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83cd0c438e
Author | SHA1 | Date |
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Nuno Sempere | 83cd0c438e | 1 year ago |
Nuno Sempere | 29ad7c3156 | 1 year ago |
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## Libraries
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library(ggplot2)
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## Read data
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setwd("/home/loki/Documents/core/ea/fresh/misc/ea-hbd") ## change to the folder in your computer
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data <- read.csv("2020ssc_public.csv", header=TRUE, stringsAsFactors = FALSE)
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## Restrict analysis to EAs
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data_EAs <- data[data["EAID"] == "Yes",]
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View(data_EAs)
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n=dim(data_EAs)[1]
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n
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## Find biodiversity question
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colnames(data_EAs)
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colnames(data_EAs)[47]
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## Process biodiversity question for EAs
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tally <- list()
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tally$options = c(1:5, "NA")
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tally$count = sapply(tally$options, function(x){ sum(data_EAs[47] == x, na.rm = TRUE) })
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tally$count[6] = sum(is.na(data_EAs[47]))
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tally$count
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tally = as.data.frame(tally)
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tally
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## Plot prevalence of belief within EA
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titulo='Prevalence of attitudes towards "human biodiversity"\n amongst EA SlateStarCodex survey respondents in 2020'
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subtitulo='"How would you describe your opinion of the the idea of "human biodiversity",\n eg the belief that races differ genetically in socially relevant ways?"\n (1 = very unfavorable, 5 = very favorable), n=993'
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(ggplot(data = tally, aes(x =options, y = count)) +
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geom_histogram(
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stat="identity",
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position= position_stack(reverse = TRUE),
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fill="navyblue"
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))+
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scale_y_continuous(limits = c(0, 300))+
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labs(
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title=titulo,
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subtitle=subtitulo,
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x="answers",
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y="answer count",
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legend.title = element_blank(),
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legend.text.align = 0
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)+
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theme(
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legend.title = element_blank(),
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plot.subtitle = element_text(hjust = 0.5),
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plot.title = element_text(hjust = 0.5),
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legend.position="bottom"
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) +
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geom_text(aes(label=count, size = 2), colour="#000000",size=2.5, vjust = -0.5)
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height=5
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width=height*(1+sqrt(5))/2
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ggsave("q_hbd_EAs.png" , units="in", width=width, height=height, dpi=800)
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## Process biodiversity question for all SSC respondents
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tally2 <- list()
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tally2$options = c(1:5, "NA")
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tally2$count = sapply(tally2$options, function(x){ sum(data[47] == x, na.rm = TRUE) })
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tally2$count[6] = sum(is.na(data[47]))
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tally2$count
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n=dim(data)[1]
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n
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tally2 = as.data.frame(tally2)
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tally2
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tally
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## Plot
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titulo='Prevalence of attitudes towards "human biodiversity"\n amongst all SlateStarCodex survey respondents in 2020'
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subtitulo='"How would you describe your opinion of the the idea of "human biodiversity",\n eg the belief that races differ genetically in socially relevant ways?"\n (1 = very unfavorable, 5 = very favorable), n=7339'
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(ggplot(data = tally2, aes(x =options, y = count)) +
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geom_histogram(
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stat="identity",
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position= position_stack(reverse = TRUE),
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fill="navyblue"
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))+
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scale_y_continuous(limits = c(0, 2000))+
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labs(
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title=titulo,
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subtitle=subtitulo,
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x="answers",
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y="answer count",
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legend.title = element_blank(),
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legend.text.align = 0
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)+
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theme(
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legend.title = element_blank(),
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plot.subtitle = element_text(hjust = 0.5),
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plot.title = element_text(hjust = 0.5),
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legend.position="bottom"
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) +
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geom_text(aes(label=count, size = 2), colour="#000000",size=2.5, vjust = -0.5)
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height=5
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width=height*(1+sqrt(5))/2
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ggsave("q_hbd_all.png" , units="in", width=width, height=height, dpi=800)
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Prevalence of belief in "human biodiversity" amongst self-reported EA respondents in the 2020 SlateStarCodex Survey
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=====================================================================================================================
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Note: This post presents some data which might inform downstream questions, rather than providing a fully cooked perspective on its own. For this reason, I have tried to not really express many opinions here. Readers might instead be interested in more fleshed out perspectives on the Bostrom affair, e.g., [here](https://rychappell.substack.com/p/text-subtext-and-miscommunication) in favor or [here](https://www.pasteurscube.com/why-im-personally-upset-with-nick-bostrom-right-now/) against.
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## Graph
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![](https://i.imgur.com/xYy9frR.png)
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## Discussion
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### Selection effects
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I am not sure whether EAs who answered the EA forum are a representative sample of all EAs. It might not be, if SSC readers have shared biases and assumptions distinct from those of the EA population as a whole. That said, raw numerical numbers will be accurate, e.g., we can say that "at least 57 people who identified as EAs in 2020 strongly agree with the human biodiversity hypothesis".
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### Question framing effects
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I think the question as phrased is likely to *overestimate* belief in human biodiversity, because the phrasing seems somewhat inocuous, and in particular because "biodiversity" has positive mood affiliation. I think that fewer people would answer positively to a less inocuous sounding version, e.g., "How would you describe your opinion of the the idea of "human biodiversity",\n eg the belief that some races are genetically stupider than others? (1 = very unfavorable, 5 = very favorable)".
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For a review of survey effects, see [A review of two books on survey-making](https://forum.effectivealtruism.org/posts/DCcciuLxRveSkBng2/a-review-of-two-books-on-survey-making).
