Bias tests look for violations of basic universal properties of rational belief such as subadditivity of probabilities or anchoring on randomly-generated numbers. I propose a new one for the temporal consistency of beliefs: agents who believe that the net evidence for a claim c from t1 to t2 is positive or negative must then satisfy the inequalities that P(c, t1)<P(c, t2) & P(c, t1)>P(c, t2), respectively. A failure to update in the direction of the believed net evidence indicates that nonrational reasons are influencing the belief in c; the larger the net evidence without directional updates, the more that nonrational reasons are influencing c. Extended to a population level, this suggests that a heuristic measurement of the nonrational grounds for belief can be conducted using long-term public opinion surveys of important issues combined with contemporary surveys of estimated net evidence since the start of the opinion surveys to compare historical shifts in public opinion on issues with the net evidence on those issues.
A friend of yours tells you he’s worried he saw a snake on his driveway yesterday which he thinks may be a poisonous coral snake rather than a harmless snake; he gives it 50-50 chance - it looked a lot like a coral snake, but he didn’t think this state had any poisonous snakes. You see him the next day and ask him about the snake. “Terrible news!” he says. “I looked it up on Wikipedia, and turns out, this state does have poisonous snakes, coral snakes even.” How unfortunate. So what probability does he think it is a coral snake? His probability must have gone up, after all. “Oh, 50-50.” What? Is he sure about that? “Sure I’m sure. I still wonder if it was a coral snake or not…” Your friend is fond of gambling, so you know he has not misspoken; he knows what a probability is. You politely end the conversation and conclude that while you have little idea if it was a coral snake or not, you do know your friend is fundamentally not thinking straight on the issue of snakes: he understood that he found net evidence for the snake being a coral snake, but somehow did not update his beliefs in the right direction. Whatever his thinking process, it is non-rational; perhaps he has herpetophobia and is in denial, or has some reason to lie about this.
It can be hard to decide whether someone’s conclusions are irrational because they could have different priors, have different causal models, have been exposed to different evidence, have different preferences, and so on. But there are a few hard rules for bare minimums of rationality: no contradictions; conjunctions are equally or less likely than any of their conjuncts; disjunctions are equally or more likely than any disjuncts; probabilities of exhaustive sets of claims sum to 1; 0 and 1 are not degrees of belief; and - net evidence for a claim increases the posterior probability of that claim. (Or to put it another, per Bayes rule , for arbitrary P(A) and P(), if P(B|A) > 1 then P(A|B) > P(A); is a contradiction.) And what applies to coral snakes applies to everything else - if your friend agrees evidence suggests his pool was a bad buy, he should be less optimistic about it than he was when he bought it, and so on. Your friend might have totally different priors or causal models or life experiences or political affiliations, but whatever they are, he still must make his net evidence and update direction jive. Updating is not sufficient for rationality (one can still have wrong models which indicate something is net evidence which shouldn’t be, or update too much, or be irrational on other matters) and updating doesn’t itself show notable rationality (perhaps one was just profoundly ignorant about a topic), but it is necessary.
We can broaden it further beyond individuals. If someone fails to update their earlier estimate towards their claimed weight of evidence, then they are wrong. What about everyone else? If you surveyed your neighbors and your friend, they would agree that however much one should believe it was a coral snake, upon learning that coral snakes do in fact live around here, it is terrible news and evidence for the snake being a coral snake. They might not agree with a starting 50% probability, and might argue about whether the Wikipedia article should matter a lot or a little (“whenever I check a WP article, it’s always vandalized”), but they would agree that the evidence is in favor of a coral snake and that the correct increase is definitely not 0% or -5%, and anyone who changes their belief that way is just wrong. Hence, for your neighborhood as a whole, each person is wrong if they don’t change their earlier probability upwards.
Can we broaden it further? If (for some reason, perhaps because we too suffer from herpetophobia) we have surveys of your neighbors about the risk of snakes on their part of this mortal plane going back decades, then we can employ the same trick: ask them what they think the weight of evidence about coral snakes is, and their current probability, and compare to their old probability.
Can we broaden it further? There are few long-term surveys of opinions of the same people, so this heuristic is hard to apply. But what applies to your neighborhood should also generally apply to populations over time, barring relatively exotic changes in population composition like natural selection for high religiosity priors. Now we ask everyone what they think, or they think the general population thinks, the net weight of evidence has been. (Somewhat like Bayesian truth serum.) If there is some issue which 100 years ago split the population 50-50 on, and everyone agrees that events/data/research since then have generally favored one side of the issue, and everyone is also meeting bare minimums of rationality, we should see that weight of evidence reflected in proportions shifting towards the winning side. We definitely do not expect to see surveys reporting the split remains exactly 50-50. If it does, it suggests that the population is not dealing with the issue rationally but for other reasons like personal advantage or politics or cognitive biases.
