From cf5370ae0362688888bcf161e8a9146bc3a48c4f Mon Sep 17 00:00:00 2001
From: im359 <im359@cornell.edu>
Date: Fri, 20 Mar 2026 13:46:51 -0400
Subject: [PATCH] feat: add maximin analysis script, update core libraries to
 use native len(), and generate final comparison strip plots

---
 analysis/sf_c_44_maximin_plot.pdf             | Bin 0 -> 18724 bytes
 analysis/sf_c_44_plot.pdf                     | Bin 0 -> 19366 bytes
 analysis/sf_c_44_stats.txt                    |   6 +
 analysis/sf_e_110_maximin_plot.pdf            | Bin 0 -> 37440 bytes
 analysis/sf_e_110_plot.pdf                    | Bin 0 -> 38128 bytes
 analysis/sf_e_110_stats.txt                   |   6 +
 analyze.py                                    | 168 +++++++++
 analyze_maximin.py                            | 157 ++++++++
 .../committee_generation/leximin.py           |   6 +-
 .../committee_generation/maximin.py           |   2 +-
 .../committee_generation/newleximin.py        | 268 ++++++++++++++
 .../committee_generation/og_leximin.py        | 334 ++++++++++++++++++
 .../committee_generation/op1_leximin.py       | 250 +++++++++++++
 .../committee_generation/op2_leximin.py       | 273 ++++++++++++++
 .../committee_generation/op4_leximin.py       | 213 +++++++++++
 15 files changed, 1679 insertions(+), 4 deletions(-)
 create mode 100644 analysis/sf_c_44_maximin_plot.pdf
 create mode 100644 analysis/sf_c_44_plot.pdf
 create mode 100644 analysis/sf_c_44_stats.txt
 create mode 100644 analysis/sf_e_110_maximin_plot.pdf
 create mode 100644 analysis/sf_e_110_plot.pdf
 create mode 100644 analysis/sf_e_110_stats.txt
 create mode 100644 analyze.py
 create mode 100644 analyze_maximin.py
 create mode 100644 src/sortition_algorithms/committee_generation/newleximin.py
 create mode 100644 src/sortition_algorithms/committee_generation/og_leximin.py
 create mode 100644 src/sortition_algorithms/committee_generation/op1_leximin.py
 create mode 100644 src/sortition_algorithms/committee_generation/op2_leximin.py
 create mode 100644 src/sortition_algorithms/committee_generation/op4_leximin.py

diff --git a/analysis/sf_c_44_maximin_plot.pdf b/analysis/sf_c_44_maximin_plot.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..8d905c834da4516641a57200193508795a6aafa1
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diff --git a/analysis/sf_c_44_stats.txt b/analysis/sf_c_44_stats.txt
new file mode 100644
index 0000000..af6dbbe
--- /dev/null
+++ b/analysis/sf_c_44_stats.txt
@@ -0,0 +1,6 @@
+Validation: PASS
+Sum of Probs: 44.0000 (Target k=44)
+Average Time: 1.62s
+Gini Fairness: 52.7260%
+Min Prob: 0.085937
+Max Prob: 1.000000
diff --git a/analysis/sf_e_110_maximin_plot.pdf b/analysis/sf_e_110_maximin_plot.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..d9228485894489613517047ca1db6944a0544576
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HcmV?d00001

diff --git a/analysis/sf_e_110_stats.txt b/analysis/sf_e_110_stats.txt
new file mode 100644
index 0000000..05a20c7
--- /dev/null
+++ b/analysis/sf_e_110_stats.txt
@@ -0,0 +1,6 @@
+Validation: PASS
+Sum of Probs: 110.0000 (Target k=110)
+Average Time: 169.60s
+Gini Fairness: 51.6610%
+Min Prob: 0.026144
+Max Prob: 1.000000
diff --git a/analyze.py b/analyze.py
new file mode 100644
index 0000000..1b35083
--- /dev/null
+++ b/analyze.py
@@ -0,0 +1,168 @@
+# coding: utf-8
+import csv
+import argparse
+import logging  # <-- NEW: Imported the logging module!