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### Interpreting as a probability
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This isn't really all that meaningful, but we can assign percentages to each answer as follows:
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- 1: 5%
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- 2: 20%
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- 3: 50%
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- 4: 80%
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- 5: 95%
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- NA: 50%
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The above requires a judgment call to assign probabilities to numbers in a Likert scale. In particular, I am making the judgment call that 1 and 5 correspond to 5% and 95%, rather than e.g., 0% and 100%, or 1% and 99%, based on my forecasting experience.
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And then we can calculate an implicit probability as follows
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```
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( 174 * 0.03 + 227 * 0.2 + 288 * 0.5 + 175 * 0.8 + 57 * 0.95 + 22 * 0.5) / 993
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```
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The above calculation outputs 0.4025..., which, in a sense, means that SSC survey respondents which self-identified as EA assigned, as a whole, a 40% credence to the human biodiversity hypothesis.
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### Comparison with all SSC respondents
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![](https://i.imgur.com/h7vllAm.png)
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## Code to replicate this
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In an R runtime, run:
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```
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## Libraries
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library(ggplot2)
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## Read data
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setwd("/home/loki/Documents/core/ea/fresh/misc/ea-hbd") ## change to the folder in your computer
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data <- read.csv("2020ssc_public.csv", header=TRUE, stringsAsFactors = FALSE)
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## Restrict analysis to EAs
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data_EAs <- data[data["EAID"] == "Yes",]
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View(data_EAs)
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n=dim(data_EAs)[1]
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n
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## Find biodiversity question
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colnames(data_EAs)
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colnames(data_EAs)[47]
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## Process biodiversity question for EAs
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tally <- list()
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tally$options = c(1:5, "NA")
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tally$count = sapply(tally$options, function(x){ sum(data_EAs[47] == x, na.rm = TRUE) })
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tally$count[6] = sum(is.na(data_EAs[47]))
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tally$count
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tally = as.data.frame(tally)
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tally
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## Plot prevalence of belief within EA
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titulo='Prevalence of attitudes towards "human biodiversity"\n amongst EA SlateStarCodex survey respondents in 2020'
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subtitulo='"How would you describe your opinion of the the idea of "human biodiversity",\n eg the belief that races differ genetically in socially relevant ways?"\n (1 = very unfavorable, 5 = very favorable), n=993'
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(ggplot(data = tally, aes(x =options, y = count)) +
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geom_histogram(
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stat="identity",
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position= position_stack(reverse = TRUE),
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fill="navyblue"
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))+
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scale_y_continuous(limits = c(0, 300))+
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labs(
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title=titulo,
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subtitle=subtitulo,
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x="answers",
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y="answer count",
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legend.title = element_blank(),
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legend.text.align = 0
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)+
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theme(
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legend.title = element_blank(),
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plot.subtitle = element_text(hjust = 0.5),
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plot.title = element_text(hjust = 0.5),
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legend.position="bottom"
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) +
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geom_text(aes(label=count, size = 2), colour="#000000",size=2.5, vjust = -0.5)
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height=5
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width=height*(1+sqrt(5))/2
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ggsave("q_hbd_EAs.png" , units="in", width=width, height=height, dpi=800)
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## Process biodiversity question for all SSC respondents
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tally_all_ssc <- list()
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tally_all_ssc$options = c(1:5, "NA")
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tally_all_ssc$count = sapply(tally_all_ssc$options, function(x){ sum(data[47] == x, na.rm = TRUE) })
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tally_all_ssc$count[6] = sum(is.na(data[47]))
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tally_all_ssc$count
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tally_all_ssc = as.data.frame(tally_all_ssc)
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tally_all_ssc
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tally
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## Plot
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titulo='Prevalence of attitudes towards "human biodiversity"\n amongst all SlateStarCodex survey respondents in 2020'
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subtitulo='"How would you describe your opinion of the the idea of "human biodiversity",\n eg the belief that races differ genetically in socially relevant ways?"\n (1 = very unfavorable, 5 = very favorable), n=993'
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(ggplot(data = tally_all_ssc, aes(x =options, y = count)) +
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geom_histogram(
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stat="identity",
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position= position_stack(reverse = TRUE),
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fill="navyblue"
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))+
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scale_y_continuous(limits = c(0, 2000))+
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labs(
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title=titulo,
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subtitle=subtitulo,
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x="answers",
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y="answer count",
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legend.title = element_blank(),
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legend.text.align = 0
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)+
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theme(
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legend.title = element_blank(),
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plot.subtitle = element_text(hjust = 0.5),
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plot.title = element_text(hjust = 0.5),
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legend.position="bottom"
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) +
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geom_text(aes(label=count, size = 2), colour="#000000",size=2.5, vjust = -0.5)
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height=5
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width=height*(1+sqrt(5))/2
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ggsave("q_hbd_all.png" , units="in", width=width, height=height, dpi=800)
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```
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The file 2020ssc_public.csv is no longer available in the [SSC blogpost](https://slatestarcodex.com/2020/01/20/ssc-survey-results-2020/), but it can easily be created from the .xlsx file, or I can make it available for a small donation to the AMF.
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<p><section id='isso-thread'>
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<noscript>Javascript needs to be activated to view comments.</noscript>
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</section></p>
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|
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There will always be a Voigt-Kampff test
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========================================
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In the film *Blade Runner*, the Voight-Kampff test is a fictional procedure used to distinguish androids from humans. In the normal course of events, humans and androids are pretty much indistiguishable, except when talking about very specific kinds of emotions and memories.
