Feature: Add Fair Lotteries algorithms and GCR baseline

[dotandanino]

Description

This PR introduces the randomized algorithms from the AAAI-24 paper "Fair Lotteries for Participatory Budgeting," alongside a baseline implementation of the Greedy Cohesive Rule (GCR).

Files Added

• Fair_Lotteries_for_Participatory_Budgeting.py
• pabutools/rules/gcr/ (module files)
• pabutools/rules/lottery/ (module files)
• tests/test_bw_algorithms.py

Testing

• All 151 tests and 85 subtests pass successfully locally.

[Simon-Rey]

Thank you very much for your submission. I have quickly looked at the formatting/writing up of the code. There are few comments of the things I would like you to fix before merging ;)

I have not checked the code itself, I assume that you have included sufficient tests to trust that the functions behave as expected.

[Simon-Rey]

Thanks for the improvements. I've made some new comments, we're almost there ;)

[codecov-commenter]

Codecov Report

❌ Patch coverage is 79.09605% with 74 lines in your changes missing coverage. Please review.
✅ Project coverage is 84.81%. Comparing base (49105f3) to head (36eccd7).
⚠️ Report is 35 commits behind head on main.

Files with missing lines	Patch %	Lines
pabutools/analysis/justifiedrepresentation.py	15.21%	39 Missing ⚠️
pabutools/rules/lottery/lottery_rule.py	84.21%	33 Missing ⚠️
pabutools/rules/gcr/gcr_rule.py	96.61%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #67      +/-   ##
==========================================
- Coverage   85.33%   84.81%   -0.52%     
==========================================
  Files          53       58       +5     
  Lines        4165     4518     +353     
==========================================
+ Hits         3554     3832     +278     
- Misses        611      686      +75     

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[dotandanino]

Hello dear Simon, We fixed the comments and would like recheck

[Simon-Rey]

First the tests fail, so please fix and re-run the tests before pushing.

[Simon-Rey]

Then, I don't really understand the functions in "justifiedrepresentation.py". I am not sure they deserve to be in the package. One reason is that they all use objects and types that are different from the ones used in the package (cost dicts instead of simply the in-built Project class). Second reason is that I am not fully convinced by the "random" function that just sample some groups. I don't really see why would people use that. If anything, I would want a full perfect check that maybe has an extra parameter to just sample few groups. Do you need these functions elsewhere? If not, then I would just not include them in the PR.