+from argparse import ArgumentParser
+from dataclasses import dataclass
+from math import ceil, isclose
+from pathlib import Path
+import time
+from typing import Dict, List, Any, NewType, Union, Tuple
+import sys
+import os
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+from scipy.stats.mstats import gmean
+
+sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), 'src')))
+
+try:
+    from sortition_algorithms.committee_generation.leximin import find_distribution_leximin
+except ImportError as e:
+    print(f"CRITICAL ERROR: Could not locate leximin.py. Details: {e}")
+    exit(1)
+
+AgentId = NewType("AgentId", Any)
+FeatureCategory = NewType("FeatureCategory", str)
+Feature = NewType("Feature", str)
+
+@dataclass
+class FeatureInfo:
+    min: int
+    max: int
+    selected: int = 0
+    remaining: int = 0
+
+ProbAllocation = NewType("ProbAllocation", Dict[AgentId, float])
+
+@dataclass
+class Instance:
+    k: int
+    categories: Dict[FeatureCategory, Dict[Feature, FeatureInfo]]
+    agents: Dict[AgentId, Dict[FeatureCategory, Feature]]
+
+def read_instance(feature_file: Union[str, Path], pool_file: Union[str, Path], k: int) -> Instance:
+    feature_info = {}
+    with open(feature_file, "r", encoding="utf-8") as file:
+        reader = csv.DictReader(file)
+        for line in reader:
+            category = FeatureCategory(line["category"])
+            feature = Feature(line["name"]) 
+            if category not in feature_info:
+                feature_info[category] = {}
+            feature_info[category][feature] = FeatureInfo(min=int(line["min"]), max=int(line["max"]))
+
+    categories = list(feature_info)
+    agents = {}
+    with open(pool_file, "r", encoding="utf-8") as file:
+        reader = csv.DictReader(file)
+        for i, line in enumerate(reader):
+            agent_id = AgentId(str(i))
+            agents[agent_id] = {category: Feature(line[category]) for category in categories}
+            for category in categories:
+                feature_info[category][Feature(line[category])].remaining += 1
+    return Instance(k=k, categories=feature_info, agents=agents)
+
+def leximin_probabilities(instance: Instance, backend: str = "mip") -> ProbAllocation:
+    portfolio, output_probs, _ = find_distribution_leximin(
+        instance.categories, 
+        instance.agents, 
+        instance.k, 
+        [], 
+        solver_backend=backend
+    )
+    selection_probs = {agent_id: 0. for agent_id in instance.agents}
+    for panel, probability in zip(portfolio, output_probs):
+        for agent_id in panel:
+            selection_probs[agent_id] += probability
+    return ProbAllocation(selection_probs)
+
+@dataclass
+class ProbAllocationStats:
+    gini: float
+    geometric_mean: float
+    min: float
+    max: float  
+
+def compute_prob_allocation_stats(alloc: ProbAllocation) -> ProbAllocationStats:
+    n = len(alloc)
+    k = round(sum(alloc.values()))
+    sorted_probs = sorted(alloc.values())
+    gini = sum((2 * i - n + 1) * prob for i, prob in enumerate(sorted_probs)) / (n * k)
+    geometric_mean = gmean([max(p, 1e-10) for p in sorted_probs])
+    mini = min(sorted_probs)
+    maxi = max(sorted_probs) 
+    return ProbAllocationStats(gini=gini, geometric_mean=geometric_mean, min=mini, max=maxi)
+
+def analyze_instance(instance_name: str, instance: Instance, backend: str, num_runs: int = 3):
+    Path("analysis").mkdir(exist_ok=True)
+    print(f"Running analysis with {backend} backend ({num_runs} runs)...")
+    
+    timings = []
+    alloc = None
+    for i in range(num_runs):
+        start_time = time.time()
+        alloc = leximin_probabilities(instance, backend)
+        timings.append(time.time() - start_time)
+        print(f"  Run {i + 1}/{num_runs} complete.")