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Similarly, as language models or image-producing neural networks continue to increase in size and rise in capabilities, it seems plausible that there will still be ways of identifying them as such.
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<figure>
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<img src="https://i.imgur.com/a6JjlQT.jpg" alt="Image produced by DALLE-2" class="img-frontpage-center">
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<br><figcaption>Image produced by DALLE-2 with the prompt "Voight-Kampff test". Note the water mark at the bottom, as well as the inability to produce text.</figcaption>
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</figure>
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For example, for image models:
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- They may have watermarks or stenographic messages which could be used to detect them
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- They may have a bias towards particular types of prettiness or perfection
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- They may not render certain complicated details, like hands, teeth, letters, etc.
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- They may struggle with compositionality, light, consistency, etc.
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And for language models:
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- They may not have good models of things that humans don't often talk about, like intimate fears, shame, or the specific details of sexual attraction.
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- They may not be up to the latest news, if they are only trained on events up to a certain point in the past.
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- They may have a distinctly bland speech.
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- They may have catchphrases or favour certain ways of expressing themselves
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- They may struggle to produce original thoughts and ideas
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- They may have idiosyncratic challenges, like not being able to decode ASCII art, not getting certain jokes, etc.
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![](https://i.imgur.com/mSkUDyQ.png)
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*From left to right: original historical image, image of myself, combination of the two produced using DALLE-2 to modify the jacket to also have a white shirt. This is a small-scale example of how the idiosyncrasies that allow us to unmask DALLE-2 do not matter to its ability to produce value: I like the third image a lot and I am using it on my social media profiles.*
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But much like in the original *Blade Runner* movie, these details may not really matter for their economic impact, and the fact that a way exists at all of identifying them will be even less relevant. Similarly, the fact that DALLE-2 and other image models have difficulties correctly rendering teeth or objects in relationship to each other doesn't really reflect their current ability or future potential to replace many thousands of artists, and generally shape the demand curves of art.
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I was thinking about this because I was recently forecasting on a question about "AGI", where "AGI" was defined as a system that: "is capable of passing adversarial Turing test against a top-5% human, who has access to experts." But such a system might take a really long time to be developed, even if the economic impact of an AI system is pretty great, because such a system might still have its own idiosyncrasies.
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Ultimately, this makes me think that nitpicks and gotchas about ways to differentiate humans and machines aren't just all that relevant to predicting their future impact. What I care about is closer to the real-world impact of these machines.
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That's all for now.
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<p><section id='isso-thread'>
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<noscript>Javascript needs to be activated to view comments.</noscript>
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</section></p>
|
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<h1>EA no longer an expanding empire.</h1>
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<p>PS: Please don’t share this newsletter.</p>
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<p>In early 2022, the Effective Altruism movement was triumphant. Sam Bankman-Fried was very utilitarian and very cool, and there was such a wealth of funding that the bottleneck was capable people to implement projects. If you had been in the effective altruism community for a while, it was relatively easy to acquire funding. New organizations popped up like mushrooms.</p>
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<p>Now the situation looks different. Samo Burja has this interesting book on <a href="https://samoburja.com/wp-content/uploads/2020/11/Great_Founder_Theory_by_Samo_Burja_2020_Manuscript.pdf">Great Founder Theory</a>, from which I’ve gotten the notion of an “expanding empire”. In an expanding empire, like a startup, there are new opportunities and land to conquer, and members can be rewarded with parts of the newly conquered land. The optimal strategy here is <em>unity</em> in the face of adversity. EA in 2022 was just that, a united social movement playing together against the cruelty of nature and history.</p>
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<p>My sense is that the tendency for EA in 2023 and going forward will be less like that. With funding drying, EA will now have to economize and prioritize between different causes. Funding is now more limited, not only because the SBF empire collapsed, but also because the stock market collapsed, which means that Open Philanthropy—now the main funder once again—also has less money. And with economizing in the background, internecine fights become more worth it, because the EA movement isn’t trying to grow the pie together, but rather each part will be trying to defend its share of the pie. Fewer offices all over the place, fewer regrantors to fund moonshots. More frugality. You get the idea.</p>
|
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<p>But note that the EA community is mostly made out of very nice people trying their best to do good, so I expect that the above paragraphs will just describe a directional difference, rather than an absolute level.</p>
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<p>Personally, some steps to consider might be:</p>
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<ul>
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<li>Looking for other communities.
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<ul>
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<li>I’ve personally retreated a bit into forecasting and linux programming.</li>
|
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<li>And I’ve added comments and a <a href="https://nunosempere.com/.subscribe/">subscription option</a> to my <a href="https://nunosempere.com/blog/">blog</a>, to be a bit less dependent on the EA forum.</li>
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</ul>
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</li>
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<li>Explictly expecting less funding, fewer EA™ jobs.</li>
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<li>Re-evaluate earning to give.</li>
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</ul>
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|
@ -0,0 +1,21 @@
|
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EA no longer an expanding empire.
|
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=================================
|
||||
|
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PS: Please don't share this newsletter.
|
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|
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In early 2022, the Effective Altruism movement was triumphant. Sam Bankman-Fried was very utilitarian and very cool, and there was such a wealth of funding that the bottleneck was capable people to implement projects. If you had been in the effective altruism community for a while, it was relatively easy to acquire funding. New organizations popped up like mushrooms.