(Or possibly we messed up somehow. For example, we’ve misunderstood the survey questions: terminology or popular understanding could have changed to the point where the position of one side has become different to its position now, in the same way that American political party platforms of 2000 bear scarcely any resemblance to those of 1900 of the same name, or how the Christianity of 500 AD differed drastically from 100 AD.)
These directions do not need to be the exactly same over all time periods or for all issues. For example, consider the question of whether there is alien life on other planets in the Solar system or in other solar systems in the universe from the period 1500 to 1900, 1900 to 2016, and 1500 to 2016. Isaac Newton and other natural philosophers speculated about life on other planets and throughout the universe, and I think the net weight of evidence as astronomy and biology progressed was heavily on the possibility of life with an ever-expanding universe to generate life somewhere, and so the direction of belief would have been increasing towards 1900 for life in the Solar system and universe; but then, as progress continued further, there was a drastic reversal of fortune - the canals on Mars were debunked, spectroscopy showed no signatures of life, the launch of space probes showed that Venus was not a garden planet but a sulfuric-rain molten-lead hellhole while Mars was a freeze-dried husk of sand sans life; and after the abrupt extinguishing of hopes for Solar life, Enrico Fermi famously asked ‘where are they’ with no hints of radio activity or stellar engineering after billions of years even as development of rocketry and space technology demonstrated that advanced alien civilizations could colonize the entire galaxy in merely millions of years. And who knows, perhaps some clear signal of life will yet be discovered and the weight of evidence will abruptly swing back in favor of life in the universe. Another example might be behavioral genetics and intelligence tests, for which there is an extraordinary disparity between expert beliefs and the general public’s beliefs, and for which an equally extraordinary amount of evidence has been published in the past decade on the role of genetics in individual differences in everything from human evolution over the past few thousand years to the presence of dysgenics to the genetic bases of intelligence/personality/income/violence/health/longevity; surveyed experts would doubtless indicate strong weights of evidence against the long-dominant blank slatism and show accordingly changed beliefs, and a survey of the general public might show little or no weights of evidence and belief shifts - but that is not evidence for strongly nonrational public beliefs because it might simply reflect considerable ignorance about the scientific research, which have been minimally reported on and when reported on, the meaning & implications minimized. So depending on the time period, question, and group the update might be up or down - but as long as it’s consistent, that’s fine.
An example of an application of the net evidence heuristic might be cryonics. Many objections were raised to cryonics at the start: religious and dualist objections; cell lysosomes would ‘explode’ immediately after death, erasing all information before vitrification; personality and memories were encoded in the brain not as stable chemical or biological structures but as complex electrical dynamics which would be erased immediately upon death; cryonics organizations would disappear or would routinely fail to keep corpses at liquid nitrogen temperatures; scanning technology would never be able to scan even a small fraction of a brain and Moore’s law would halt long before coming anywhere near the equivalent of a brain, rendering upload permanently impossible; nuclear war would obviate the issue along with Western civilization, or if not that, then the long-anticipated hyperinflation of the US dollar would bankrupt cryonics organizations; laws would be passed forbidding the practice; angry mobs of religious fanatics would destroy the facilities; the expense would be far too much for anyone but millionaires to afford; and so on. Given all this, it is unsurprising that cryonics was not super cool and few people believed in it or did it. I don’t know of any surveys, but as a proxy, the number of memberships of early cryonics groups and later ALCOR suggest that cryonics could count perhaps a few hundred or perhaps thousand out of the US population of 180m in the 1960s or so. In the half-century since then, cryonics has survived all challenges: materialism is the order of the day; lysosomes do not explode; personality and memory are not encoded as anything fragile but as durable properties of the brain; cryonics organizations using the nonprofit model have done well at surviving and keeping all corpses stored without ever thawing; scanning technology has advanced massively and it is now conventional wisdom that at some point it may be possible to scan a brain; Moore’s law has continued the whole time; there have been no serious legal danger to cryonics in the USA, nor have there ever been any riots or lynch mobs; median American household real income has increased ~3x from 1960 to 2016; cryonics has demonstrated ever larger proofs of concept such as reviving a vitrified kidney and demonstrating that C. elegans memories are preserved upon revival; and in general neuroscience has moved strongly towards an information-theoretic point of view. I would say that the net weight of evidence for cryonics is massively positive. Cryonics has never looked more possible. So half a century later with this massive weight of evidence and a much wealthier & larger (~324m) US population (likewise globally), what membership numbers do we find for ALCOR and CI? We find… 1,101 members in September 2016 and 1446 respectively. In other words, far from increasing, it may actually have fallen per capita, implying beliefs about cryonics have gotten more pessimistic rather than optimistic.