+    
+    total_prob = sum(alloc.values())
+    is_valid = isclose(total_prob, instance.k, rel_tol=1e-5)
+    
+    stats = compute_prob_allocation_stats(alloc)
+    
+    log_path = Path("analysis") / f"{instance_name}_{instance.k}_stats.txt"
+    with open(log_path, "w") as f:
+        f.write(f"Validation: {'PASS' if is_valid else 'FAIL'}\n")
+        f.write(f"Sum of Probs: {total_prob:.4f} (Target k={instance.k})\n")
+        f.write(f"Average Time: {sum(timings)/num_runs:.2f}s\n")
+        f.write(f"Gini Fairness: {stats.gini:.4%}\n")
+        f.write(f"Min Prob: {stats.min:.6f}\n")
+        f.write(f"Max Prob: {stats.max:.6f}\n")
+    
+    n = len(alloc)
+    probs = list(alloc.values())
+    
+    plt.figure(figsize=(10, 3)) 
+    
+    rng = np.random.default_rng(42)
+    jitter = 0.22
+    y_vals = rng.uniform(-jitter, jitter, size=n)
+    
+    plt.scatter(probs, y_vals, s=18, alpha=0.55, color="tab:blue", label="Leximin")
+    
+    plt.axvline(x=instance.k/n, color='black', linestyle='--', linewidth=1, label=f'Equalized (k/n = {instance.k/n:.4f})')
+    plt.axvline(x=stats.min, color='red', linestyle=':', alpha=0.5, label=f'Min: {stats.min:.4f}')
+    plt.axvline(x=stats.max, color='orange', linestyle=':', alpha=0.5, label=f'Max: {stats.max:.4f}')
+    
+    plt.yticks([0], ["Leximin"])
+    plt.grid(axis="x", alpha=0.25)
+    plt.ylim(-0.6, 0.6)
+    plt.title(f"Marginal Selection Probabilities: {instance_name} (n={n}, k={instance.k})")
+    plt.xlabel("Selection Probability")
+    plt.legend(loc="upper right")
+    
+    output_path = Path("analysis") / f"{instance_name}_{instance.k}_plot.pdf"
+    plt.savefig(output_path, bbox_inches="tight")
+    plt.close()
+    
+    print(f"VALIDATION: {'✅ PASS' if is_valid else '❌ FAIL'} (Sum={total_prob:.2f})")
+    print(f"Gini Score: {stats.gini:.4%}")
+    print(f"Min/Max Probs: {stats.min:.6f} / {stats.max:.6f}")
+
+if __name__ == '__main__':
+    # --- NEW: Turn on the "chatty" debug logs! ---
+    # To make it less spammy later, change logging.DEBUG to logging.INFO
+    logging.basicConfig(level=logging.INFO, format='%(levelname)s: %(message)s')
+    
+    parser = ArgumentParser()
+    parser.add_argument('instance_name')
+    parser.add_argument('panel_size', type=int)
+    parser.add_argument('--backend', default='mip')
+    args = parser.parse_args()
+
+    data_path = Path("data") / f"{args.instance_name}_{args.panel_size}"
+    instance = read_instance(data_path / "categories.csv", data_path / "respondents.csv", args.panel_size)
+    analyze_instance(args.instance_name, instance, args.backend)
\ No newline at end of file
diff --git a/analyze_maximin.py b/analyze_maximin.py
new file mode 100644
index 0000000..3025c5b
--- /dev/null
+++ b/analyze_maximin.py
@@ -0,0 +1,157 @@
+# coding: utf-8
+import csv
+import argparse
+from argparse import ArgumentParser
+from dataclasses import dataclass
+from math import ceil, isclose
+from pathlib import Path
+import time
+from typing import Dict, List, Any, NewType, Union, Tuple
+import sys
+import os
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+from scipy.stats.mstats import gmean
+
+sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), 'src')))
+
+# IMPORT SWAPPED TO MAXIMIN
+try:
+    from sortition_algorithms.committee_generation.maximin import find_distribution_maximin
+except ImportError as e:
+    print(f"CRITICAL ERROR: Could not locate maximin.py. Details: {e}")
+    exit(1)
+
+AgentId = NewType("AgentId", Any)
+FeatureCategory = NewType("FeatureCategory", str)
+Feature = NewType("Feature", str)
+
+@dataclass
+class FeatureInfo:
+    min: int
+    max: int
+    selected: int = 0
+    remaining: int = 0
+
+ProbAllocation = NewType("ProbAllocation", Dict[AgentId, float])
+
+@dataclass
+class Instance:
+    k: int
+    categories: Dict[FeatureCategory, Dict[Feature, FeatureInfo]]
+    agents: Dict[AgentId, Dict[FeatureCategory, Feature]]
+
+def read_instance(feature_file: Union[str, Path], pool_file: Union[str, Path], k: int) -> Instance:
+    feature_info = {}
+    with open(feature_file, "r", encoding="utf-8") as file:
+        reader = csv.DictReader(file)
+        for line in reader:
+            category = FeatureCategory(line["category"])
+            feature = Feature(line["name"]) 
+            if category not in feature_info:
+                feature_info[category] = {}
+            feature_info[category][feature] = FeatureInfo(min=int(line["min"]), max=int(line["max"]))
+
+    categories = list(feature_info)
+    agents = {}
+    with open(pool_file, "r", encoding="utf-8") as file:
+        reader = csv.DictReader(file)
