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QUESTION: Can you comment on additivity assumptions for the valuations of the agents?
Peter van Emde Boas
Question: how about mechanisms involving randomness?
QUESTION: Does the Balinski-Young result on inevitability of the non-monotonicity (Alabama paradox) apply here?
QUESTION: Do you have any idea of what sort of algorithm would give all monotonicity properties and WWEF1? Is possible that it will be implementable as a picking sequence?
Have you considered taking an agent with high weight and replacing her with several agents having smaller weights — this would work only with some very specific weight distributions?
I’m not sure I fully got Siddharth Barman’s question, but there is an impossibility on deterministic allocations being strategyproof, but that’s in settings where agents can influence the weights of others, which is not this case
(It’s in Aziz et al., AIJ 2019)
QUESTION: Did you turn up any of the examples that have non-unique minimal integer weights?