What can we conclude from the size of weight of evidence and observed shifts or lack thereof? If we survey people asking for net weight of evidence, they will be probabilistically unsophisticated and it’s unlikely anyone, even experts, can easily assert that the claim “democracy is the best form of government” is exactly 2x as likely as in 1667; we might ask for a rating on a scale 1-5. We can look for surveys on a range of popular issues such as global warming, whether AI is possible, or atheism, and use the longest time-series we can for each issue to calculate a shift in belief odds. Then we can survey contemporary people and ask for their estimate of the weight of evidence. Finally, we can divide the rating by the odds shift to rank issues by how much changes in evidence correlates with shifts in belief. This ranking, a sort of “rationality quotient”, might be interesting and correlate with our intuitive expectations about in what areas are beliefs most non-rational. (My guess at some of the results: the durability of religious belief will likely contradict the weight of evidence, while AI and global warming will show more updating.)
Why might this method work? It might seem a bit akin to asking “do you think you are wrong about something?” to ask questions about weight of evidence and opinion changes, as the normative requirement here is so basic and guessable. Why would it help to split apart Bayesian updating and ask about such a specific part rather than focus on something more important like what the priors were or what the posterior probability is? But I think the method might work precisely because it splits apart absolute levels of belief from changes in beliefs: someone holding a particular belief like theism feels like it is a harmless question and can safely admit that the last few centuries haven’t been too great for theism, because it doesn’t threaten whether their belief is >50% in the way that a blunter question like “do you agree that theism has been debunked?” might - it would be socially undesirable to admit that one’s belief has fallen a large amount, but it is safe to admit that it has slipped an unspecified amount. This is similar to how Bayesian truth serum avoids self-serving biases by asking about other people (“do you use drugs?” “oh gosh no, I am a good person and not an addict” “how many people in your community use drugs?” “all of them”). The questions can also be split between respondents, limiting their ability to infer what test is being done and what normative standard responses are being compared against and adjust their responses.
If this works out, it offers something valuable: an objective, easy, widely-applicable test of long-run population rationality, which controls for individual differences in priors and causal models and knowledge.
A friend of yours tells you he’s worried he saw a snake on his driveway yesterday which he thinks may be a poisonous coral snake rather than a harmless snake; he gives it 50-50 chance - it looked a lot like a coral snake, but he didn’t think this state had any poisonous snakes. You see him the next day and ask him about the snake. “Terrible news!” he says. “I looked it up on Wikipedia, and turns out, this state does have poisonous snakes, coral snakes even.” How unfortunate. So what probability does he think it is a coral snake? His probability must have gone up, after all. “Oh, 50-50.” What? Is he sure about that? “Sure I’m sure. I still wonder if it was a coral snake or not…” Your friend is fond of gambling, so you know he has not misspoken; he knows what a probability is. You politely end the conversation and conclude that while you have little idea if it was a coral snake or not, you do know your friend is fundamentally not thinking straight on the issue of snakes: he understood that he found net evidence for the snake being a coral snake, but somehow did not update his beliefs in the right direction. Whatever his thinking process, it is non-rational; perhaps he has herpetophobia and is in denial, or has some reason to lie about this.
It can be hard to decide whether someone’s conclusions are irrational because they could have different priors, have different causal models, have been exposed to different evidence, have different preferences, and so on. But there are a few hard rules for bare minimums of rationality: no contradictions; conjunctions are equally or less likely than any of their conjuncts; disjunctions are equally or more likely than any disjuncts; probabilities of exhaustive sets of claims sum to 1; 0 and 1 are not degrees of belief; and - net evidence for a claim increases the posterior probability of that claim. (Or to put it another, per Bayes rule \propto P(A) \cdot P(B|A) "P(A|B) \propto P(A) \cdot P(B|A)")
, for arbitrary P(A) and P(), if P(B|A) > 1 then P(A|B) > P(A);  \le P(A)) \land (P(A) \gt 1) "(P(A|B) \le P(A)) \land (P(A) \gt 1)")
is a contradiction.) And what applies to coral snakes applies to everything else - if your friend agrees evidence suggests his pool was a bad buy, he should be less optimistic about it than he was when he bought it, and so on. Your friend might have totally different priors or causal models or life experiences or political affiliations, but whatever they are, he still must make his net evidence and update direction jive. Updating is not sufficient for rationality (one can still have wrong models which indicate something is net evidence which shouldn’t be, or update too much, or be irrational on other matters) and updating doesn’t itself show notable rationality (perhaps one was just profoundly ignorant about a topic), but it is necessary.