+        for i, line in enumerate(reader):
+            agent_id = AgentId(str(i))
+            agents[agent_id] = {category: Feature(line[category]) for category in categories}
+            for category in categories:
+                feature_info[category][Feature(line[category])].remaining += 1
+    return Instance(k=k, categories=feature_info, agents=agents)
+
+def maximin_probabilities(instance: Instance, backend: str = "mip") -> ProbAllocation:
+    portfolio, output_probs, _ = find_distribution_maximin(
+        instance.categories, 
+        instance.agents, 
+        instance.k, 
+        [], 
+        solver_backend=backend
+    )
+    selection_probs = {agent_id: 0. for agent_id in instance.agents}
+    for panel, probability in zip(portfolio, output_probs):
+        for agent_id in panel:
+            selection_probs[agent_id] += probability
+    return ProbAllocation(selection_probs)
+
+@dataclass
+class ProbAllocationStats:
+    gini: float
+    geometric_mean: float
+    min: float
+    max: float  
+
+def compute_prob_allocation_stats(alloc: ProbAllocation) -> ProbAllocationStats:
+    n = len(alloc)
+    k = round(sum(alloc.values()))
+    sorted_probs = sorted(alloc.values())
+    gini = sum((2 * i - n + 1) * prob for i, prob in enumerate(sorted_probs)) / (n * k)
+    geometric_mean = gmean([max(p, 1e-10) for p in sorted_probs])
+    mini = min(sorted_probs)
+    maxi = max(sorted_probs) 
+    return ProbAllocationStats(gini=gini, geometric_mean=geometric_mean, min=mini, max=maxi)
+
+def analyze_instance(instance_name: str, instance: Instance, backend: str, num_runs: int = 1):
+    Path("analysis").mkdir(exist_ok=True)
+    print(f"Running MAXIMIN analysis with {backend} backend ({num_runs} runs)...")
+    
+    timings = []
+    alloc = None
+    for i in range(num_runs):
+        start_time = time.time()
+        alloc = maximin_probabilities(instance, backend)
+        timings.append(time.time() - start_time)
+        print(f"  Run {i + 1}/{num_runs} complete.")
+    
+    total_prob = sum(alloc.values())
+    is_valid = isclose(total_prob, instance.k, rel_tol=1e-5)
+    
+    stats = compute_prob_allocation_stats(alloc)
+    
+    # Plotting (Scatter Strip Plot Aesthetic)
+    n = len(alloc)
+    probs = list(alloc.values())
+    
+    plt.figure(figsize=(10, 3)) 
+    
+    rng = np.random.default_rng(42)
+    jitter = 0.22
+    y_vals = rng.uniform(-jitter, jitter, size=n)
+    
+    # Changed dot color to Red for Maximin
+    plt.scatter(probs, y_vals, s=18, alpha=0.55, color="tab:red", label="Maximin")
+    
+    plt.axvline(x=instance.k/n, color='black', linestyle='--', linewidth=1, label=f'Equalized (k/n = {instance.k/n:.4f})')
+    plt.axvline(x=stats.min, color='red', linestyle=':', alpha=0.5, label=f'Min: {stats.min:.4f}')
+    plt.axvline(x=stats.max, color='orange', linestyle=':', alpha=0.5, label=f'Max: {stats.max:.4f}')
+    
+    plt.yticks([0], ["Maximin"])
+    plt.grid(axis="x", alpha=0.25)
+    plt.ylim(-0.6, 0.6)
+    plt.title(f"Maximin Selection Probabilities: {instance_name} (n={n}, k={instance.k})")
+    plt.xlabel("Selection Probability")
+    plt.legend(loc="upper right")
+    
+    output_path = Path("analysis") / f"{instance_name}_{instance.k}_maximin_plot.pdf"
+    plt.savefig(output_path, bbox_inches="tight")
+    plt.close()
+    
+    print(f"VALIDATION: {'✅ PASS' if is_valid else '❌ FAIL'} (Sum={total_prob:.2f})")
+    print(f"Gini Score: {stats.gini:.4%}")
+    print(f"Min/Max Probs: {stats.min:.6f} / {stats.max:.6f}")
+
+if __name__ == '__main__':
+    parser = ArgumentParser()
+    parser.add_argument('instance_name')
+    parser.add_argument('panel_size', type=int)
+    parser.add_argument('--backend', default='mip')
+    args = parser.parse_args()
+
+    data_path = Path("data") / f"{args.instance_name}_{args.panel_size}"
+    instance = read_instance(data_path / "categories.csv", data_path / "respondents.csv", args.panel_size)
+    analyze_instance(args.instance_name, instance, args.backend)
\ No newline at end of file
diff --git a/src/sortition_algorithms/committee_generation/leximin.py b/src/sortition_algorithms/committee_generation/leximin.py
index 1a17c89..628a3a8 100644
--- a/src/sortition_algorithms/committee_generation/leximin.py
+++ b/src/sortition_algorithms/committee_generation/leximin.py
@@ -249,8 +249,8 @@ def _run_leximin_main_loop(
     fixed_probabilities: dict[str, float] = {}
     reduction_counter = 0
 
-    while len(fixed_probabilities) < people.count:
-        logger.debug(f"Fixed {len(fixed_probabilities)}/{people.count} probabilities.")
