Clone-Robust Weights in Metric Spaces: Handling Redundancy Bias in Benchmark Aggregation

Damien Berriaud, Roger Wattenhofer

Keywords: Redundancy Bias, Near-Clones, Weight Sharing, Local Voting, Metric Space

TL;DR: This paper introduces a theoretical framework for weighting elements in a metric space and proposes clone-proof representation functions that distribute importance fairly by ensuring similar elements share weights.

Abstract:

We are given a set of elements in a metric space. The distribution of the elements is arbitrary, possibly adversarial. Can we weigh the elements in a way that is resistant to such (adversarial) manipulations?
This problem arises in various contexts. For instance, the elements could represent data points, requiring robust domain adaptation. Alternatively, they might represent tasks to be aggregated into a benchmark; or questions about personal political opinions in voting advice applications.
This article introduces a theoretical framework for dealing with such problems. We propose clone-proof weighting functions as a solution concept. These functions distribute importance across elements of a set such that similar objects (``clones'') share (some of) their weights, thus avoiding a potential bias introduced by their multiplicity.
Our framework extends the maximum uncertainty principle to accommodate general metric spaces and includes a set of axioms - symmetry, continuity, and clone-proofness - that guide the construction of weighting functions.
Finally, we address the existence of weighting functions satisfying our axioms in the significant case of Euclidean spaces and propose a general method for their construction.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 1240