This write-up is intended to be a summary of Chapter 2 (How could we be so wrong) of On the Overwhelming Importance of Shaping the Far Future by Nicholas Beckstead. The chapter originally spans ~12000 words, here we summarize the main points in ~1800 words.
This chapter of Beckstead’s thesis discusses Bayesian Ethics, evidence of error in moral intuition and some biases specific to longtermism. I have omitted the discussion only relevant to the latter.
In the first section, the standard Bayesian framework for scientific inquiry is introduced.
In the second section, the framework is applied to moral philosophy to argue that when assigning credence to moral theories we should:
In the next three sections, three bodies of evidence are presented favoring the conclusion that human moral intuition about specific cases is prone to error:
In the sixth section, it is argued that there are specific biases that make humans underestimate the importance of the far future.
In the seventh and last section Beckstead summarizes his arguments and conclusions.
In this summary I group the first two sections explaining the Bayesian approach to Ethics together, as well as the three sections providing evidence against the reliability of moral intuition. I will not cover the sixth section - interested readers can read the original text.
In the first two sections, Beckstead introduces Bayesian curve fitting and argues that it applies to moral philosophy as well as to scientific inquiry.
His main takeaway from that proposition is that to the extent that we expect moral intuitions to be biased we should rely less on fit to intuition and counterexamples when assigning credence to moral theories.

In the problem of curve-fitting we have a collection of noisy data points (“observations”) and a set of curves (“models”), both relating an input X into an output Y. We want to find the model that best explains the observations we have collected and will better extrapolate to the inputs we have not seen yet.
In Bayesian curve fitting we start by assigning a prior credence to each possible model based on background information, basic epistemic standards (eg simplicity) and basic hunches, and then update it based on the observations and our hypothesis of how the observations might be noisy or biased. Beckstead summarizes the approach with the following figure:

Bayesian curve fitting as a method of scientific inquiry is fairly standard and well argued for in other texts.
Beckstead draws two key implications out of it:
Beckstead claims that our moral intuitions are a kind of noisy data, and that our credences in moral theories should be updated in accordance with our best epistemic theory, ie Bayesian analysis.
Beckstead summarizes the translation of Bayesian curve fitting from scientific grounds to moral philosophy grounds with the following table:

Beckstead discusses a possible objection to the Bayesian approach to Ethics: moral philosophy is a priori and requires different methodological standards. He counters arguing that Bayesian updating is a reasonable approximation of how people change their beliefs as they think. By way of an example of a priori reasoning working this way he suggests a math student figuring out if every differentiable function is continuous by trying out examples.
Now, Beckstead claims that our moral intuitions are especially noisy and biased, and thus we should rely more on our moral priors, as he discussed in the previous section. From this proposition Beckstead draws two main conclusions:
In the sections 3-5 Beckstead brings evidence in favor of the claim that our moral intuitions are especially noisy. He talks about 1) historical moral mistakes, 2) the scientific literature on human bias, and 3) some impossibility results showing that some of our strongest moral intuitions are mutually inconsistent.
Beckstead preemptively addresses some arguments against his claims:
Beckstead cites as evidence Kahneman and Tversky’s seminal work on heuristics and biases. He then explains three types of biases:

Beckstead appeals to intuition to argue that we should expect that there are many unknown moral biases. He also cites some experiments on bias to argue that philosophers are no less prone to moral bias.
Beckstead argues that these impossibility results should prompt us to 1) doubt our moral intuitions and 2) accept that no moral theory will be able to explain in a satisfactory way many of our moral intuitions.
Verbatim from the thesis:
Learning about moral errors through history, biased heuristics generating our moral judgments, and a collection of impossibility results should tell us that our moral judgments are subject to errors that are hard to detect and hard to correct. In light of this, we should trust intuition less and rely on our priors more. We should not expect to find a theory that fits all of most condent moral judgments, and we should largely be engaged in an exercise in damage control, especially in population ethics. Finally, we should expect these error processes to lead us to significantly underestimate the importance of shaping the far future.
This summary was written by Jaime Sevilla, summer fellow at the Future of Humanity Institute. The source material is due to Nicholas Beckstead, and I have directly reused many sentences from his work. This representation of Beckstead's work is only as correct as my understanding of it - if critiquing the original work please consult the source rather than presume my characterisation of it is correct. I do not necessarily endorse the conclusions reached by Beckstead.
I want to thank Max Daniel and Alex Hill for their insightful comments and thoughtful discussion over the draft of this summary.
Thanks for writing this, I found it interesting and it significantly increased the likelihood I'd read the original.