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Worker Utility as Hysteresis: A Preisach Model of Transaction Acceptance in Gig Labour Markets

This paper proposes a Preisach hysteresis model for gig worker transaction acceptance that leverages latent utility surfaces and price-to-threshold encodings to simultaneously reduce wage costs by 21.3% and increase fill rates by 9.7% by exploiting the directional asymmetry of worker preferences.

Original authors: Piotr Frydrych

Published 2026-06-04

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Piotr Frydrych

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to understand why people accept or reject job offers on a gig platform (like Uber or TaskRabbit). The traditional way economists look at this is like a simple light switch: there is a specific "reservation wage." If the pay is above that number, the worker says "Yes." If it’s below, they say "No."

But this paper argues that human workers aren’t simple light switches. They are more like thermostats with memory.

The Core Idea: The "Thermostat" Worker

The authors use a concept from physics called the Preisach Model, which is usually used to describe how magnets remember their history. They apply this to gig workers.

Think of every worker as having two different temperature settings in their head:

The "Turn On" Temperature ( $\alpha$ ): The pay needs to be this high for them to start working.
The "Turn Off" Temperature ( $\beta$ ): The pay needs to drop below this lower number for them to quit.

Here is the twist: The "Turn Off" temperature is lower than the "Turn On" temperature. This creates a "buffer zone" or an indifference zone.

If you are currently working, and the pay drops a little bit (but stays above the "Turn Off" temperature), you keep working. You don’t quit immediately.
If you are currently not working, and the pay rises a little bit (but stays below the "Turn On" temperature), you still don’t start. You wait.

This is called hysteresis (pronounced hye-stuh-ree-sis). It means your current decision depends not just on the current price, but on your history. Did you just quit? Or did you just get hired? The same price can mean "Yes" for one person and "No" for another, depending on where they came from.

The Problem: We Can’t See the "Temperature"

The problem for the platform is that they can’t see these internal temperatures. They only see the final result: Accepted or Rejected. It’s like trying to figure out how a thermostat works by only looking at whether the heater is on or off, without seeing the dial.

The Solution: A Two-Stage Detective Job

The researchers built a computer system to guess these hidden temperatures. They did it in two steps:

Step 1: The "Twin" Neural Network
They trained an AI to look at thousands of past jobs and estimate two invisible numbers for every new job offer:

Utility of Acceptance ( $U_1$ ): How good does this job look to people who did take it?
Utility of Rejection ( $U_0$ ): How bad does this job look to people who rejected it?

The AI is forced to learn these two numbers together. It’s like having two detectives looking at the same crime scene from opposite sides. The difference between these two numbers ( $U_1 - U_0$ ) is called the "Gap." This Gap represents the size of that "indifference zone" or buffer. A wide gap means workers are very picky and have strong memories of past prices. A narrow gap means they are more flexible.

Step 2: The Price-to-Threshold Check
The AI doesn’t just look at the raw pay. It looks at the pay relative to those hidden thresholds. It asks: "Is this price sitting comfortably inside the 'Yes' zone, or is it dangerously close to the 'No' zone?"

They fed this information into a second AI (an XGBoost classifier) to predict if the job would be accepted.

What They Found

Workers Judge Relatively, Not Absolutely: The model worked much better when it compared the price to the worker’s hidden thresholds rather than just looking at the dollar amount. This confirms that workers think in terms of "Is this better or worse than what I’m used to?" rather than "Is this $20?"
The "Hysteresis" Signature: The model confirmed that price cuts hurt acceptance rates more than price raises help them. If you lower the price, you lose workers who stay "switched off" until the price goes back up significantly. It’s harder to win them back than it is to lose them.
Two Types of Workers: The data revealed two distinct groups:
- Retail/General Workers: Low pay, very predictable, small indifference zones.
- Specialist Workers: High pay, very picky, large indifference zones.
  The model spotted this split automatically, without being told to look for it.

The Surprising Business Result

The most interesting part is what happens when you use this model to set prices. The researchers ran a simulation to see what would happen if the platform used their model to adjust wages for 36,891 jobs.

The result was counter-intuitive:

For 74% of jobs: The workers were already very likely to accept the job (probability > 80%). The model said, "You are paying too much for this certainty." It recommended cutting the wage by a median of 31%. Because the workers were so sure to accept, the platform could save money without losing the job.
For 25% of jobs: The workers were unlikely to accept. The model said, "You are underpaying relative to their threshold." It recommended raising the wage by a median of 7% to get them to say "Yes."

The Net Effect: By cutting wages where they were too high and raising them where they were too low, the platform would save 21.3% on total wages while increasing the number of filled jobs by 9.7%.

Why This Matters

The paper argues that standard models fail because they treat all workers as if they have a single, static "reservation wage." But in reality, workers have history-dependent thresholds. They have a "buffer zone" where they stick with their current status (working or not working) unless the price changes dramatically.

By recognizing this "thermostat" behavior, platforms can stop guessing and start pricing with precision—cutting costs where workers are loyal and raising prices where workers are hesitant, all while understanding that the past matters just as much as the present.

Technical Summary: Worker Utility as Hysteresis: A Preisach Model of Transaction Acceptance in Gig Labour Markets

1. Problem Statement and Theoretical Motivation
The paper addresses the limitations of canonical job-search models, which treat worker acceptance as a static threshold rule based on a single reservation wage. The authors argue this framework fails in gig labor markets for two reasons: first, reservation wages are non-stationary, shifting with experience and competitive pressure; second, and more fundamentally, the aggregate response of a worker pool is not the response of a representative agent but an integral over a population of heterogeneous thresholds.

