The Delusional Hedge Algorithm as a Model of Human Learning from Diverse Opinions

TL;DR

<3-5 sentence high-level summary> This work addresses how people learn from diverse opinions when direct access to event features and ground-truth labels is unavailable. It extends the hedge algorithm to a semi-supervised setting via the delusional hedge, which uses a delusional loss on unlabeled trials weighted by a parameter to update source trust. Across two experiments, human behavior aligns with the delusional hedge, with stronger effects in fully unsupervised conditions and demonstrations that trust also depends on consistency with reliable sources, not just supervised accuracy. The findings offer a formal account of human social learning from conflicting opinions and guide the design of more realistic algorithms for weighing multiple information sources.

Abstract

Whereas cognitive models of learning often assume direct experience with both the features of an event and with a true label or outcome, much of everyday learning arises from hearing the opinions of others, without direct access to either the experience or the ground truth outcome. We consider how people can learn which opinions to trust in such scenarios by extending the hedge algorithm: a classic solution for learning from diverse information sources. We first introduce a semi-supervised variant we call the delusional hedge capable of learning from both supervised and unsupervised experiences. In two experiments, we examine the alignment between human judgments and predictions from the standard hedge, the delusional hedge, and a heuristic baseline model. Results indicate that humans effectively incorporate both labeled and unlabeled information in a manner consistent with the delusional hedge algorithm -- suggesting that human learners not only gauge the accuracy of information sources but also their consistency with other reliable sources. The findings advance our understanding of human learning from diverse opinions, with implications for the development of algorithms that better capture how people learn to weigh conflicting information sources.

Figures (4)

• Figure 1: Human experimental setup. Panel (a) shows a 1D space $[0,300]$ where "fruits" are placed, with three sources having different decision boundaries $\theta$, and the true boundary at $\theta^* = 150$. Panels (b)-(d) display the user interface: (b) shows the three sources providing their opinions on the hidden fruit, while the participant makes a prediction; (c) reveals the true label post-prediction in labeled trials; and (d) shows the display omitting the label feedback in unlabeled trials.
• Figure 2: Comparison of participant responses with the standard hedge algorithm, the delusional hedge algorithm, and the accuracy-majority heuristic over 100 time steps. Each row represents a different level of supervision (from $p_{visible} = 0$ to $p_{visible} = 1$), and each column corresponds to one of the four unique combinations of source opinions $(b_{t, far}, b_{t, middle}, b_{t, near})$. Within each line plot, the black line shows the moving average of the ratio of participants predicting $\hat{y_t} = 1$ (y-axis) over the 100 time steps (x-axis), and the blue, red, and purple lines represent the prediction probability of the standard Hedge algorithm, the delusional hedge algorithm, and the accuracy-majority heuristic, respectively, averaged across participants at each time step. Grey dots depict the proportion of participants with $\hat{y_t} = 1$ at each time step, with dot size denoting participant count.
• Figure 3: Under five supervision levels ($0 \leq p_{visible} \leq 1$), the trust assigned to each source at the final state ($p_{Tk}$) by the standard hedge algorithm and the delusional hedge algorithm (top row), along with the accuracy (or majority ratio if accuracy is undefined) used by the accuracy-majority heuristic (second row), as well as participants’ source ratings (third and forth rows), and proportion of times each source was chosen as most accurate or most often in the majority (bottom row). The bars for sources color-coded as dark blue (Near), blue (Middle), and violet (Far). The ratings and responses designed to gauge participants' trust in sources are color-coded as green. The error bars display the standard errors.
• Figure 4: Under the "M=F" and "M=N" conditions, the trust assigned to each source at the final state ($p_{Tk}$) by the standard hedge algorithm and the delusional hedge algorithm (top row), along with the accuracy (or majority ratio if accuracy is undefined) used by the accuracy-majority heuristic (second row), as well as participants’ source ratings (third and forth rows). The bars for sources color-coded as dark blue (Near), blue (Middle), and violet (Far). The ratings designed to gauge participants' trust in sources are color-coded as green. The error bars display the standard errors.