Keaton Ellis | Searcharxiv

arXiv2026

Should I State or Should I Show? Aligning AI with Human Preferences

As AI agents become more autonomous, properly aligning their objectives with human preferences becomes increasingly important. We study how effectively an AI agent learns a human principal's preference in choice under risk via stated versus revealed preferences. We conduct an online experiment in which subjects state their preferences through written instructions ("prompts") and reveal them through choices in a series of binary lottery questions ("data"). We find that on average, an AI agent given revealed-preference data predicts subjects' choices more accurately than an AI agent given stated-preference prompts. Further analysis suggests that the gap is driven by subjects' difficulty in translating their own preferences into written instructions. When given a choice between which information source to give to an AI agent, a large portion of subjects fail to select the more informative one. Moreover, when predictions from the two sources conflict, we find that the AI agent aligns more frequently with the prompt, despite its lower accuracy. Overall, these results highlight the revealed preference approach as a powerful mechanism for communicating human preferences to AI agents, but its success depends on careful implementation.

econ.GN↗

arXiv2019

Multi-Symbol Forbidden Configurations

An $r$-matrix is a matrix with symbols in $\{0,1,\dots,r-1\}$. A matrix is simple if it has no repeated columns. Let the support of a matrix $F$, $\text{supp}(F)$ be the largest simple matrix such that every column in $\text{supp}(F)$ is in $F$. For a family of $r$-matrices $\mathcal{F}$, we define $\text{forb}(m,r,\mathcal{F})$ as the maximum number of columns of an $m$-rowed, $r$-matrix $A$ such that $F$ is not a row-column permutation of $A$ for all $F \in \mathcal{F}$. While many results exist for $r=2$, there are fewer for larger numbers of symbols. We expand on the field of forbidding matrices with $r$-symbols, introducing a new construction for lower bounds of the growth of $\text{forb}(m,r,\mathcal{F})$ (with respect to $m$) that is applicable to matrices that are either not simple or have a constant row. We also introduce a new upper bound restriction that helps with avoiding non-simple matrices, limited either by the asymptotic bounds of the support, or the size of the forbidden matrix, whichever is larger. Continuing the trend of upper bounds, we represent a well-known technique of standard induction as a graph, and use graph theory methods to obtain asymptotic upper bounds. With these techniques we solve multiple, previously unknown, asymptotic bounds for a variety of matrices. Finally, we end with block matrices, or matrices with only constant row, and give bounds for all possible cases.

math.CO↗