To model this heterogeneity and the resulting path-dependence, the authors propose the Preisach hysteresis model, originally developed for magnetic materials. In this framework, each worker is modeled as a binary switching element (a hysteron) defined by a pair of thresholds $(\alpha, \beta)$ with $\alpha \geq \beta$ . A worker accepts a transaction if utility exceeds $\alpha$ and rejects if it falls below $\beta$ . Between these thresholds lies an "indifference zone" where the decision depends on history (status quo bias). This structure naturally generates hysteresis: price decreases depress acceptance rates more than equivalent increases restore them, because workers whose acceptance threshold $\alpha$ was crossed by a decline remain "switched off" until wages rise back above $\alpha$ .

2. Methodology
Direct estimation of the threshold density $\mu(\alpha, \beta)$ from binary transaction data is ill-posed. Instead, the authors employ a two-stage estimation pipeline that recovers the first moments of the threshold distribution via conditional mean utilities.

Stage 1: Dual-Output Neural Network (Utility Estimation)
The authors estimate two latent utility surfaces from transaction data:
- $U_1(X)$ : The acceptance utility (conditional mean utility of accepted transactions).
- $U_0(X)$ : The rejection utility (conditional mean utility of rejected transactions).
These are estimated jointly using a dual-output neural network with a shared encoder (256 → 128 neurons, LeakyReLU activations) and two independent output heads. The loss function combines Mean Squared Error (MSE) for each subpopulation with a margin penalty ( $\lambda = 0.5$ ) that enforces the structural constraint $U_1 \geq U_0$ for accepted transactions. This ensures the "Preisach gap" ( $U_1 - U_0$ ) serves as a non-parametric proxy for the population’s net disposition to accept.
Stage 2: XGBoost Classification
The classification of transaction acceptance is performed by an XGBoost gradient boosted tree classifier. The input features include:
- The Preisach gap ( $\hat{U}_1 - \hat{U}_0$ ).
- Five "clip-stabilised" price-to-threshold features derived from a log-price-strength proxy ($lps$). These features encode the relative position of the current offer with respect to the estimated utility surfaces (e.g., price relative to rejection centroid $r_0$ , signed distance from acceptance centroid $d_1$ ).
This encoding explicitly captures where the current offer sits within the indifference zone, rather than relying on raw utility estimates.

3. Data and Experimental Setup
The study utilizes 36,891 transaction records from a Polish gig platform covering retail, hospitality, logistics, and healthcare. The data originates from a period (March–May 2024) where offered wages were varied $\pm10–20\%$ relative to category baselines. While not a pre-registered randomized controlled trial, the dataset provides observational variation in prices and market conditions. The overall acceptance rate was 84.4%.

4. Key Results

Predictive Performance: On a held-out test set ( $n=7,378$ ), the two-stage pipeline achieved a Jaccard index of 0.827 and an ROC AUC of 0.799.
Feature Importance: The encoding of price relative to estimated thresholds (specifically the ratio features $r_0, r_1$ ) provided the largest single gain in performance (+11.0 pp AUC for XGBoost regressor surfaces; +1.4 pp for dual-output NN surfaces). This confirms that workers evaluate offers relative to reference points (thresholds) rather than in absolute terms.
Hysteresis Signature: The model confirms directional asymmetry: price decreases depress completion rates more than equivalent increases raise them. However, the authors note that causal identification of this asymmetry requires a randomized price experiment, as observational data is confounded by endogenous price-setting (operators raising prices on difficult shifts).
Economic Paradox and Positional Decomposition: Applying the model’s wage recommendations to the full dataset simultaneously reduced the total wage bill by 21.3% and increased the expected fill rate by 9.7 percentage points. This result is driven by a positional decomposition:
- 74.2% of transactions: Already had $P(\text{accept}) > 0.80$ . The model recommended wage cuts (median 31% saving), releasing cost buffers while keeping acceptance probability high (mean post-cut $P = 0.972$ ).
- 25.4% of transactions: Had $P(\text{accept}) < 0.80$ . The model recommended modest wage increases (median 7%), recovering transactions that would otherwise go unfilled.
- A model without an explicit indifference zone cannot locate each transaction’s starting position precisely enough to execute both moves simultaneously.

5. Significance and Contributions
The paper claims three primary contributions:

Theoretical: It establishes the Preisach operator as a theoretically grounded model for worker utility in disaggregated labor markets, formalizing reference-dependence and status quo bias through a structural indifference zone.
Methodological: It develops a tractable estimation strategy that avoids the ill-posed direct recovery of threshold density by using conditional mean utilities ( $U_1, U_0$ ) as primary estimands, implemented via a dual-output neural network with structural margin constraints.
Empirical: It demonstrates that encoding the price-to-threshold relationship explicitly yields the largest predictive gains, providing evidence that workers respond to prices relative to thresholds. The empirical Preisach plane reveals market segmentation (e.g., retail vs. specialist clusters) and the geometry of acceptance decisions that are invisible in representative-agent models.

The authors conclude that the Preisach model does not merely fit the data but organizes it, revealing the indifference band and market segments as inherent features of the binary decision data. They emphasize that while the cross-sectional estimator identifies the threshold distribution, dynamic hysteresis requires further experimental validation.