the US is as a neutral framework, where any culture can thrive, anyone from any background can succeed, all are treated fairly & with dignity.

Obviously the US has never lived up to that ideal, but as Obama said so eloquently, the struggle to come closer & closer to that ideal *is* America — it’s the most American thing of all. All those outsiders who forced the US to be more fair & open are the real American heroes.

Reactionaries, on a deep & fundamental level, do not share that vision of America. To them, America is a white, patriarchal, “Judeo-Christian” nation — a particular people, a particular culture. Sure, we’ll accept guests, Others can live here, but never forget who’s in charge.

In some sense it’s a trivial question: Do you say “happy holidays” & accommodate everyone or say “merry Christmas” & implicitly tell everyone who’s not a Christian to accept, without complaint, that they are secondary, subsidiary, peripheral — *less*.

But within that trivial question is embedded ALL the questions facing the US. Are we trying to be a genuine multiethnic, multicultural, diverse society, united by a framework of neutral rules that treat us all the same? Do we want everyone to feel welcome, with equal citizenship?

Or are we, at root, a white patriarchal Christian society that, at its discretion/whims, sometimes allows other kinds of people to live among us? Is the declining dominance of that subculture tantamount to America itself declining? Is diversity our enemy, as Tucker Carlson says?

That fundamental struggle is reflected, in a fractal way, in the silly fight over Christmas. It’s just one more way for the hegemonic demographic/subculture to tell the rest of us, “if we don’t get to dominate, we’re erased, and we’ll blow it all up before that happens.”

You’re seeing it everywhere now with rising right-wing violence & extremism. On some level, white patriarchal Christian culture already realizes that loss is inevitable — and it is fully ready to bring the whole structure down before it will live as equals among equals.

The real question this raises for me — the ultimate question of America, really — is whether it’s *possible* to have a true multiethnic multicultural society of equals. Is it possible for everyone to be happy even if no one gets to hear their special holiday greeting in public?

Or are there just too many reactionaries, too many people for whom the only alternative to domination is submission/humiliation, too many people who simply can’t *conceive* of genuine equality, for the thing to work? Can a country w/ NO privileged culture survive & prosper?

I dunno. (I used to be a confident Yes, a confident believer in the possibility of true democracy, but now . . . I dunno.)

Unquote.

Remember when they said allowing same-sex couples to marry would “destroy the institution of marriage”? 

I’ll say it again. When the authoritarians hear “we’re all in this together”, they think it’s a threat.