LW - Important open problems in voting by Closed Limelike Curves

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Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Important open problems in voting, published by Closed Limelike Curves on July 2, 2024 on LessWrong.
Strategy-resistance
Identify, or prove impossibility, of a voting system which incentivizes
1. A strictly sincere ranking of all candidates in the zero-information setting, where it implements a "good" social choice rule such as the relative (normalized) utilitarian rule, a Condorcet social choice rule, or the Borda rule.
2. In a Poisson game or similar setting: a unique semi-sincere Nash equilibrium that elects the Condorcet winner (if one exists), similar to those shown for approval voting by Myerson and Weber (1993) and Durand et al. (2019).
Properties of Multiwinner voting systems
There's strikingly little research on multiwinner voting systems. You can find a table of criteria for single-winner systems on Wikipedia, but if you try and find the same for multi-winner systems, there's nothing. Here's 9 important criteria we can judge multiwinner voting systems on:
1. Independence of Irrelevant Alternatives
2. Independence of Universally-Approved Candidates
3. Monotonicity
4. Participation
5. Precinct-summability
6. Polynomial-time approximation scheme
7. Proportionality for solid coalitions
8. Perfect representation in the limit
9. Core-stability (may need to be approximated within a constant factor)
I'm curious which combinations of these properties exist. Probabilistic/weighted voting systems are allowed.
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