# Heads or Tails: A Simple Example of Causal Abstractive Simulation

arXiv: https://arxiv.org/abs/2509.01136 · HTML: https://mlsanity.com/paper/2509.01136/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Out of One, Many: Using Language Models to Simulate Human Samples](https://mlsanity.com/paper/2209.06899/) (2022)
- [Using Large Language Models to Simulate Multiple Humans and Replicate Human Subject Studies](https://mlsanity.com/paper/2208.10264/) (2022)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Simulacra as Conscious Exotica](https://mlsanity.com/paper/2402.12422/) (2024)

## Abstract (arXiv)

This note illustrates how a variety of causal abstraction arXiv:1707.00819 arXiv:1812.03789, defined here as causal abstractive simulation, can be used to formalize a simple example of language model simulation. This note considers the case of simulating a fair coin toss with a language model. Examples are presented illustrating the ways language models can fail to simulate, and a success case is presented, illustrating how this formalism may be used to prove that a language model simulates some other system, given a causal description of the system. This note may be of interest to three groups. For practitioners in the growing field of language model simulation, causal abstractive simulation is a means to connect ad-hoc statistical benchmarking practices to the solid formal foundation of causality. Philosophers of AI and philosophers of mind may be interested as causal abstractive simulation gives a precise operationalization to the idea that language models are role-playing arXiv:2402.12422. Mathematicians and others working on causal abstraction may be interested to see a new application of the core ideas that yields a new variation of causal abstraction.