We can broaden it further beyond individuals. If someone fails to update their earlier estimate towards their claimed weight of evidence, then they are wrong. What about everyone else? If you surveyed your neighbors and your friend, they would agree that however much one should believe it was a coral snake, upon learning that coral snakes do in fact live around here, it is terrible news and evidence for the snake being a coral snake. They might not agree with a starting 50% probability, and might argue about whether the Wikipedia article should matter a lot or a little (“whenever I check a WP article, it’s always vandalized”), but they would agree that the evidence is in favor of a coral snake and that the correct increase is definitely not 0% or -5%, and anyone who changes their belief that way is just wrong. Hence, for your neighborhood as a whole, each person is wrong if they don’t change their earlier probability upwards.
Can we broaden it further? If (for some reason, perhaps because we too suffer from herpetophobia) we have surveys of your neighbors about the risk of snakes on their part of this mortal plane going back decades, then we can employ the same trick: ask them what they think the weight of evidence about coral snakes is, and their current probability, and compare to their old probability.
Can we broaden it further? There are few long-term surveys of opinions of the same people, so this heuristic is hard to apply. But what applies to your neighborhood should also generally apply to populations over time, barring relatively exotic changes in population composition like natural selection for high religiosity priors. Now we ask everyone what they think, or they think the general population thinks, the net weight of evidence has been. (Somewhat like Bayesian truth serum.) If there is some issue which 100 years ago split the population 50-50 on, and everyone agrees that events/data/research since then have generally favored one side of the issue, and everyone is also meeting bare minimums of rationality, we should see that weight of evidence reflected in proportions shifting towards the winning side. We definitely do not expect to see surveys reporting the split remains exactly 50-50. If it does, it suggests that the population is not dealing with the issue rationally but for other reasons like personal advantage or politics or cognitive biases.
(Or possibly we messed up somehow. For example, we’ve misunderstood the survey questions: terminology or popular understanding could have changed to the point where the position of one side has become different to its position now, in the same way that American political party platforms of 2000 bear scarcely any resemblance to those of 1900 of the same name, or how the Christianity of 500 AD differed drastically from 100 AD.)
These directions do not need to be the exactly same over all time periods or for all issues. For example, consider the question of whether there is alien life on other planets in the Solar system or in other solar systems in the universe from the period 1500 to 1900, 1900 to 2016, and 1500 to 2016. Isaac Newton and other natural philosophers speculated about life on other planets and throughout the universe, and I think the net weight of evidence as astronomy and biology progressed was heavily on the possibility of life with an ever-expanding universe to generate life somewhere, and so the direction of belief would have been increasing towards 1900 for life in the Solar system and universe; but then, as progress continued further, there was a drastic reversal of fortune - the canals on Mars were debunked, spectroscopy showed no signatures of life, the launch of space probes showed that Venus was not a garden planet but a sulfuric-rain molten-lead hellhole while Mars was a freeze-dried husk of sand sans life; and after the abrupt extinguishing of hopes for Solar life, Enrico Fermi famously asked ‘where are they’ with no hints of radio activity or stellar engineering after billions of years even as development of rocketry and space technology demonstrated that advanced alien civilizations could colonize the entire galaxy in merely millions of years. And who knows, perhaps some clear signal of life will yet be discovered and the weight of evidence will abruptly swing back in favor of life in the universe. Another example might be behavioral genetics and intelligence tests, for which there is an extraordinary disparity between expert beliefs and the general public’s beliefs, and for which an equally extraordinary amount of evidence has been published in the past decade on the role of genetics in individual differences in everything from human evolution over the past few thousand years to the presence of dysgenics to the genetic bases of intelligence/personality/income/violence/health/longevity; surveyed experts would doubtless indicate strong weights of evidence against the long-dominant blank slatism and show accordingly changed beliefs, and a survey of the general public might show little or no weights of evidence and belief shifts - but that is not evidence for strongly nonrational public beliefs because it might simply reflect considerable ignorance about the scientific research, which have been minimally reported on and when reported on, the meaning & implications minimized. So depending on the time period, question, and group the update might be up or down - but as long as it’s consistent, that’s fine.
