Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: An Epistemic Defense of Rounding Down, published by Hayley Clatterbuck on July 15, 2024 on The Effective Altruism Forum.

This post is part of WIT's CRAFT sequence. It examines one of the decision theories included in the Portfolio Builder Tool.

Executive summary

Expected value maximization (EVM) leads to problems of fanaticism, recommending that you ought to take gambles on actions that have very low probabilities of success if the potential outcomes would be extremely valuable. This has motivated some to adopt alternative decision procedures.

One common method for moderating the fanatical effects of EVM is to ignore very low probability outcomes, rounding them down to 0. Then, one maximizes EV across the remaining set of sufficiently probable outcomes.

We can distinguish between two types of low probabilities that could be candidates for rounding down. A decision-theoretic defense of rounding down states that we should (or are permitted to) round down low objective chances. An epistemic defense states that we should (or are permitted to) round down low subjective credences that reflect uncertainty about how the world really is.

Rounding down faces four key objections:

The choice of a threshold for rounding down (i.e., how low a probability must be before we round it to 0) is arbitrary.

It implies that normative principles change at some probability threshold, which is implausible.

It ignores important outcomes and thus leads to bad decisions.

It either gives no or bad advice about how to make decisions among options under the threshold.

Epistemic rounding down fares much better with respect to these four objections than does decision-theoretic rounding down.

The resolution or specificity of our evidence constrains our ability to distinguish between probabilistic hypotheses. Our evidence does not typically have enough resolution to give us determinate probabilities for very improbable outcomes. In such cases, we sometimes have good reasons for rounding them down to 0.

1. Intro

Expected value maximization is the most prominent and well-defended theory about how to make decisions under uncertainty. However, it famously leads to problems of fanaticism: it recommends pursuing actions that have extremely small values of success when the payoffs, if successful, would be astronomically large. Because many people find these recommendations highly implausible, several solutions have been offered that retain many of the attractive features of EVM but rule out fanatical results.

One solution is to dismiss outcomes that have very low probabilities - in effect, rounding them down to 0 - and then maximizing EV among the remaining set of sufficiently probable outcomes. This "truncated EVM" strategy yields more intuitive results about what one ought to do in paradigm cases where traditional EVM recommends fanaticism. It also retains many of the virtues of EVM, in that it provides a simple and mathematically tractable way of balancing probabilities and value.

However, rounding down faces four key objections.[1] The first two suggest that rounding down will sometimes keep us from making correct decisions, and the second two present problems of arbitrariness:

1. Ignores important outcomes: events that have very low probabilities are sometimes important to consider when making decisions.

2. Disallows decisions under the threshold: every event with a probability below the threshold is ignored. Therefore, rounding down precludes us from making rational decisions about events under the threshold, sometimes leading to violations of Dominance.

3. Normative arbitrariness: rounding down implies that normative principles governing rational behavior change discontinuously at some cut-off of probability. This is unparsimonious and unmotivated.

4. Threshold arbitrariness: the choice of a threshold...