+    while len(fixed_probabilities) < len(people):
+        logger.debug(f"Fixed {len(fixed_probabilities)}/{len(people)} probabilities.")
 
         dual_model, dual_agent_vars, dual_cap_var = _dual_leximin_stage(
             people,
@@ -321,7 +321,7 @@ def find_distribution_leximin(
 
     # Find initial committees that cover every possible agent
     committees, covered_agents, initial_report = generate_initial_committees(
-        new_committee_solver, agent_vars, 3 * people.count
+        new_committee_solver, agent_vars, 3 * len(people)
     )
     report.add_report(initial_report)
 
diff --git a/src/sortition_algorithms/committee_generation/maximin.py b/src/sortition_algorithms/committee_generation/maximin.py
index d5265ce..09ca690 100644
--- a/src/sortition_algorithms/committee_generation/maximin.py
+++ b/src/sortition_algorithms/committee_generation/maximin.py
@@ -297,7 +297,7 @@ def find_distribution_maximin(
 
     # Find initial committees that cover every possible agent
     committees, covered_agents, init_report = generate_initial_committees(
-        new_committee_solver, agent_vars, people.count
+        new_committee_solver, agent_vars, len(people)
     )
     report.add_report(init_report)
 
diff --git a/src/sortition_algorithms/committee_generation/newleximin.py b/src/sortition_algorithms/committee_generation/newleximin.py
new file mode 100644
index 0000000..55f8467
--- /dev/null
+++ b/src/sortition_algorithms/committee_generation/newleximin.py
@@ -0,0 +1,268 @@
+# ABOUTME: Leximin algorithm for committee generation.
+# ABOUTME: Maximizes minimum probability, breaking ties by second-lowest, third-lowest, etc.
+
+import logging
+from typing import Any
+
+import numpy
+
+try:
+    import gurobipy as grb
+
+    GUROBI_AVAILABLE = True
+except ImportError:
+    GUROBI_AVAILABLE = False
+    grb = None
+
+from sortition_algorithms.committee_generation.common import (
+    EPS,
+    generate_initial_committees,
+    ilp_results_to_committee,
+    setup_committee_generation,
+)
+from sortition_algorithms.committee_generation.solver import Solver, SolverSense, solver_sum
+from sortition_algorithms.features import FeatureCollection
+from sortition_algorithms.people import People
+from sortition_algorithms.utils import RunReport, logger
+
+
+def _dual_leximin_stage(
+    people: People,
+    committees: set[frozenset[str]],
+    fixed_probabilities: dict[str, float],
+) -> tuple:
+    if not GUROBI_AVAILABLE:
+        msg = "Leximin algorithm requires Gurobi solver which is not available"
+        raise RuntimeError(msg, "gurobi_not_available", {})
+
+    assert len(committees) != 0
+
+    model = grb.Model()
+    agent_vars = {agent_id: model.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0) for agent_id in people}  
+    cap_var = model.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0)  
+    model.addConstr(
+        grb.quicksum(agent_vars[agent_id] for agent_id in people if agent_id not in fixed_probabilities) == 1
+    )
+    for committee in committees:
+        model.addConstr(grb.quicksum(agent_vars[agent_id] for agent_id in committee) <= cap_var)
+    model.setObjective(
+        cap_var
+        - grb.quicksum(fixed_probabilities[agent_id] * agent_vars[agent_id] for agent_id in fixed_probabilities),
+        grb.GRB.MINIMIZE,
+    )
+
+    model.setParam("Method", 2)  # optimize via barrier only
+    model.setParam("Crossover", 0)  # deactivate cross-over
+
+    return model, agent_vars, cap_var
+
+
+def _add_report_update(
+    report: RunReport, dual_obj: float, value: float, upper: float, committees: set[frozenset[str]]
+) -> None:
+    at_most = f"{dual_obj - upper + value:.2%}"
