Since the dawn of time, decision theorists have wondered why expected utility is the right way to evaluate options. Sure, it satisfies the usual axioms of decision theory, like von Neumann & Morgenstern’s independence axiom or Savage’s sure-thing principle. But so do other decision rules. For example, suppose there are three possible outcomes, with utilities $1$, $4$, and $9$. And imagine that you evaluate a gamble where the probabilities of these outcomes are, respectively, $p_1$, $p_2$, and $p_3$, using the following formula: $$ p_1 \sqrt{1} + p_2 \sqrt{4} + p_3 \sqrt{9}.... Read more

It’s only natural to place less trust in the judgment of those who disagree with you. After all, from your point of view, those people are mistaken! And making mistakes is a sign of incompetence. This kind of distrust is actually baked into a number of models in social epistemology (for example: here, here, and here). I gave an argument against the rationality of one such model in a previous post.... Read more

Academic philosophers have just been handed a golden ticket. And, as far as I can tell, we’re responding by looking around for the nearest garbage can to toss it away in. LLMs have made MPUs cheap as hell. With a little human guidance, you can crank out the kind of papers that make up 95% of what we publish in a few hours. Soon (already?), human guidance may not even be necessary.... Read more

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