Coherentism, Dutch Books, and Inadequate Data
Why politics is very difficult
1 A Dutch book, politician, and guy named Ludwig walk into a bar
“Jar one has in it a number that’s smaller than the number in jar two. Jar three has a number in it. Do you think jar three has a bigger number than jar two?” asked the sentient Dutch book.
“How should I know,” said Ludwig, unfamiliar with Dutch book arguments.
“I believe that jar three has a much larger number and that we’re going to take that number to Washington,” said the second observer, who happened to be a politician.
“Okay,” said the Dutch book. “So you’d say you’re 50/50 on jar two having a bigger number than jar three.”
“Yes,” said Ludwig.
“Would you also say you’re 50/50 on Jar one having a bigger number than jar three.”
“Yes,” said Ludwig again. “I have no evidence either way.”
“So your probability assessment does not change between two numbers, even though you know one of them is larger than the other.”
“Hmm… that does not seem right.”
Dutch book (condescendingly): “Okay, so now let’s say that we know that number 4 is bigger than number 2, number 5 is bigger than number 4, number 6 is bigger than number 5, etc. Surely number 10000000000000000000000000000000000000000000000 is predicted to be larger than number 3.”
Ludwig: “I suppose.”
Dutch book: “You’ve committed yourself to a contradiction. The problem is, if you have imprecise probabilities then you think that even though A>B A and B can both likely = C, in terms of their expected value. However, if the expected value of A=C and B=C then A=B. However, we’ve stipulated that A does not equal C. So all this is a fancy way of saying that you have to have precise probabilities and update on the evidence.”
Ludwig: “Okay, but what does this have to do with politics broadly.”
Dutch book: “We’ll get to that. But now suppose that we know that jar one has a negative number. At this point, what number would you predict is the most likely minimum number to be greater than jar three.”
Ludwig: “I don’t know.”
Dutch book: “I’m not asking about knowledge, I’m asking about probabilistic assessments. Are you really saying you think it’s equally likely across all numbers.”
Ludwig: “Yes.”
Dutch book: “So you’d say the odds of it being in the first 100^100^100^100^100^100^100 numbers is zero, because each number has equal odds and 100^100^100^100^100^100^100/ infinity equals zero.”
Ludwig: “No, that doesn’t seem right.”
Dutch book: “That’s why you need to assign credence’s. For me I’d say somewhere around 9.”
Ludwig: “But didn’t you pull that number out of nowhere.”
Dutch book: “Well, that number came from my best intuitive assessment of the evidence. None of the evidence is very good. But we have to assign credence’s, otherwise our opinion becomes unchanged by more evidence. Consider another case. What do you think the odds are that jar three has a bigger number than jar thirteen.”
Ludwig: “I don’t know.”
Dutch book: “And what odds do you think that jar three has a bigger number than jar fifty.”
Ludwig: “I don’t know.”
Dutch book: “So your credence is equal for both numbers, even though 50 is strictly less likely to be smaller than three than thirteen. Imagine you had to assign betting odds to each case. You can’t opt out. What odds would you assign for jar three having a bigger number than jar fifty.”
Ludwig: “Hmm… 1%.
Dutch book: “Okay, still can’t opt out, what odds would you assign to jar three having a bigger number than jar thirteen.”
Ludwig: “Hmm… I guess 25%.”
Dutch book: “Okay, that’s reasonable. The broad point is that ‘I don’t know,’ isn’t a good enough answer if you have to make a choice—otherwise you don’t update on the evidence and you can, through a series of mutually agreed upon bets be bled out of all of your money.”
Ludwig: “Okay, this all makes sense—but like, the title of the article talked about politics and coherentism and also a politician was brought in for no reason so like—what does this have to do with politics.”
Dutch book: “Well, let’s say you feel confident that a simplified earned income tax credit, which just pays money to low income workers, would be better policy than a minimum wage. However, there’s no empirical data on whether or not the minimum wage is good or bad. What odds would you give to the minimum wage being good.”
Ludwig: “Well, I’d say 50/50, no evidence either way.”
Politician: (looks into camera) “You know Dutch book, I believe people deserve a living wage.”
Dutch book: “And there’s also no data about the earned income tax credit. How likely would you say it is that it’s good.”
Ludwig: “50/50, no evidence either way.”