+    dual_obj_str = f"{dual_obj:.2%}"
+    gap_str = f"{value - upper:.2%}"
+    report.add_message_and_log(
+        "leximin_is_at_most",
+        log_level=logging.DEBUG,
+        at_most=at_most,
+        dual_obj_str=dual_obj_str,
+        num_committees=len(committees),
+        gap_str=gap_str,
+    )
+
+
+def _run_leximin_column_generation_loop(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    dual_model: Any,  
+    dual_agent_vars: dict[str, Any],  
+    dual_cap_var: Any,  
+    committees: set[frozenset[str]],
+    fixed_probabilities: dict[str, float],
+    people: People,
+    reduction_counter: int,
+    report: RunReport,
+) -> tuple[bool, int]:
+    while True:
+        dual_model.optimize()
+        if dual_model.status != grb.GRB.OPTIMAL:
+            for agent_id in fixed_probabilities:
+                fixed_probabilities[agent_id] = max(0.0, fixed_probabilities[agent_id] - 0.0001)
+            dual_model, dual_agent_vars, dual_cap_var = _dual_leximin_stage(
+                people,
+                committees,
+                fixed_probabilities,
+            )
+            logger.debug(f"Status: {dual_model.status} REDUCE PROBS for {reduction_counter}th time.")
+            reduction_counter += 1
+            continue
+
+        agent_weights = {agent_id: agent_var.x for agent_id, agent_var in dual_agent_vars.items()}
+        new_committee_solver.set_objective(
+            solver_sum(agent_weights[agent_id] * agent_vars[agent_id] for agent_id in people), SolverSense.MAXIMIZE
+        )
+        new_committee_solver.optimize()
+        new_set = ilp_results_to_committee(new_committee_solver, agent_vars)  
+        value = new_committee_solver.get_objective_value()  
+
+        upper = dual_cap_var.x  
+        dual_obj = dual_model.objVal  
+
+        _add_report_update(report, dual_obj, value, upper, committees)
+        if value <= upper + EPS:
+            for agent_id, agent_weight in agent_weights.items():
+                if agent_weight > EPS and agent_id not in fixed_probabilities:
+                    fixed_probabilities[agent_id] = max(0, dual_obj)
+            return True, reduction_counter  
+
+        assert new_set not in committees
+        committees.add(new_set)
+        dual_model.addConstr(grb.quicksum(dual_agent_vars[agent_id] for agent_id in new_set) <= dual_cap_var)
+
+
+def _solve_leximin_primal_for_final_probabilities(
+    committees: set[frozenset[str]], fixed_probabilities: dict[str, float]
+) -> list[float]:
+    primal = grb.Model()
+    committee_vars = [primal.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0) for _ in committees]
+    eps = primal.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0)
+    primal.addConstr(grb.quicksum(committee_vars) == 1)  
+    for agent_id, prob in fixed_probabilities.items():
+        agent_probability = grb.quicksum(
+            comm_var for committee, comm_var in zip(committees, committee_vars, strict=False) if agent_id in committee
+        )
+        primal.addConstr(agent_probability >= prob - eps)
+    primal.setObjective(eps, grb.GRB.MINIMIZE)
+    primal.optimize()
+
+    probabilities = numpy.array([comm_var.x for comm_var in committee_vars]).clip(0, 1)
+    return list(probabilities / sum(probabilities))
+
+
+def _run_leximin_main_loop(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    committees: set[frozenset[str]],
+    people: People,
+    report: RunReport,
+) -> dict[str, float]:
+    fixed_probabilities: dict[str, float] = {}
+    reduction_counter = 0
+
+    while len(fixed_probabilities) < people.count:
+        logger.debug(f"Fixed {len(fixed_probabilities)}/{people.count} probabilities.")
