Undergraduate Research at IMD Returns in Summer 2021
IMD’s second annual summer research program is underway, in collaboration with Wellesley College’s Science Center Summer Research Program. For the next several months, six Wellesley math and computer science students will work on the following projects:
Eliza Zizka ’22 is working on interpreting some standard results in social choice theory, such as Arrow’s Theorem and the Gibbard-Satterthwaite Theorem, in terms of category theory. She will try to establish a framework by which social choice functions can be regarded in terms of functors between certain categories and recast some of the standard criteria and properties of social choice functions in terms of this language.
Anastasia Brooks ’23 and Ava Mock ’23 are working on applications of combinatorial topology to power indices. They will use simplicial complexes to model coalition structures where some of the coalitions are not possible. They are hoping that the topology of simplicial complexes will provide new formulas for the Banzhaf and Shapley-Shubik indices for this generalized setup where not all coalitions are allowed.
Hayley Grape ’23 is working on an algorithm to find an “average” redistricting map out of a set of randomly generated maps. She is experimenting with defining distance metrics to identify a central map within a set.
Audrey Ballarin ’23 and Heeba Nazeer ’23 are identifying properties of a central delegation mechanism for a liquid democracy system. They are exploring algorithmic possibilities for minimizing concentrated power, capping power, and splitting individual votes between delegates.