Dutch book: “But surely you know that the phrase no evidence is misleading. Additionally, you’ve made the exact mistake that we talked about earlier. You know that earned income tax credits are better than minimum wage increases but you assign equal probability to each of them being good. If we know that A is better than B then A has to be more likely to be good than B.”
Ludwig: “I suppose.”
Dutch book: “So you have to give precise credences to these things. To have a coherent utility function that can’t be money pumped, you have to have probabilities be precise. If you think that a minimum wage is probably good, on any plausible assumptions, raising the minimum wage to 11 dollars from what it is currently is more likely to be good than raising it from 11 to 17 dollars. So now I ask you again—what’s your probability that raising the minimum wage to 11 dollars an hour is good.”
Ludwig: “Well, assuming no other information, I’d say about 41% and maybe 60% for the earned income tax credit.”
Dutch book: “Okay good, you have precise credence’s. That’s why you can’t be agnostic about political issues, you have to assign credences, even if you have limited information. But here’s why politics is so difficult. We have to assign precise credences to things—we can’t just say we’re unsure or things are ‘probably good.’ However, all of our beliefs are wrapped up in (hopefully) coherent webs of beliefs. But when everything is conditional on everything else and then new information comes in it can skew the ideal probability in weird ways. That’s why politics becomes so difficult. If I think that universal healthcare and the minimum wage are great policies those will likely influence lots of views. If I later find out that they’re likely bad then that shifts the probability distribution of all my views. But there’s also a problem of trapped priors . Let’s say I start out very confident that the minimum wage is bad. This informs many of my views on other things. I think that policies like the minimum wage are also necessarily very bad. I think that people who support the minimum wage are obviously foolish—their support for the minimum wage counts against taking them seriously. Well, I conclude that all the smart people who understand economics are uniformly against rent control and the earned income tax credit. So I conclude that rent control and the earned income tax credit are obviously bad. And then I realize that the people who have an iota of understanding of the basic economics of the minimum wage and rent control are all really strongly anti Biden. So I conclude that Biden must be terrible. And those people are concerned about a rigged election, so I conclude the election must be rigged.”
Ludwig: “I didn’t realize Dutch books had echo chambers—but that makes sense.”
2 You’d think after the Dutch book, the other two would have ducked
As I’ve gotten older I’ve become less confident about my political views. When I was thirteen or so, I thought that people who disagreed with me were obviously wrong and ignorant of basic economics. However, over time I’ve realized that this assumption was false—many were wrong and ignorant of basic economics, but many others were quite smart and knew more about economics than I did. The fundamental problem of politics is two fold.
1 Even if there were a good way to make political decisions no one would do it. A lot of people watch fox news or cnn. I think it’s safe to say that watching fox news or cnn are not the best ways to form true political beliefs. They tend to only represent their own parties talking points. But perhaps more insidiously, the constant barrage of negative sentiment toward one political party makes it very difficult to ever support that political party. Repeatedly building up negative affect makes people increasingly confident in their views—but the process that lead them to their views was not a rational process. If I watch every day embarrassing stories about Trump or Biden, over time I’ll feel increasingly confident that they’re very bad.
When I hear people praise Biden (same applies to Trump, but I’ll just talk about Biden to save words) I’ll think that they’re ignorant—but not ignorant in a way that can be broken down into concrete facts. They’re ignorant of the general narrative that I hold to be correct, a narrative whose focal point is roughly “Biden bad, very very bad.” They’re ignorant the same way that a person who claims that love is not valuable is ignorant. But this very strong sentiment wasn’t caused by rational argument, so rational arguments can’t dissuade me of the sentiment.
This causes me to dismiss those who praise Biden, and defer to those who criticize him—causing me to be more confident of my views. I’ll presumably listen to the people who talk about how terrible Biden is more, so I’ll be inundated with messages confirming my narrative. And the messages confirming my narrative will be the same amorphous sentiment building message that made me confident of my narrative in the first place. I’ll watch fox news and frequently hear stories about migrants committing crime, and democrats excusing looting and rioting, burning down cities. I’ll hear about super high gas prices in individual areas and democrats attempting to cancel Christmas. I’ll hear horror stories about long wait lines in Canada for healthcare, of five year old’s dying because they can’t get a routine medical treatment.