+
+        dual_model, dual_agent_vars, dual_cap_var = _dual_leximin_stage(
+            people,
+            committees,
+            fixed_probabilities,
+        )
+
+        should_break, reduction_counter = _run_leximin_column_generation_loop(
+            new_committee_solver,
+            agent_vars,
+            dual_model,
+            dual_agent_vars,
+            dual_cap_var,
+            committees,
+            fixed_probabilities,
+            people,
+            reduction_counter,
+            report,
+        )
+        if should_break:
+            break
+
+    return fixed_probabilities
+
+
+def find_distribution_leximin(
+    features: FeatureCollection,
+    people: People,
+    number_people_wanted: int,
+    check_same_address_columns: list[str],
+    solver_backend: str = "highspy",
+) -> tuple[list[frozenset[str]], list[float], RunReport]:
+    if not GUROBI_AVAILABLE:
+        msg = "Leximin algorithm requires Gurobi solver which is not available"
+        raise RuntimeError(msg, "gurobi_not_available", {})
+
+    report = RunReport()
+    report.add_message_and_log("using_leximin_algorithm", logging.INFO)
+    grb.setParam("OutputFlag", 0)
+
+    new_committee_solver, agent_vars = setup_committee_generation(
+        features, people, number_people_wanted, check_same_address_columns, solver_backend
+    )
+
+    # cap initial committees at 100 to speedup
+    committees, covered_agents, initial_report = generate_initial_committees(
+        new_committee_solver, agent_vars, 100
+    )
+    report.add_report(initial_report)
+
+    fixed_probabilities = _run_leximin_main_loop(new_committee_solver, agent_vars, committees, people, report)
+
+    probabilities_normalised = _solve_leximin_primal_for_final_probabilities(committees, fixed_probabilities)
+
+    # ==========================================
+    # WHITEBOARD VALIDATION CHECKS
+    # ==========================================
+    total_prob = sum(probabilities_normalised)
+    min_prob = min(fixed_probabilities.values()) if fixed_probabilities else 0.0
+    
+    print("\n" + "="*50)
+    print(f"WHITEBOARD CHECKS (Dataset size: {people.count})")
+    print("="*50)
+    
+    # Check 1: Do probabilities add to 1?
+    print(f"1. Do probabilities add to 1? -> {total_prob:.6f} ", end="")
+    if abs(total_prob - 1.0) < 1e-5:
+        print("(✅ PASS)")
+    else:
+        print("(❌ FAIL)")
+        
+    # Check 2: The exact objective (lowest selection probability)
+    print(f"2. Objective (Lowest Selection Prob) -> {min_prob:.6f}")
+    print("="*50)
+
+    # ==========================================
+    # STRIP PLOTS & CSV GENERATION
+    # ==========================================
+    try:
+        import csv
+        import matplotlib.pyplot as plt
+
+        dataset_size = people.count
+        print(f"\nGenerating CSV and Strip Plot for dataset size {dataset_size}...")
+
+        # save to CSV
+        csv_filename = f"individual_probs_{dataset_size}.csv"
+        with open(csv_filename, mode='w', newline='') as file:
+            writer = csv.writer(file)
+            writer.writerow(["Agent_ID", "Selection_Probability"])
+            for agent_id, prob in fixed_probabilities.items():
+                writer.writerow([agent_id, f"{prob:.6f}"])
+
+        # generate Strip Plot
+        prob_values = list(fixed_probabilities.values())
+        plt.figure(figsize=(10, 3))
+        plt.scatter(prob_values, [0] * len(prob_values), alpha=0.3, color='blue', edgecolors='none')
+        plt.title(f'Strip Plot of Selection Probabilities (N={dataset_size})', fontsize=14)
+        plt.xlabel('Probability of being selected', fontsize=12)
+        plt.yticks([])
+        plt.gca().spines['left'].set_visible(False)
+        plt.gca().spines['right'].set_visible(False)
+        plt.gca().spines['top'].set_visible(False)
+        plt.tight_layout()
+
+        img_filename = f"strip_plot_{dataset_size}.png"
+        plt.savefig(img_filename, dpi=300)
+        plt.close() # Close figure to save memory
+        print(f"✅ Saved {csv_filename} and {img_filename}!\n")
+    except Exception as e:
+        print(f"⚠️ Could not generate plot/csv: {e}\n")
+
+    return list(committees), probabilities_normalised, report
\ No newline at end of file
diff --git a/src/sortition_algorithms/committee_generation/og_leximin.py b/src/sortition_algorithms/committee_generation/og_leximin.py
new file mode 100644
index 0000000..628a3a8
--- /dev/null
+++ b/src/sortition_algorithms/committee_generation/og_leximin.py
@@ -0,0 +1,334 @@
+# ABOUTME: Leximin algorithm for committee generation.
