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

Nima Anari, Gagan Goel+1 more|arXiv (Cornell University)|May 10, 2014

Mobile Crowdsensing and Crowdsourcing2 references7 citations

TL;DR

This paper presents a novel, truthful, budget-feasible mechanism for large-scale crowdsourcing markets that achieves a competitive ratio of $1 - 1/e \approx 0.63$, which is optimal. The mechanism generalizes proportional sharing and uses a parameterized allocation rule with carefully designed payments to ensure truthfulness and budget feasibility, significantly improving upon prior bounds in large markets where individual worker costs are small relative to the requester's budget.

ABSTRACT

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.

Motivation & Objective

• To design a truthful, budget-feasible mechanism for large-scale crowdsourcing markets where individual worker costs are small relative to the requester's budget.
• To close the gap between known upper bounds and achievable approximation ratios in large markets, where prior mechanisms were suboptimal.
• To establish that $1 - 1/e$ is the optimal approximation ratio achievable by any truthful, budget-feasible mechanism.
• To extend the framework to submodular utility functions, providing improved mechanisms for large markets.

Proposed method

• Proposes a parameterized class of envy-free, truthful mechanisms based on a generalized proportional sharing rule.
• Designs a payment rule that ensures truthfulness by aligning incentives with reported costs.
• Uses a greedy sequence construction and threshold-based allocation to approximate the optimal solution under budget constraints.
• Applies a rounding procedure to convert fractional allocations into integral ones while preserving approximation guarantees.
• Introduces a budget reduction technique to convert almost budget-feasible mechanisms into strictly budget-feasible ones with minimal loss in approximation.
• Employs Hoeffding bounds to analyze concentration of utility and cost in large markets.

Experimental results

Research questions

• RQ1 Can a truthful, budget-feasible mechanism achieve a better approximation ratio than $1/2$ in large crowdsourcing markets?
• RQ2 Is the $1 - 1/e$ approximation ratio tight for truthful, budget-feasible mechanisms in large markets?
• RQ3 Can the framework be extended to submodular utility functions while maintaining strong approximation guarantees?
• RQ4 How can almost budget-feasible mechanisms be transformed into strictly budget-feasible ones without significant loss in performance?

Key findings

• The proposed mechanism achieves a competitive ratio of $1 - 1/e \approx 0.63$, which is optimal and unimprovable by any truthful mechanism.
• The mechanism is proven to be optimal by showing that no truthful, budget-feasible mechanism can achieve a ratio better than $1 - 1/e$.
• For submodular utility functions, the paper presents a polynomial-time mechanism with improved approximation ratio over prior work.
• The mechanism can be converted into a strictly budget-feasible one with approximation ratio arbitrarily close to $1/2$ in large markets.
• The large market assumption—where individual costs are small relative to the budget—enables significant improvement over prior impossibility results from small-market settings.