If I try to argue these points to my liberal friends, they’ll laugh, because the arguments are not very good. The fact that there are several gruesome stories of immigrants murdering people in brutal ways isn’t a good argument against immigration. The fact that one five year old died from inability to get a routine medical treatment is not a very good argument against universal healthcare. But it’s sure as hell a good way of getting a person who is already against universal healthcare or immigration to be stronger in their convictions.
If you’re a democrat reading this, you’re probably feeling very happy at this point at my criticism of those ignorant, dumb republicans. Well, because it’s important to piss off everyone reading this, I shall point out the obvious: this applies to you too.
I’ll preface this by saying I’m extremely pro covid vaccine. I think it’s unambiguously a good thing. However, it is obvious that frequent commentary about anti-vaxxers dying of covid is the same type of political message. The point is to just communicate a general sentiment—that those stupid anti-vaxxers who won’t get the vaccine keep dying. If you think this is a good argument, consider how you’d feel if an antivaxxer made a similar argument. If an MSNBC host died of covid after getting the vaccine, that would obviously be a terrible argument against getting vaccinated.
There’s constant coverage of people showing up at schoolboard meetings and doing terrible things. This coverage occurs with no quantitative data on how much it’s happening. It’s not clear what information people should gain from this coverage—other than the fact that sometimes people yell or are violent at school meetings. However, reading a constant stream of stories of people violently showing up to schoolboard meetings causes people to internalize the message that right wingers concerned about mask mandates, online learning, and crt in schools are violent fascists. This constant coverage inoculates people to considering arguments for the conservative positions. Note, I’m not taking any stance on how correct any of the positions are—merely on the bad ways people form political beliefs.
When Joe Rogan got covid, there was frequent coverage of him taking Ivermectin, which was frequently referred to as horse dewormer. I think criticism of Rogan was very reasonable—Ivermectin likely does not work for covid. However, the constant referral to it as horse de-wormer was obviously misleading. Yes, covid is used as a horse de-wormer. It is also used as a human dewormer. Ivermectin is a real drug that works for treating some things—it just doesn’t seem to work for treating covid. But constant coverage of ivermectin as horse dewormer makes it very easy to dismiss evidence for it out of hand as conjured up by crackpots taking horse dewormer.
If you don’t think that this coverage was seriously misleading, you might have brain worms and perhaps should take Ivermectin :). Imagine if the covid vaccine also could be given to bats to treat pneumonia. You would surely find it misleading if a headline was “Biden gets pneunomnia treatment for bats.”
But the problem is, egregious misrepresentations get used by the other side as evidence that what you’re saying is nonsense. Tons of conservative outlets and pro ivermectin outlets covered the eggregious misrepresentation. So now, rather than engaging with credible people like Avi Bitterman , who argue compellingly against Ivermectin, the main takeaway from those who are pro Ivermectin is that the people opposed to Ivermectin have two arguments.
1 Falsely claiming that there’s no evidence for Ivermectin working. This is false—there’s certainly some evidence, better evidence just seems to contradict the theory.
2 Mocking Ivermectin as horse paste.
So now everyone leaves the Ivermectin dispute more sure that they’re right and entirely ignorant of best version of the other side’s arguments. This is bad.
Remember when a bunch of paragraphs back I said there are two basic problems with politics. Well, that was all an explanation of the first one. The second one is that there are just way too many variables to be able to form accurate beliefs about things.
Suppose I think there’s a 40% chance that a 15 dollar per hour minimum wage is good, a 90% chance that the EITC is better than the minimum wage, a 50+x credence in the desirability of unions, where x is half the credence I have in the desirability of the minimum wage, 30% + 1/2 x credence in universal healthcare being good, and a credence in democrats of being better than republicans of 60% + 5% multiplied by (my credence in the desirability of unions plus my credence in the desirability of universal healthcare). I then learn that the economy does better under democrats, so I increase my credence in democrats being better, which spills over to increasing my credence in all the aforementioned policies being good. I then discover solid evidence that universal healthcare is bad, leading my credence in universal healthcare being good to become 10%. What should by credence be in the minimum wage now?
