Reproduce “Almost optimal manipulation of a pair of alternatives” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Jacek Szybowski, Konrad Kułakowski, Sebastian Ernst
A method is introduced to quantify the difficulty of manipulating rankings derived from pairwise comparisons by finding the minimal changes needed to equate the priorities of two selected alternatives. The approach leverages orthogonal projections to compute the closest manipulated matrix and proposes an Ease of Manipulation Index (EMI), demonstrating that manipulating specific alternatives does not alter the relative priorities of others.
Key insights
- Achieving a direct rank reversal of two alternatives is often difficult, but finding the closest matrix that equates their priorities is mathematically tractable and serves as an "almost optimal" manipulation.
- The "tie space," where two selected alternatives have equal priorities, is a linear subspace with a provable dimension and an explicitly constructible basis.
- Orthogonal projection onto this tie space results in a manipulated matrix where only the targeted alternatives' priorities are affected (equated to their original arithmetic mean), while others remain unchanged.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.