Mechanism Design for Crowdsourcing: An Optimal 1-1/e Competitive Budget-Feasible Mechanism for Large Markets

In this paper we consider a mechanism design problem in the context of large-scale crowdsourcing markets such as Amazon’s Mechanical Turk, ClickWorker, CrowdFlower. In these markets, there is a requester who wants to hire workers to accomplish some tasks. Each worker is assumed to give some utility to the requester. Moreover each worker has a minimum cost that he wants to get paid for getting hired. This minimum cost is assumed to be private information of the workers. The question then is - if the requester has a limited budget, how to design a direct revelation mechanism that picks the right set of workers to hire in order to maximize the requester’s utility. We note that although the previous work has studied this problem, a crucial difference in which we deviate from earlier work is the notion of large-scale markets that we introduce in our model. Without the large market assumption, it is known that no mechanism can achieve an approximation factor better than 0.414 and 0.5 for deterministic and randomized mechanisms respectively (while the best known deterministic and randomized mechanisms achieve an approximation ratio of 0.292 and 0.33 respectively). In this paper, we design a budget-feasible mechanism for large markets that achieves an approximation factor of 1-1/e (i.e. almost 0.63). Our mechanism can be seen as a generalization of an alternate way to look at the proportional share mechanism which is used in all the previous works so far on this problem. Interestingly, we also show that our mechanism is optimal by showing that no truthful mechanism can achieve a factor better than 1-1/e; thus, fully resolving this setting. Finally we consider the more general case of submodular utility functions and give new and improved mechanisms for the case when the markets are large.

💡 Research Summary

The paper studies a classic reverse‑auction setting that models crowdsourcing platforms such as Amazon Mechanical Turk, ClickWorker, and CrowdFlower. A requester has a limited budget B and wishes to hire a subset of workers. Each worker i privately knows a cost c_i (the minimum payment he requires) and provides a known utility u_i to the requester if hired. The goal is to design a direct‑revelation mechanism that (i) is truthful (dominant‑strategy incentive compatible), (ii) never pays a worker less than his cost (individual rationality), (iii) never exceeds the budget (budget‑feasibility), and (iv) maximizes the requester’s total utility.

Large‑market assumption.
The authors introduce a “large market” model: the maximum individual cost c_max is negligible compared to the budget, i.e., θ = c_max / B → 0. This captures real crowdsourcing environments where thousands of workers each demand only a tiny fraction of the total budget. Under this assumption, the authors can break the impossibility barriers known for the general case (0.414 for deterministic, 0.5 for randomized mechanisms).

From proportional share to a parametrized family.
The paper first revisits the proportional‑share mechanism (used in Singer 2010 and Chen et al. 2011), which selects a single utility‑to‑cost ratio cutoff λ and hires all workers with ratio ≥ λ, paying each the same “price per unit of utility”. This simple scheme yields a 1/6–1/3 approximation. The authors then generalize it by introducing a single‑parameter allocation rule f : ℝ_+ →