Compute smallest quota for which properties are satisfied

[DominikPeters]

As a measure of proportionality, it could be interesting to be able to compute the smallest quota for which a property like JR, EJR+, core is satisfied. For a committee satisfying the property the quota will be n/k or smaller (with smaller values corresponding to "more representative"), and for failures it will be larger.

For JR and EJR+, it should be possible to find this value in polynomial time by relatively straightforward adaptation of the property checking algorithms (so it is a natural place to start working there). For PJR/EJR/FJR/core, it might be possible to get this value by adding a variable to the ILP and optimizing it.

I'm unsure where this should be put. Conceptually it makes sense as a scoring function. But it could also be part of some extended output of the property checker, or be a separate property.

[martinlackner]

Good idea! Finding suitable algorithms for the main proportionality notions (and implementing them) could be a nice student research project.

I'm unsure where this should be put. Conceptually it makes sense as a scoring function. But it could also be part of some extended output of the property checker, or be a separate property.

properties.py is the right place. scores.py is meant for scores related to the computation of ABC voting rules.

[erelsgl]

Great idea. Does it make sense to also check this notion for stronger properties such as Average-JR, which cannot be satisfied with the n/k quota? (Average-JR = for every subset of L quotas who agree on L candidates, the average satisfaction of the voters in the subset is at least L. Stronger than EJR, which only requires that the maximum satisfaction is at least L. Arguably it is more natural than EJR).