|
||||
|
||||
Now the situation looks different. Samo Burja has this interesting book on [Great Founder Theory](https://samoburja.com/wp-content/uploads/2020/11/Great_Founder_Theory_by_Samo_Burja_2020_Manuscript.pdf), from which I've gotten the notion of an "expanding empire". In an expanding empire, like a startup, there are new opportunities and land to conquer, and members can be rewarded with parts of the newly conquered land. The optimal strategy here is *unity* in the face of adversity. EA in 2022 was just that, a united social movement playing together against the cruelty of nature and history.
|
||||
|
||||
My sense is that the tendency for EA in 2023 and going forward will be less like that. With funding drying, EA will now have to economize and prioritize between different causes. Funding is now more limited, not only because the SBF empire collapsed, but also because the stock market collapsed, which means that Open Philanthropy—now the main funder once again—also has less money. And with economizing in the background, internecine fights become more worth it, because the EA movement isn't trying to grow the pie together, but rather each part will be trying to defend its share of the pie. Fewer offices all over the place, fewer regrantors to fund moonshots. More frugality. You get the idea.
|
||||
|
||||
But note that the EA community is mostly made out of very nice people trying their best to do good, so I expect that the above paragraphs will just describe a directional difference, rather than an absolute level.
|
||||
|
||||
Personally, some steps to consider might be:
|
||||
|
||||
- Looking for other communities.
|
||||
- I've personally retreated a bit into forecasting and linux programming.
|
||||
- And I've added comments and a [subscription option](https://nunosempere.com/.subscribe/) to my [blog](https://nunosempere.com/blog/), to be a bit less dependent on the EA forum.
|
||||
- Explictly expecting less funding, fewer EA™ jobs.
|
||||
- Re-evaluate earning to give.
|
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|
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no matter where you stand
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=========================
|
||||
<div style="margin-left: auto; margin-right: auto;">When in a dark night the chamber of guf whispers<br>that I have failed, that I am failing, that I'll fail<br>I become mute, lethargic, frightful and afraid<br>of the pain I'll cause and the pain I'll endure.<br><br>Many were the times that I started but stopped<br>Many were the balls that I juggled and dropped<br>Many the people I discouraged and spooked<br>And the times I did good, I did less than I'd hoped<br><br>And then I remember that measure is unceasing,<br>that if you are a good man, why not a better man?<br>that if a better man, why not a great man?<br><br>and if you are a great man, why not yet a god?<br>And if a god, why not yet a better god?<br>measure is unceasing, no matter where you stand<br></div>
|
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|
||||
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|
||||
|
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|
||||
<h1>Just-in-time Bayesianism</h1>
|
||||
|
||||
<h2>Summary</h2>
|
||||
|
||||
<p>I propose a variant of subjective Bayesianism that I think captures some important aspects of how humans<sup id="fnref:1"><a href="#fn:1" rel="footnote">1</a></sup> reason in practice given that Bayesian inference is normally too computationally expensive. I compare it to some theories in the philosophy of science and briefly mention possible alternatives. In conjuction with Laplace’s law, I claim that it might be able to explain some aspects of <a href="https://astralcodexten.substack.com/p/trapped-priors-as-a-basic-problem">trapped priors</a>.</p>
|
||||
|
||||
<h2>A motivating problem in subjective Bayesianism</h2>
|
||||
|
||||
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
|
||||
|
||||
|
||||
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||||
|
||||
|
||||
<!-- Note: to correctly render this math, compile this markdown with
|
||||
/usr/bin/markdown -f fencedcode -f ext -f footnote -f latex $1
|
||||
where /usr/bin/markdown is the discount markdown binary
|
||||
https://github.com/Orc/discount
|
||||
http://www.pell.portland.or.us/~orc/Code/discount/
|
||||
-->
|
||||
|
||||
|
||||
<p>Bayesianism as an epistemology has elegance and parsimony, stemming from its inevitability as formalized by <a href="https://en.wikipedia.org/wiki/Cox's_theorem">Cox’s</a> <a href="https://nunosempere.com/blog/2022/08/31/on-cox-s-theorem-and-probabilistic-induction/">theorem</a>. For this reason, it has a certain magnetism as an epistemology.</p>
|
||||
|
||||
<p>However, consider the following example: a subjective Bayesian which has only two hypothesis about a coin:</p>
|
||||
|
||||
<p>\[
|
||||
\begin{cases}
|
||||
\text{it has bias } 2/3\text{ tails }1/3 \text{ heads }\\
|
||||
\text{it has bias } 1/3\text{ tails }2/3 \text{ heads }
|
||||
\end{cases}
|
||||
\]</p>
|
||||
|
||||
<p>Now, as that subjective Bayesian observes a sequence of coin tosses, he might end up very confused. For instance, if he only observes tails, he will end up assigning almost all of his probability to the first hypothesis. Or if he observes 50% tails and 50% heads, he will end up assigning equal probability to both hypotheses. But in neither case are his hypotheses a good representation of reality.</p>
|
||||
|
||||
<p>Now, this could be fixed by adding more hypotheses, for instance some probability density to each possible bias. This would work for the example of a coin toss, but might not work for more complex real-life examples: representing many hypothesis about the war in Ukraine or about technological progress in their fullness would be too much for humans.<sup id="fnref:2"><a href="#fn:2" rel="footnote">2</a></sup></p>
