Characterizing Necessary Losers to Explain Tournaments Losers
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
The Flow has not summarised this story yet — read it at arXiv AI.
arXiv:2608.23446v2 Announce Type: replace Abstract: We study the problem of formally explaining why a candidate was not selected by a given tournament rule, by identifying sub-tournaments in which th...
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The paper investigates proportional representation in a temporal voting setting where a single candidate is chosen each round and voters submit ranked preferences that may evolve over time. It extends classic proportionality axioms—justified representation (JR), proportional JR (PJR), extended JR (EJR), and proportionality for solid coalitions (PSC)—to accommodate various ways of determining which top-ranked candidates are considered approved, ranging from a fixed common cutoff to individual, round‑specific cutoffs. The authors analyze which axioms can be guaranteed under different informational assumptions about future rounds, showing that while EJR is unattainable, JR, PJR, and PSC can be achieved with a fixed cutoff if all preferences are known in advance; varying cutoffs reduce guarantees, yet PJR can still be achieved efficiently for groups that agree in every round, and PSC can be satisfied without future knowledge. They also demonstrate that checking these axioms is often coNP‑complete, though some stronger axioms may be easier to verify.
The paper proposes a transparent, user‑configurable rule for selecting arguments in deliberative polls, replacing opaque learned rankers. It formalises argument selection over bipolar justification sets, introduces seven civic recommender criteria, and presents a one‑hop reversed endorsement flow rule that meets them. Experiments on 17,000 simulated runs show the rule performs comparably to random on coverage but outperforms other methods on endorsement mass and robustness under adversarial pressure.
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