The study of interactive proofs in the quantum setting has yielded profound insights in complexity theory and quantum information. A curious feature of these results is that the advantage, in terms of computational power, of quantum models over their classical counterparts is usually due to entanglement phenomena rather than quantum communication with the verifier. For example, it is known that QIP = IP = PSPACE, and QMIP with unentangled provers is equal to NEXP = MIP; on the other hand, MIP* = RE. In this work we initiate the general study of (quantum) positional multi-prover interactive proofs ((Q)PMIP), in which provers and verifiers positioned in space communicate freely save for the constraints imposed by the speed of light. We investigate how the class of languages decidable by (Q)PMIPs depends on the arrangement of the verifiers and (honest) provers. In the case of classical PMIPs, we show a dichotomy: if the arrangement satisfies what we call the "min-ball" condition, then the class is NEXP, otherwise it is PSPACE. We then exhibit an arrangement that does not satisfy the min-ball condition for which there is a quantum PMIP for EXP in the no pre-shared entanglement model. Our construction is based on positional cryptography and MIPs with no-signaling soundness. We introduce a new positional primitive, the positional hardcore bit, which allows a pair of spatially separated players to transmit a random bit to a particular location while guaranteeing that it remains strongly unguessable elsewhere.

Large language models (LLMs) often exhibit sycophancy: agreement with user stance even when it conflicts with the model’s opinion. While prior work has mostly studied this in single-agent settings, it remains underexplored in collaborative multi-agent systems. We ask whether awareness of other agents’ sycophancy levels influences discussion outcomes. To investigate this, we run controlled experiments with six open-source LLMs, providing agents with peer sycophancy rankings that estimate each peer’s tendency toward sycophancy. These rankings are based on scores calculated using various static (pre-discussion) and dynamic (online) strategies. We find that providing sycophancy priors reduces the influence of sycophancy-prone peers, mitigates error-cascades, and improves final discussion accuracy by an absolute 10.5%. Thus, this is a lightweight and efficient way to reduce model sycophancy during discussions and subsequently improve downstream accuracy.