An example of an application of the net evidence heuristic might be cryonics. Many objections were raised to cryonics at the start: religious and dualist objections; cell lysosomes would ‘explode’ immediately after death, erasing all information before vitrification; personality and memories were encoded in the brain not as stable chemical or biological structures but as complex electrical dynamics which would be erased immediately upon death; cryonics organizations would disappear or would routinely fail to keep corpses at liquid nitrogen temperatures; scanning technology would never be able to scan even a small fraction of a brain and Moore’s law would halt long before coming anywhere near the equivalent of a brain, rendering upload permanently impossible; nuclear war would obviate the issue along with Western civilization, or if not that, then the long-anticipated hyperinflation of the US dollar would bankrupt cryonics organizations; laws would be passed forbidding the practice; angry mobs of religious fanatics would destroy the facilities; the expense would be far too much for anyone but millionaires to afford; and so on. Given all this, it is unsurprising that cryonics was not super cool and few people believed in it or did it. I don’t know of any surveys, but as a proxy, the number of memberships of early cryonics groups and later ALCOR suggest that cryonics could count perhaps a few hundred or perhaps thousand out of the US population of 180m in the 1960s or so. In the half-century since then, cryonics has survived all challenges: materialism is the order of the day; lysosomes do not explode; personality and memory are not encoded as anything fragile but as durable properties of the brain; cryonics organizations using the nonprofit model have done well at surviving and keeping all corpses stored without ever thawing; scanning technology has advanced massively and it is now conventional wisdom that at some point it may be possible to scan a brain; Moore’s law has continued the whole time; there have been no serious legal danger to cryonics in the USA, nor have there ever been any riots or lynch mobs; median American household real income has increased ~3x from 1960 to 2016; cryonics has demonstrated ever larger proofs of concept such as reviving a vitrified kidney and demonstrating that C. elegans memories are preserved upon revival; and in general neuroscience has moved strongly towards an information-theoretic point of view. I would say that the net weight of evidence for cryonics is massively positive. Cryonics has never looked more possible. So half a century later with this massive weight of evidence and a much wealthier & larger (~324m) US population (likewise globally), what membership numbers do we find for ALCOR and CI? We find… 1,101 members in September 2016 and 1446 respectively. In other words, far from increasing, it may actually have fallen per capita, implying beliefs about cryonics have gotten more pessimistic rather than optimistic.
What can we conclude from the size of weight of evidence and observed shifts or lack thereof? If we survey people asking for net weight of evidence, they will be probabilistically unsophisticated and it’s unlikely anyone, even experts, can easily assert that the claim “democracy is the best form of government” is exactly 2x as likely as in 1667; we might ask for a rating on a scale 1-5. We can look for surveys on a range of popular issues such as global warming, whether AI is possible, or atheism, and use the longest time-series we can for each issue to calculate a shift in belief odds. Then we can survey contemporary people and ask for their estimate of the weight of evidence. Finally, we can divide the rating by the odds shift to rank issues by how much changes in evidence correlates with shifts in belief. This ranking, a sort of “rationality quotient”, might be interesting and correlate with our intuitive expectations about in what areas are beliefs most non-rational. (My guess at some of the results: the durability of religious belief will likely contradict the weight of evidence, while AI and global warming will show more updating.)
Why might this method work? It might seem a bit akin to asking “do you think you are wrong about something?” to ask questions about weight of evidence and opinion changes, as the normative requirement here is so basic and guessable. Why would it help to split apart Bayesian updating and ask about such a specific part rather than focus on something more important like what the priors were or what the posterior probability is? But I think the method might work precisely because it splits apart absolute levels of belief from changes in beliefs: someone holding a particular belief like theism feels like it is a harmless question and can safely admit that the last few centuries haven’t been too great for theism, because it doesn’t threaten whether their belief is >50% in the way that a blunter question like “do you agree that theism has been debunked?” might - it would be socially undesirable to admit that one’s belief has fallen a large amount, but it is safe to admit that it has slipped an unspecified amount. This is similar to how Bayesian truth serum avoids self-serving biases by asking about other people (“do you use drugs?” “oh gosh no, I am a good person and not an addict” “how many people in your community use drugs?” “all of them”). The questions can also be split between respondents, limiting their ability to infer what test is being done and what normative standard responses are being compared against and adjust their responses.
If this works out, it offers something valuable: an objective, easy, widely-applicable test of long-run population rationality, which controls for individual differences in priors and causal models and knowledge.