I have no knowledge of math beyond AP statistics and calculus, but I’ve heard that matrices allegedly can be used for problems like this. Regardless, even with a very simple system with only four policies and two political parties updating on the evidence becomes nearly impossible to do consistently with my existing assumptions. It’s thus not surprising that people pick a side and then just go with whatever their side says.
In Jason Brennan’s book, an Intro to Political Philosophy, Brennan spends chapter 2 largely talking about utilitarianism. However, he quickly dismisses it based on thought experiments about utility monsters and walking away from omelas, and never revisits it. In later chapters, he discusses many of the difficult problems of political philosophy, which are easily solved by utilitarianism, but never mentions how utilitarianism solves them. Because Brennan dismissed it so quickly, he considered the probability of it being correct to be negligible, and he didn’t consider it’s broader ability to solve political problems. I think that there are pretty knock-down arguments for sacrificing everything to the utility monster and to staying in Omelas—but I think that even if Brennan were convinced that those objections failed, he would not be a utilitarian, for he spent so much time considering it bunk, that he ignored its advantages. This is the danger that lies in this belief forming web process. Sometimes, one’s web of beliefs can be fully orthogonal from the correct positions.
I’ve had views that I once regarded to be obviously true, that I now regard to be false. I once was extremely opposed to increases to the minimum wage. Now I’m probably in favor of some increases to the minimum wage. Previously I was pretty uncertain as to whether welfare was good. I am now pretty sure that it’s a good thing. A lot of this came from seeing empirical data measuring the efficacy of these things and realizing that my basic assumptions were wrong. Enough pillars of my political beliefs being uprooted caused my whole world view to shift, and pretty dramatically. But this is pretty rare. This happened mostly between the age of 15 and 17. Our beliefs are more malleable when we’re young, and I was exposed to more information by those who I regarded as clearly wrong than most people are. But many people can remain locked in terrible beliefs permanently. Priors can get completely stuck. Most people don’t change their political views much in response to contrary evidence.
You probably think that because you’re a person who reads interesting blogs like this and thinks about issues a lot, you’re immune from having a whole coherent web of false beliefs. Well, you’re probably not. Kahan conducted a study in which people were given math problems. Being better at math made them more likely to get the right answer. At first. Then, Kahan made the math problems politicized, so that getting the right answer meant betraying people’s political instincts. People who were anti gun control were given math problems, for which the correct solution found that gun control reduced crime. People who were pro gun control were given problems for which the correct answer found it increased crime. After this twist was introduced, being better at math made subjects less likely to get the correct answer. That’s… weird.
Well, people who were better at math were able to use their superior math skills to rationalize away the fact that the math contradicted their political views.
Another study found that Republicans and democrats have wildly inaccurate views of what their opponents believe. Republicans and democrats think that the other party is more than twice as likely to hold views that they consider extreme as the other party actually is to hold those views. Now, maybe you think that because you’re smart and educated you’re immune from this. Well, it turns out that more educated people were less accurate. Additionally, the more news people consumed, the less accurate they became. This provides solid evidence for the hypothesis that I outlined.
Lots of democrats think that opposition to abortion is motivated by a desire to control women’s bodies. This is obviously false. Women are actually slightly more pro life than men. When conservatives argue against abortion, they don’t do it on the basis of wanting to control women’s bodies. Presupposing that those who disagree with you have a secret, explicitly misogynist agenda, that’s supported by a large percentage of women is quite unreasonable. Any time you think your opponents aim is to make life worse for a large percentage of people, you are almost certainly wrong.
Similarly, it is unreasonable when republicans think that a large percentage of democrats have an explicit desire to make white children feel bad. The whole conversation about CRT is hopelessly muddled and ill defined. However, the aim of pro CRT people is about racial equality, not causing people to be worse off. Most people are well intentioned most of the time. However, it’s very easy to think they’re not when one is fed a constant stream of negative emotes directed at one’s political opponents.
So what should be done about this? I’m not sure that there’s a great solution. People should stop demonizing each other and should try to figure out what other people actually believe. Also, people should listen to news with which they politically disagree. Finally, people should be less confident in their political views. There are almost certainly very smart people who disagree with you on any issue. For most political views about which there are difficult disputes, I think it’s hard to have above 80% confidence that your side is right. Also, people should read non partisan sources of information—say for example blogs. In terms of good blogs that people should read, the most notable one is surely… no, modesty prevents me from finishing this sentence.