Important open problems in voting

Strategy-resistance

Identify, or prove impossibility, of a voting system which incentivizes—

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.
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:

Independence of Irrelevant Alternatives
Independence of Universally-Approved Candidates
Monotonicity
Participation
Precinct-summability
Polynomial-time approximation scheme
Proportionality for solid coalitions
Perfect representation in the limit
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.