|
||||
|
||||
<p><img src="https://i.imgur.com/vqc48uT.png" alt="" />
|
||||
<strong>Original subjective Bayesianism</strong></p>
|
||||
|
||||
<p>So on the one hand, if our set of hypothesis is too narrow, we risk not incorporating a hypothesis that reflects the real world. But on the other hand, if we try to incorporate too many hypothesis, our mind explodes because it is too tiny. Whatever shall we do?</p>
|
||||
|
||||
<h2>Just-in-time Bayesianism by analogy to just-in-time compilation</h2>
|
||||
|
||||
<p><a href="https://en.wikipedia.org/wiki/Just-in-time_compilation">Just-in-time compilation</a> refers to a method of executing programs such that their instructions are translated to machine code not at the beginning, but rather as the program is executed.</p>
|
||||
|
||||
<p>By analogy, I define just-in-time Bayesianism as a variant of subjective Bayesian where inference is initially performed over a limited number of hypothesis, but if and when these hypothesis fail to be sufficiently predictive of the world, more are searched for and past Bayesian inference is recomputed.</p>
|
||||
|
||||
<p><img src="https://i.imgur.com/bptVgcS.png" alt="" />
|
||||
<strong>Just-in-time Bayesianism</strong></p>
|
||||
|
||||
<p>I intuit that this method could be used to run a version of Solomonoff induction that converges to the correct hypothesis that describes a computable phenomenon in a finite (but still enormous) amount of time. More generally, I intuit that just-in-time Bayesianism will have some nice convergence guarantees.</p>
|
||||
|
||||
<h2>As this relates to the philosophy of science</h2>
|
||||
|
||||
<p>The <a href="https://en.wikipedia.org/wiki/Strong_programme">strong programme</a> in the sociology of science aims to explain science only with reference to the sociological conditionst that bring it about. There are also various accounts of science which aim to faithfully describe how science is actually practiced.</p>
|
||||
|
||||
<p>Well, I’m more attracted to trying to explain the workings of science with reference to the ideal mechanism from which they fall short. And I think that just-In-Time Bayesianism parsimoniously explains some aspects with reference to:</p>
|
||||
|
||||
<ol>
|
||||
<li>Bayesianism as the optimal/rational procedure for assigning degrees of belief to statements.</li>
|
||||
<li>necessary patches which result from the lack of infinite computational power.</li>
|
||||
</ol>
|
||||
|
||||
|
||||
<p>As a result, just-in-time Bayesianism not only does well in the domains in which normal Bayesianism does well:
|
||||
- It smoothly processes the distinction between background knowledge and new revelatory evidence
|
||||
- It grasps that both confirmatory and falsificatory evidence are important—which inductionism/confirmationism and naïve forms of falsificationism both fail at
|
||||
- It parsimoniously dissolves the problem of induction: one never reaches certainty, and instead accumulates Bayesian evidence.</p>
|
||||
|
||||
<p>But it is also able to shed some light in some phenomena where alternative theories of science have traditionally fared better:</p>
|
||||
|
||||
<ul>
|
||||
<li>It interprets the difference between scientific revolutions (where the paradigm changes) and normal science (where the implications of the paradigm are fleshd out) as a result of finite computational power</li>
|
||||
<li>It does a bit better at explaining the problem of priors, where the priors are just the hypothesis that humanity has had enough computing power to generate.</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<p>Though it is still not perfect</p>
|
||||
|
||||
<ul>
|
||||
<li>the “problem of priors” is still not really dissolved to a nice degree of satisfaction.</li>
|
||||
<li>the step of acquiring more hypotheses is not really explained, and it is also a feature of other philosophies of science, so it’s unclear that this is that much of a win for just-in-time Bayesianism.</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<p>So anyways, in philosophy of science the main advantages that just-in-time Bayesianism has is being able to keep some of the more compelling features of Bayesianism, while at the same time also being able to explain some features that other philosophy of science theories have.</p>
|
||||
|
||||
<h2>As it relates to ignoring small probabilities</h2>
|
||||
|
||||
<p><a href="https://philpapers.org/archive/KOSTPO-18.pdf">Kosonen 2022</a> explores a setup in which an agent ignores small probabilities of vast value, in the context of trying to deal with the “fanaticism” of various ethical theories.</p>
|
||||
|
||||
<p>Here is my perspective on this dilemma:</p>
|
||||
|
||||
<ul>
|
||||
<li>On the one hand, neglecting small probabilities has the benefit of making expected calculations computationally tractable: if we didn’t ignore at least some probabilities, we would never finish these calculations.</li>
|
||||
<li>But on the other hand, the various available methods for ignoring small probabilities are not robust. For example, they are not going to be robust to situations in which these probabilities shift (see p. 181, “The Independence Money Pump”, <a href="https://philpapers.org/archive/KOSTPO-18.pdf">Kosonen 2022</a>)
|
||||
|
||||
<ul>
|
||||
<li>For example, one could have been very sure that the Sun orbits the Earth, which could have some theological and moral implications. In fact, one could be so sure that one could assign some very small—if not infinitesimal—probability to the Earth orbitting the sun instead. But if one ignores very small probabilities ex-ante, one might not able to update in the face of new evidence.</li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<p>Just-in-time Bayesianism might solve this problem by indeed ignoring small probabilities at the beginning, but expanding the search for hypotheses if current hypotheses aren’t very predictive of the world we observe.</p>
