As Joe Biden cleared 270 last week, some people remarked on how different the narrative would’ve been had the votes been counted in a different order: It's staggering to think about how differently PA would be viewed/covered right now if the EDay/mail ballots were being counted in the opposite order. — Dave Wasserman (@Redistrict) November 5, 2020 The idea that order shouldn’t affect your final take is a classic criterion of rationality.... Read more

This is post 3 of 3 on simulated epistemic networks (code here): The Zollman Effect How Robust is the Zollman Effect? Mistrust & Polarization The first post introduced a simple model of collective inquiry. Agents experiment with a new treatment and share their data, then update on all data as if it were their own. But what if they mistrust one another? It’s natural to have less than full faith in those whose opinions differ from your own.... Read more

This is the second in a trio of posts on simulated epistemic networks: The Zollman Effect How Robust is the Zollman Effect? Mistrust & Polarization This post summarizes some key ideas from Rosenstock, Bruner, and O’Connor’s paper on the Zollman effect, and reproduces some of their results in Python. As always you can grab the code from GitHub. Last time we met the Zollman effect: sharing experimental results in a scientific community can actually hurt its chances of arriving at the truth.... Read more

I’m drafting a new social epistemology section for the SEP entry on formal epistemology. It’ll focus on a series of three papers that study epistemic networks using computer simulations. This post is the first in a series of three explainers, one on each paper. The Zollman Effect How Robust is the Zollman Effect? Mistrust & Polarization In each post I’ll summarize the main ideas and replicate some key results in Python.... Read more

In an earlier post we met the $\lambda$-continuum, a generalization of Laplace’s Rule of Succession. Here is Laplace’s rule, stated in terms of flips of a coin whose bias is unknown. The Rule of Succession Given $k$ heads out of $n$ flips, the probability the next flip will land heads is $$\frac{k+1}{n+2}.$$ To generalize we introduce an adjustable parameter, $\lambda$. Intuitively $\lambda$ captures how cautious we are in drawing conclusions from the observed frequency.... Read more

The Rule of Succession gives a simple formula for “enumerative induction”: reasoning from observed instances to unobserved ones. If you’ve observed 8 ravens and they’ve all been black, how certain should you be the next raven you see will also be black? According to the Rule of Succession, 90%. In general, the probability is $(k+1)/(n+2)$ that the next observation will be positive, given $k$ positive observations out of $n$ total.... Read more

There are four ways things can turn out with two flips of a coin: $$ HH, \quad HT, \quad TH, \quad TT.$$ If we know nothing about the coin’s tendencies, we might assign equal probability to each of these four possible outcomes: $$ Pr(HH) = Pr(HT) = Pr(TH) = Pr(TT) = 1/ 4. $$ But from another point of view, there are primarily three possibilities. If we ignore order, the possible outcomes are $0$ heads, $1$ head, or $2$ heads.... Read more

The classic “Lockean” thesis about full and partial belief says full belief is rational iff strong partial belief is rational. Hannes Leitgeb’s “Humean” thesis proposes a subtler connection. $ \newcommand\p{Pr} \newcommand{\B}{\mathbf{B}} \newcommand{\given}{\mid} $ The Humean Thesis For a rational agent whose full beliefs are given by the set $\mathbf{B}$, and whose credences by the probability function $\p$: $B \in \mathbf{B}$ iff $\p(B \given A) > t$ for all $A$ consistent with $\mathbf{B}$.... Read more

If you look at the little network diagram below, you’ll probably agree that $P$ is the most “central” node in some intuitive sense. This post is about using a belief’s centrality in the web of belief to give a coherentist account of its justification. The more central a belief is, the more justified it is. But how do we quantify “centrality”? The rough idea: the more ways there are to arrive at a proposition by following inferential pathways in the web of belief, the more central it is.... Read more

Today The Open Handbook of Formal Epistemology is available for download. It’s an open access book, the first published by PhilPapers itself. (The editors are Richard Pettigrew and me.) The book features 11 outstanding entries by 11 wonderful philosophers. “Precise Credences”, by Michael G. Titelbaum “Decision Theory”, by Johanna Thoma “Imprecise Probabilities”, by Anna Mahtani “Primitive Conditional Probabilities”, by Kenny Easwaran “Infinitesimal Probabilities”, by Sylvia Wenmackers “Comparative Probabilities”, by Jason Konek “Belief Revision Theory”, by Hanti Lin “Ranking Theory”, by Franz Huber “Full & Partial Belief”, by Konstantin Genin “Doxastic Logic”, by Michael Caie “Conditionals”, by R.... Read more