Condorcet-type properties of the linear ordering problem with ties

Source: cs.GT updates on arXiv.org — https://arxiv.org/abs/2609.19593 Date read: 2026-09-22 Connected to: L-019 Kind: content Escalation: store-only Escalation rationale:

What this is

A computational social choice paper extending the Kemeny rule (a preference aggregation mechanism) to handle tied rankings, and proving that strengthened Condorcet-type criteria hold under this extension. This is a technical optimization and axiomatic properties result within preference aggregation, not a primary theoretical investigation of the representation-rationalizability tradeoff itself.

What I took from it

The paper strengthens formal guarantees around a specific aggregation rule but does not interrogate the deeper tension between representativeness (how faithfully the aggregate ranking reflects input diversity) and rationalizability (whether the aggregate can be justified as the preference of a single coherent agent). The Kemeny rule is known to be representationally rich — it can aggregate conflicting preferences without forcing artificial consensus — but the paper does not examine whether this richness comes at the cost of auditability, interpretability, or behavioral predictability in agents who receive the aggregated output.

The extension to ties is mechanically sound but does not address whether handling ties increases the computational opacity of the aggregation, or whether agents conditioning behavior on tie-inclusive rankings exhibit different strategic behavior than agents receiving strict orderings. No evidence that the axioms tested (XCC, SCC) remain behaviorally meaningful when the aggregation protocol becomes less intelligible to its users.

Research connections

L-019: The paper demonstrates formal properties of the Kemeny aggregation rule but does not examine whether the tradeoff between representativeness and scalar justifiability changes when the protocol handles ties, or whether legibility of the aggregation process affects adoption.
seed-133: Metric formalization (Condorcet criteria as formal axioms) may lock the field into evaluating aggregation quality via axiomatic rather than behavioral or coordination-outcome measures.
seed-146: Kemeny aggregation is a form of matching proxy substitution — using distance-minimization as a proxy for "best consensus ranking" — but the paper does not examine whether this proxy's faithfulness varies with ranking complexity or tie prevalence.

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