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

In the world of work, there is a long-held belief that people decide to take a job based on a single, fixed number: a minimum wage they will not accept. If an offer is above that line, they say yes; if it is below, they say no. This idea works well for traditional jobs where a worker might wait weeks for the right opportunity. But it breaks down in the modern "gig economy," where people accept or reject short-term tasks by the minute. In these fast-moving markets, a worker's decision is rarely about a single number. It is about their history. A worker who has recently accepted many low-paying shifts might reject a slightly higher offer that they would have taken a month ago. Conversely, a worker who has been offered high pay recently might reject a standard offer that would have been acceptable yesterday. Their willingness to work depends on where they have been, not just where they are. This phenomenon, where the past shapes the present in a way that resists simple change, is known as hysteresis. Understanding this is crucial for the platforms that connect workers to tasks, because if they treat workers as if they have fixed price tags, they will misjudge how much to pay, wasting money on shifts that would have been accepted for less, or losing shifts by offering too little to workers who have already been conditioned to expect more.

A team of researchers has developed a new way to map these invisible decision-making patterns using a model originally designed to study magnets. In physics, a magnet does not just respond to the current magnetic field; it remembers how it was magnetized in the past. To describe this, scientists use a framework called the Preisach model, which imagines a material as a collection of tiny switches, each with its own unique "on" and "off" thresholds. The researchers realized that a workforce behaves exactly the same way. Each worker is like a tiny switch with two thresholds: a price high enough to make them accept a task, and a lower price at which they will finally give up and reject it. Between these two points lies a zone of indecision where the worker's choice depends entirely on what they did last time. If they last accepted, they stay in the "accept" mode until the price drops below their lower threshold. If they last rejected, they stay in the "reject" mode until the price rises above their higher threshold. This creates a lag, or a memory, in the market that standard economic models completely miss.

To test this idea, the researchers analyzed nearly 37,000 real-world transactions from a gig platform in Poland. They did not try to guess the specific price limit for every single worker, which would be impossible with the data they had. Instead, they built a two-step system to learn the shape of the market's memory. First, they used a computer program to estimate two separate "utility surfaces." One surface predicted the average satisfaction of workers who had accepted a task, and the other predicted the average satisfaction of those who had rejected it. By comparing these two surfaces, the system could calculate the "gap" between them. This gap represents the size of the indifference zone—the range of prices where a worker's history, rather than the current offer, decides the outcome. The researchers then fed this gap, along with how the current price compared to these estimated thresholds, into a second computer program designed to predict whether a new task would be accepted.

The results revealed a market that is far more complex and responsive than previously thought. The model's findings are consistent with the prediction that price changes do not affect workers symmetrically: a drop in wages appears to depress acceptance rates more than an equivalent rise in wages helps them. This is the signature of hysteresis: once workers have been conditioned to expect lower pay, it takes a much larger increase to win them back than it took to lose them in the first place. However, because the price data was not generated by a randomized experiment, this pattern is suggestive rather than definitively causal, as operators tended to raise prices specifically on difficult shifts that had already been rejected. More surprisingly, the model generated an economically paradoxical result: applied to the full dataset, the model's recommendations simultaneously reduce the total cost of labor while increasing the number of tasks that get filled. The researchers found that for about 74 percent of the transactions, the current wage was already so high that the task would be accepted even if the pay were cut significantly. For these tasks, the platform was simply overpaying. By lowering the wage just enough to stay above the acceptance threshold, the platform could save a median of 31 percent on those specific jobs without losing a single worker.

For the remaining 26 percent of tasks, the situation was the opposite. The current wages were too low to attract workers, but not so low that the tasks were impossible to fill. These were the jobs stuck in the "reject" mode of the hysteresis loop. For these specific tasks, the model recommended a modest wage increase, with a median raise of just 7 percent. This small bump was enough to push the offer over the worker's higher threshold, flipping the decision from rejection to acceptance and recovering tasks that would otherwise have gone unfilled. The study showed that by understanding the two-threshold structure of worker decisions, a platform can treat these two groups differently at the same time. It can cut costs where there is a safety buffer and raise pay where there is a barrier, achieving a 21.3 percent reduction in total wages while increasing the fill rate by nearly 10 percentage points.

The researchers also discovered that the market is not a single, uniform crowd. When they visualized the data, two distinct groups of workers emerged. One group, mostly doing retail and hospitality shifts, had low and tightly clustered price thresholds. The other group, handling specialized tasks, had much higher thresholds and a wider range of expectations. A model that treats all workers as the same would average these groups together and fail to see the specific needs of either. The new approach, by mapping the relationship between the current offer and the worker's historical thresholds, allowed the system to see these differences clearly. It showed that the key to predicting worker behavior is not knowing the absolute price of a task, but knowing where that price sits relative to the worker's personal history.

This work suggests that the old idea of a single "reservation wage" is insufficient for the gig economy. Workers do not just have a minimum price; they have a memory. Their decisions are shaped by a path of past offers, creating a zone of inertia where small changes in pay have no effect. The study demonstrates that by acknowledging this memory and modeling the gap between acceptance and rejection thresholds, platforms can make smarter, more efficient decisions. They can stop overpaying for tasks that are already easy to fill and stop underpaying for tasks that are just out of reach. The findings offer a new way to think about labor markets, one that respects the complexity of human decision-making and the power of history in shaping our economic choices.