The Minimum Wage as an Anchor: Effects on Determinations of Fairness by Humans and AI

TL;DR

This study investigates whether minimum wage acts as an anchor in fairness judgments of wages by humans and an AI model. Using Prolific crowdsourcing and OpenAI's GPT-3, the author tests how a stated minimum wage $M$ shifts the perceived fair wage $R$, and introduces AMA and ADA to quantify anchoring, including mutual-information-based distributional effects. Results show robust anchoring in humans for realistic $M$, with bimodal responses emerging for unrealistically high anchors, while GPT-3 also anchors but with a downward bias and different multimodality patterns, influenced by prompt perturbations and demographic cues. The findings reveal both similarities and important differences between human and AI judgments, with implications for labor policy design and AI fairness, explainability, and bias mitigation in automated decision-support contexts.

Abstract

I study the role of minimum wage as an anchor for judgements of the fairness of wages by both human subjects and artificial intelligence (AI). Through surveys of human subjects enrolled in the crowdsourcing platform Prolific.co and queries submitted to the OpenAI's language model GPT-3, I test whether the numerical response for what wage is deemed fair for a particular job description changes when respondents and GPT-3 are prompted with additional information that includes a numerical minimum wage, whether realistic or unrealistic, relative to a control where no minimum wage is stated. I find that the minimum wage influences the distribution of responses for the wage considered fair by shifting the mean response toward the minimum wage, thus establishing the minimum wage's role as an anchor for judgements of fairness. However, for unrealistically high minimum wages, namely $50 and $100, the distribution of responses splits into two distinct modes, one that approximately follows the anchor and one that remains close to the control, albeit with an overall upward shift towards the anchor. The anchor exerts a similar effect on the AI bot; however, the wage that the AI bot perceives as fair exhibits a systematic downward shift compared to human subjects' responses. For unrealistic values of the anchor, the responses of the bot also split into two modes but with a smaller proportion of the responses adhering to the anchor compared to human subjects. As with human subjects, the remaining responses are close to the control group for the AI bot but also exhibit a systematic shift towards the anchor. During experimentation, I noted some variability in the bot responses depending on small perturbations of the prompt, so I also test variability in the bot's responses with respect to more meaningful differences in gender and race cues in the prompt, finding anomalies in the distribution of responses.

Figures (7)

• Figure 1: Minimum Wage acts as an anchor on humans' and AI's determination of what constitutes a fair wage. The distribution of what human respondents consider a fair wage for a materials worker depending on the stated minimum wage is depicted by the violin plot in red. The mean and three standard deviations of the responses from GPT-3 are shown in blue. Left of zero is the control, showing the distribution of responses when no minimum wage is stated in the prompt. The black dashed line shows the mean control response, and the green dashed line provides a linear reference for where the responses would appear if they exactly equal the minimum wage. Note the systematic shift between human workers and GPT-3, on average $5.32, possibly due to the outdated nature of data used to train GPT-3. The same plots, with GPT-3's responses shifted up to align the responses, is shown in Fig. \ref{['fig:aligned']} (right), along with the response with aligned controls (left).
• Figure 2: Populations Split for Unrealistic Anchors. For unrealistic anchors, the responses of Prolific workers (left) split into two populations (bottom left), with the majority of respondents following the anchor and the rest remaining closer to the control but with a systematic upward shift. For GPT-3 (right), however, the two populations are distributed differently from the Prolific Workers, with a small percentage of responses following the unrealistic anchor and the majority remaining close to the control (bottom-right). Fig. \ref{['fig:splash']} corresponds to the inset in the top-left plot. The left column can be visualized as a violin plot based on population statistics, as shown in Fig. \ref{['fig:violin']}.
• Figure 3: Populations Split for Unrealistic anchors. The violin plot extends Fig. \ref{['fig:splash']} for unrealistic anchors up to $100. The two distinct modes are seen corresponding to minimum wage $50 and $100. The errorbar plot for GPT-3 is shifted to the right for visibility.
• Figure 4: Prolific.co Worker Responses to prompts including reference to minimum wage ranging from $0 to $100. Note that axes are not normalized. The horizontal axis shows the value of the anchor, and the vertical axis the percentage of responses to that anchor. For high anchors, the distribution splits into two distinct modes (Fig. \ref{['fig:bimodal']}).
• Figure 5: Controls for Prolific workers (left) and GPT-3 (right). Note that the horizontal axis indicates the number of responses for Prolific workers, and the percentage probability mass for GPT-3.