Flexible reward plans for crowdsourced tasks

Yuko Sakurai, Masato Shinoda, Satoshi Oyama, Makoto Yokoo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


We develop flexible reward plans to elicit truthful predictive probability distribution over a set of uncertain events from workers. In general, strictly proper scoring rules for categorical events only reward a worker for an event that actually occurred. However, different incorrect predictions vary in quality, and the principal would like to assign different rewards to them, according to her subjective similarity among events; e.g. a prediction of overcast is closer to sunny than rainy. We propose concrete methods so that the principal can assign rewards for incorrect predictions according to her similarity between events. We focus on two representative examples of strictly proper scoring rules: spherical and quadratic, where a worker’s expected utility is represented as the inner product of her truthful predictive probability and her declared probability. In this paper, we generalize the inner product by introducing a reward matrix that defines a reward for each prediction outcome pair. We first show that if the reward matrix is symmetric and positive definite, both the spherical and quadratic proper scoring rules guarantee the maximization of a worker’s expected utility when she truthfully declares her prediction. We next compare our rules with the original spherical/quadratic proper scoring rules in terms of the variance of rewards obtained by workers. Finally, we show our experimental results using Amazon Mechanical Turk.

Original languageEnglish
Title of host publicationPRIMA 2015
Subtitle of host publicationPrinciples and Practice of Multi-Agent Systems - 18th International Conference, Proceedings
EditorsPaolo Torroni, Andrea Omicini, Jane Hsu, Qingliang Chen, Paolo Torroni, Andrea Omicini, Jane Hsu, Qingliang Chen, Serena Villata, Serena Villata
PublisherSpringer Verlag
Number of pages16
ISBN (Print)9783319255231, 9783319255231
Publication statusPublished - 2015
Event18th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2015 - Bertinoro, Italy
Duration: Oct 26 2015Oct 30 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other18th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2015

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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