|
||||
|
||||
<h2>Some other related theories and alternatives.</h2>
|
||||
|
||||
<ul>
|
||||
<li>Non-Bayesian epistemology: e.g., falsificationism, positivism, etc.</li>
|
||||
<li><a href="https://www.alignmentforum.org/posts/Zi7nmuSmBFbQWgFBa/infra-bayesianism-unwrapped">Infra-Bayesianism</a>, a theory of Bayesianism which, amongst other things, is robust to adversaries filtering evidence</li>
|
||||
<li><a href="https://intelligence.org/files/LogicalInduction.pdf">Logical induction</a>, which also seems uncomputable on account of considering all hypotheses, but which refines itself in finite time</li>
|
||||
<li>Predictive processing, in which an agent changes the world so that it conforms to its internal model.</li>
|
||||
<li>etc.</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<h2>As this relates to the trapped problem of priors</h2>
|
||||
|
||||
<p>In <a href="https://astralcodexten.substack.com/p/trapped-priors-as-a-basic-problem">Trapped Priors As A Basic Problem Of Rationality</a>, Scott Alexander considers the case of a man who was previously unafraid of dogs, and then had a scary experience related to a dog—for our purposes imagine that they were bitten by a dog.</p>
|
||||
|
||||
<p>Just-in-time Bayesianism would explain this as follows.</p>
|
||||
|
||||
<ul>
|
||||
<li>At the beginning, the man had just one hypothesis, which is “dogs are fine”</li>
|
||||
<li>The man is bitten by a dog. Society claims that this was a freak accident, but this doesn’t explain the man’s experiences. So the man starts a search for new hypotheses</li>
|
||||
<li>After the search, the new hypotheses and their probabilities might be something like:</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<p>\[
|
||||
\begin{cases}
|
||||
\text{Dogs are fine, this was just a freak accident }\\
|
||||
\text{Society is lying. Dogs are not fine, but rather they bite with a frequency of } \frac{2}{n+2}\text{, where n is the number of total encounters the man has had}
|
||||
\end{cases}
|
||||
\]</p>
|
||||
|
||||
<p>The second estimate is the estimate produced by <a href="https://en.wikipedia.org/wiki/Rule_of_succession">Laplace’s law</a>—an instance of Bayesian reasoning given an ignorance prior—given one “success” (a dog biting a human) and \(n\) “failures” (a dog not biting a human).</p>
|
||||
|
||||
<p>Now, because the first hypothesis assigns very low probability to what the man has experienced, most of the probability goes to the second hypothesis.</p>
|
||||
|
||||
<p>But now, with more and more encounters, the probability assigned by the second hypothesis, will be as \(\frac{2}{n+2}\), where \(n\) is the number of times the man interacts with a dog. But this goes down very slowly:</p>
|
||||
|
||||
<p><img src="https://imgur.com/nIbnexh.png" alt="" /></p>
|
||||
|
||||
<p>In particular, you need to experience around as many interactions as you previously have without a dog for \(p(n) =\frac{2}{n+2}\) to halve. But note that this in expectation produces another dog bite! Hence the trapped priors.</p>
|
||||
|
||||
<h2>Conclusion</h2>
|
||||
|
||||
<p>In conclusion, I sketched a simple variation of subjective Bayesianism that is able to deal with limited computing power. I find that it sheds some clarity in various fields, and considered cases in the philosophy of science, discounting small probabilities in moral philosophy, and the applied rationality community.</p>
|
||||
<div class="footnotes">
|
||||
<hr/>
|
||||
<ol>
|
||||
<li id="fn:1">
|
||||
I think that the model has more explanatory power when applied to groups of humans that can collectively<a href="#fnref:1" rev="footnote">↩</a></li>
|
||||
<li id="fn:2">
|
||||
In the limit, we would arrive at Solomonoff induction, a model of perfect inductive inference that assigns a probability to all computable hypothesis. <a href="http://www.vetta.org/documents/legg-1996-solomonoff-induction.pdf">Here</a> is an explanation of Solomonoff induction<sup id="fnref:3"><a href="#fn:3" rel="footnote">3</a></sup>.<a href="#fnref:2" rev="footnote">↩</a></li>
|
||||
<li id="fn:3">
|
||||
The author appears to be the <a href="https://en.wikipedia.org/wiki/Shane_Legg">cofounder of DeepMind</a>.<a href="#fnref:3" rev="footnote">↩</a></li>
|
||||
</ol>
|
||||
</div>
|
||||
|
After Width: | Height: | Size: 16 KiB |
@ -0,0 +1,31 @@
|
||||
library(ggplot2)
|
||||
library(ggthemes)
|
||||
|
||||
l = list()
|
||||
l$n = c(1:100)
|
||||
l$p = 2/(l$n + 2)
|
||||
|
||||
l <- as.data.frame(l)
|
||||
|
||||
title_text = "Probability assigned by Laplace's rule of succession\nas the number of trials increases"
|
||||
label_x_axis = "number of trials"
|
||||
label_y_axis = "probability"
|
||||
ggplot(data=l, aes(x=n, y=p))+
|
||||
geom_point(size = 0.5, color="navyblue")+
|
||||
labs(
|
||||
title=title_text,
|
||||
subtitle=element_blank(),
|
||||
x=label_x_axis,
|
||||
y=label_y_axis
|
||||
) +
|
||||
theme_tufte() +
|
||||
theme(
|
||||
legend.title = element_blank(),
|
||||
plot.title = element_text(hjust = 0.5),
|
||||
plot.subtitle = element_text(hjust = 0.5),
|
||||
legend.position="bottom",
|
||||
legend.box="vertical",
|
||||
axis.text.x=element_text(angle=60, hjust=1),
|
||||
plot.background=element_rect(fill = "white",colour = NA)
|
||||
)
|
||||
|
@ -0,0 +1,137 @@
|
||||
Just-in-time Bayesianism
|
||||
========================
|
||||
|
||||
I propose a simple variant of subjective Bayesianism that I think captures some important aspects of how humans[^1] reason in practice given that Bayesian inference is normally too computationally expensive. I apply it to the problem of [trapped priors](https://astralcodexten.substack.com/p/trapped-priors-as-a-basic-problem), to discounting small probabilities, and mention how it relates to other theories in the philosophy of science.
