# Important open problems in voting

post by Closed Limelike Curves · 2024-07-01T02:53:44.690Z · LW · GW · 1 comments## Contents

Strategy-resistance Properties of Multiwinner voting systems None 1 comment

**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.

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## comment by Nathan Helm-Burger (nathan-helm-burger) · 2024-07-02T00:40:07.017Z · LW(p) · GW(p)

I'm not sure how well this translates to multi winner elections, but I think it's a cool method.

Minimum Partial Consensus Voting Fair group decisions via non-deterministic proportional consensus

Jobst Heitzig, Forest W. Simmons and Sara M. Constantino

Springer Nature 2021

paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3751225