# Optimal Impartial Selection

• Applications accepted all year round
• Competition Funded PhD Project (Students Worldwide)

## Project Description

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2020 for students seeking funding, or in January 2020 or April 2020 for self-funded students. The deadline for funded applications is the 31st of January 2020. The deadline for China Scholarship Council Scheme applications is 12th January 2020.

This project will be supervised by Dr. Felix Fischer.

Impartial selection is the problem of selecting some of the members of a group of individuals based on nominations from other members of the group, in such a way that no individual can influence their own chance of being selected. The problem was first considered independently by Holzman and Moulin [2013] and by Alon et al. [2011] and has since then been studied quite extensively in economics, mathematics, and computer science. It has applications in peer review, committee elections, performance appraisals, and many other situations where members of a group are selected for an award or assigned a task. Of particular interest are optimal mechanisms, which subject to impartiality select individuals who receive as many nominations as possible.

If we identify individuals with the vertices of graph and nominations with directed edges in that graph, a mechanisms for impartial selection is given by a function that maps every directed graph to a probability distribution over its vertices and satisfies certain constraints across the set of all graphs with the same number of vertices. A mechanism is optimal if among all such functions it maximizes the minimum expected overall indegree of the set of vertices selected, where the minimum is taken over the set of all graphs.

Optimal impartial mechanisms are currently known only for the selection of a single individual [Fischer and Klimm, 2015] and in the limit as the number of individuals to be selected goes to infinity [Alon et al., 2011]. For all other cases upper and lower bounds have been given on the maximum quality of the individuals selected [Bjelde et al., 2017]. These results were obtained using fairly elemantary techniques from discrete probability and linear optimization.

A PhD project on optimal impartial selection could for example pursue better upper and lower bounds for the selection of two or more individuals, seek improvements for the special case without abstentions, where each individual must submit at least one nomination, or study mechanisms for a more general problem where nominations can vary in intensity.

The application procedure is described on the School website. For further inquiries please contact Dr. Felix Fischer at . This project is eligible for full funding, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process.

## Funding Notes

This project is eligible for full funding, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs.

This project can be undertaken as a self-funded project. Self-funded applications are accepted year-round for a January, April or September start.

We welcome applicants through the China Scholarship Council Scheme (deadline for applications 12th January 2020).

The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award we offer family friendly benefits and support part-time study.

## References

N. Alon, F. Fischer, A. D. Procaccia, and M. Tennenholtz. Sum of us: Strategyproof selection from the selectors. In Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge, pages 101–110, 2011.

A. Bjelde, F. Fischer, and M. Klimm. Impartial selection and the power of up to two choices. ACM Transactions on Economics and Computation, 5(4):21:1–21:20, 2017.

F. Fischer and M. Klimm. Optimal impartial selection. SIAM Journal on Computing, 44 (5):1263–1285, 2015.

R. Holzman and H. Moulin. Impartial nominations for a prize. Econometrica, 81(1):173–196, 2013.

## How good is research at Queen Mary University of London in Mathematical Sciences?

FTE Category A staff submitted: 34.80

Research output data provided by the Research Excellence Framework (REF)

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