|
||||
|
||||
### A motivating problem in subjective Bayesianism
|
||||
|
||||
Bayesianism as an epistemology has elegance and parsimony, stemming from its inevitability as formalized by [Cox's](https://en.wikipedia.org/wiki/Cox's_theorem) [theorem](https://nunosempere.com/blog/2022/08/31/on-cox-s-theorem-and-probabilistic-induction/). For this reason, it has a certain magnetism as an epistemology.
|
||||
|
||||
However, consider the following example: a subjective Bayesian which has only two hypothesis about a coin:
|
||||
|
||||
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
|
||||
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||||
<!-- Note: to correctly render this math, compile this markdown with
|
||||
/usr/bin/markdown -f fencedcode -f ext -f footnote -f latex $1
|
||||
where /usr/bin/markdown is the discount markdown binary
|
||||
https://github.com/Orc/discount
|
||||
http://www.pell.portland.or.us/~orc/Code/discount/
|
||||
-->
|
||||
|
||||
|
||||
\[
|
||||
\begin{cases}
|
||||
\text{it has bias } 2/3\text{ tails }1/3 \text{ heads }\\
|
||||
\text{it has bias } 1/3\text{ tails }2/3 \text{ heads }
|
||||
\end{cases}
|
||||
\]
|
||||
|
||||
Now, as that subjective Bayesian observes a sequence of coin tosses, he might end up very confused. For instance, if he only observes tails, he will end up assigning almost all of his probability to the first hypothesis. Or if he observes 50% tails and 50% heads, he will end up assigning equal probability to both hypotheses. But in neither case are his hypotheses a good representation of reality.
|
||||
|
||||
Now, this could be fixed by adding more hypotheses, for instance some probability density to each possible bias. This would work for the example of a coin toss, but might not work for more complex real-life examples: representing many hypothesis about the war in Ukraine or about technological progress in their fullness would be too much for humans.[^2]
|
||||
|
||||
<img src="https://i.imgur.com/vqc48uT.png" alt="pictorial depiction of the Bayesian algorithm" style="display: block; margin-left: auto; margin-right: auto; width: 30%;" >
|
||||
|
||||
So on the one hand, if our set of hypothesis is too narrow, we risk not incorporating a hypothesis that reflects the real world. But on the other hand, if we try to incorporate too many hypothesis, our mind explodes because it is too tiny. Whatever shall we do?
|
||||
|
||||
### Just-in-time Bayesianism by analogy to just-in-time compilation
|
||||
|
||||
[Just-in-time compilation](https://en.wikipedia.org/wiki/Just-in-time_compilation) refers to a method of executing programs such that their instructions are translated to machine code not at the beginning, but rather as the program is executed.
|
||||
|
||||
By analogy, I define just-in-time Bayesianism as a variant of subjective Bayesian where inference is initially performed over a limited number of hypothesis, but if and when these hypothesis fail to be sufficiently predictive of the world, more are searched for and past Bayesian inference is recomputed. This would look as follows:
|
||||
|
||||
<img src="https://i.imgur.com/CwLA5EG.png" alt="pictorial depiction of the JIT Bayesian algorithm" style="display: block; margin-left: auto; margin-right: auto; width: 50%;" >
|
||||
|
||||
I intuit that this method could be used to run a version of Solomonoff induction that converges to the correct hypothesis that describes a computable phenomenon in a finite (but still enormous) amount of time. More generally, I intuit that just-in-time Bayesianism will have some nice convergence guarantees.
|
||||
|
||||
### As this relates to...
|
||||
|
||||
#### ignoring small probabilities
|
||||
|
||||
[Kosonen 2022](https://philpapers.org/archive/KOSTPO-18.pdf) explores a setup in which an agent ignores small probabilities of vast value, in the context of trying to deal with the "fanaticism" of various ethical theories.
|
||||
|
||||
Here is my perspective on this dilemma:
|
||||
|
||||
- On the one hand, neglecting small probabilities has the benefit of making expected calculations computationally tractable: if we didn't ignore at least some possibilities, we would never finish these calculations.
|
||||
- But on the other hand, the various available methods for ignoring small probabilities are not robust. For example, they are not going to be robust to situations in which these probabilities shift (see p. 181, "The Independence Money Pump", [Kosonen 2022](https://philpapers.org/archive/KOSTPO-18.pdf)).
|
||||
- For example, one could have been very sure that the Sun orbits the Earth---which could have some theological and moral implications---and thus initially assign a ver small probability to the reverse. But if one ignores very small probabilities ex-ante, one might not able to update in the face of new evidence.
|
||||
- Similarly, one could have assigned very small probability to a world war. But if one initialy discarded this probability completely, one would not be able to update in the face of new evidence as war approaches.
|
||||
|
||||
Just-in-time Bayesianism might solve this problem by indeed ignoring small probabilities at the beginning, but expanding the search for hypotheses if current hypotheses aren't very predictive of the world we observe. In particular, if the chance of a possibility rises continuously before it happens, just-in-time Bayesianism might have some time to deal with new unexpected possibilities.
|
||||
|
||||
#### ...the problem of trapped priors
|
||||
|
||||
In [Trapped Priors As A Basic Problem Of Rationality](https://astralcodexten.substack.com/p/trapped-priors-as-a-basic-problem), Scott Alexander considers the case of a man who was previously unafraid of dogs, and then had a scary experience related to a dog---for our purposes imagine that they were bitten by a dog.
|
||||
|
||||
Just-in-time Bayesianism would explain this as follows.
|
||||
|
||||
- At the beginning, the man had just one hypothesis, which is "dogs are fine"
|
||||
- The man is bitten by a dog. Society claims that this was a freak accident, but this doesn't explain the man's experiences. So the man starts a search for new hypotheses
|
||||
- After the search, the new hypotheses and their probabilities might be something like:
|
||||
|
||||
\[
|
||||
\begin{cases}
|
||||
\text{Dogs are fine, this was just a freak accident }\\
|
||||
\text{Society is lying. Dogs are not fine, but rather they bite with a frequency of } \frac{2}{n+2}\text{, where n is the number of total encounters the man has had}
|
||||
\end{cases}
|
||||
\]
|
||||
|
||||
The second estimate is the estimate produced by [Laplace's law](https://en.wikipedia.org/wiki/Rule_of_succession)---an instance of Bayesian reasoning given an ignorance prior---given one "success" (a dog biting a human) and \(n\) "failures" (a dog not biting a human).
|
||||
|
||||
Now, because the first hypothesis assigns very low probability to what the man has experienced, a whole bunch of the probability goes to the second hypothesis. Note that the prior degree of credence to assign to this second hypothesis *isn't* governed by Bayes' law, and so one can't do a straightforward Bayesian update.
|
||||
|
||||
But now, with more and more encounters, the probability assigned by the second hypothesis, will be as \(\frac{2}{n+2}\), where \(n\) is the number of times the man interacts with a dog. But this goes down very slowly:
|
||||
|
||||
![](https://i.imgur.com/UntdNrR.png)
|
||||
|
||||
In particular, you need to experience around as many interactions as you previously have without a dog for \(p(n) =\frac{2}{n+2}\) to halve. But note that this in expectation approximately produces another dog bite! Hence the optimal move might be to avoid encountering new evidence (because the chance of another dog bite is now too large), hence the trapped priors.
|
||||
|
||||
#### ...philosophy of science
|
||||
|
||||
The [strong programme](https://en.wikipedia.org/wiki/Strong_programme) in the sociology of science aims to explain science only with reference to the sociological conditionst that bring it about. There are also various accounts of science which aim to faithfully describe how science is actually practiced.
|
||||
|
||||
Well, I'm more attracted to trying to explain the workings of science with reference to the ideal mechanism from which they fall short. And I think that just-in-time Bayesianism parsimoniously explains some aspects with reference to:
|
||||
|
||||
1. Bayesianism as the optimal/rational procedure for assigning degrees of belief to statements.
|
||||
2. necessary patches which result from the lack of infinite computational power.
|
||||
|
||||
As a result, just-in-time Bayesianism not only does well in the domains in which normal Bayesianism does well:
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- It smoothly processes the distinction between background knowledge and new revelatory evidence
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- It grasps that both confirmatory and falsificatory evidence are important---which inductionism/confirmationism and naïve forms of falsificationism both fail at
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- It parsimoniously dissolves the problem of induction: one never reaches certainty, and instead accumulates Bayesian evidence.
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But it is also able to shed some light in some phenomena where alternative theories of science have traditionally fared better:
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- It interprets the difference between scientific revolutions (where the paradigm changes) and normal science (where the implications of the paradigm are fleshd out) as a result of finite computational power
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- It does a bit better at explaining the problem of priors, where the priors are just the hypothesis that humanity has had enough computing power to generate.
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Though it is still not perfect
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- the "problem of priors" is still not really dissolved to a nice degree of satisfaction.
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- the step of acquiring more hypotheses is not really explained, and it is also a feature of other philosophies of science, so it's unclear that this is that much of a win for just-in-time Bayesianism.
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So anyways, in philosophy of science the main advantages that just-in-time Bayesianism has is being able to keep some of the more compelling features of Bayesianism, while at the same time also being able to explain some features that other philosophy of science theories have.
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### Some other related theories and alternatives.
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- Non-Bayesian epistemology: e.g., falsificationism, positivism, etc.
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- [Infra-Bayesianism](https://www.alignmentforum.org/posts/Zi7nmuSmBFbQWgFBa/infra-bayesianism-unwrapped), a theory of Bayesianism which, amongst other things, is robust to adversaries filtering evidence
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- [Logical induction](https://intelligence.org/files/LogicalInduction.pdf), which also seems uncomputable on account of considering all hypotheses, but which refines itself in finite time
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- Predictive processing, in which an agent changes the world so that it conforms to its internal model.
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- etc.
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### Conclusion
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In conclusion, I sketched a simple variation of subjective Bayesianism that is able to deal with limited computing power. I find that it sheds some clarity in various fields, and considered cases in the philosophy of science, discounting small probabilities in moral philosophy, and the applied rationality community.
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[^1]: I think that the model has more explanatory power when applied to groups of humans that can collectively reason.
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[^2]: In the limit, we would arrive at Solomonoff induction, a model of perfect inductive inference that assigns a probability to all computable hypothesis. [Here](http://www.vetta.org/documents/legg-1996-solomonoff-induction.pdf) is an explanation of Solomonoff induction[^3].
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[^3]: The author appears to be the [cofounder of DeepMind](https://en.wikipedia.org/wiki/Shane_Legg).
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<p>
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<section id='isso-thread'>
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