+# ABOUTME: Maximizes minimum probability, breaking ties by second-lowest, third-lowest, etc.
+
+import logging
+from typing import Any
+
+import numpy
+
+try:
+    import gurobipy as grb
+
+    GUROBI_AVAILABLE = True
+except ImportError:
+    GUROBI_AVAILABLE = False
+    grb = None
+
+from sortition_algorithms.committee_generation.common import (
+    EPS,
+    generate_initial_committees,
+    ilp_results_to_committee,
+    setup_committee_generation,
+)
+from sortition_algorithms.committee_generation.solver import Solver, SolverSense, solver_sum
+from sortition_algorithms.features import FeatureCollection
+from sortition_algorithms.people import People
+from sortition_algorithms.utils import RunReport, logger
+
+
+def _dual_leximin_stage(
+    people: People,
+    committees: set[frozenset[str]],
+    fixed_probabilities: dict[str, float],
+) -> tuple:
+    """Implements the dual LP described in `find_distribution_leximin`, but where P only ranges over the panels
+    in `committees` rather than over all feasible panels:
+    minimize ŷ - Σ_{i in fixed_probabilities} fixed_probabilities[i] * yᵢ
+    s.t.     Σ_{i ∈ P} yᵢ ≤ ŷ                              ∀ P
+             Σ_{i not in fixed_probabilities} yᵢ = 1
+             ŷ, yᵢ ≥ 0                                     ∀ i
+
+    Args:
+        people: People object with all agents
+        committees: set of feasible committees
+        fixed_probabilities: dict mapping agent_id to fixed probability
+
+    Returns:
+        tuple of (grb.Model, dict[str, grb.Var], grb.Var) - (model, agent_vars, cap_var)
+
+    Raises:
+        RuntimeError: If Gurobi is not available
+    """
+    if not GUROBI_AVAILABLE:
+        msg = "Leximin algorithm requires Gurobi solver which is not available"
+        raise RuntimeError(msg, "gurobi_not_available", {})
+
+    assert len(committees) != 0
+
+    model = grb.Model()
+    agent_vars = {agent_id: model.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0) for agent_id in people}  # yᵢ
+    cap_var = model.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0)  # ŷ
+    model.addConstr(
+        grb.quicksum(agent_vars[agent_id] for agent_id in people if agent_id not in fixed_probabilities) == 1
+    )
+    for committee in committees:
+        model.addConstr(grb.quicksum(agent_vars[agent_id] for agent_id in committee) <= cap_var)
+    model.setObjective(
+        cap_var
+        - grb.quicksum(fixed_probabilities[agent_id] * agent_vars[agent_id] for agent_id in fixed_probabilities),
+        grb.GRB.MINIMIZE,
+    )
+
+    # Change Gurobi configuration to encourage strictly complementary ("inner") solutions. These solutions will
+    # typically allow to fix more probabilities per outer loop of the leximin algorithm.
+    model.setParam("Method", 2)  # optimize via barrier only
+    model.setParam("Crossover", 0)  # deactivate cross-over
+
+    return model, agent_vars, cap_var
+
+
+def _add_report_update(
+    report: RunReport, dual_obj: float, value: float, upper: float, committees: set[frozenset[str]]
+) -> None:
+    at_most = f"{dual_obj - upper + value:.2%}"
+    dual_obj_str = f"{dual_obj:.2%}"
+    gap_str = f"{value - upper:.2%}"
+    report.add_message_and_log(
+        "leximin_is_at_most",
+        log_level=logging.DEBUG,
+        at_most=at_most,
+        dual_obj_str=dual_obj_str,
+        num_committees=len(committees),
+        gap_str=gap_str,
+    )
+
+
+def _run_leximin_column_generation_loop(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    dual_model: Any,  # grb.Model
+    dual_agent_vars: dict[str, Any],  # dict[str, grb.Var]
+    dual_cap_var: Any,  # grb.Var
+    committees: set[frozenset[str]],
+    fixed_probabilities: dict[str, float],
+    people: People,
+    reduction_counter: int,
+    report: RunReport,
+) -> tuple[bool, int]:
+    """Run the column generation inner loop for leximin optimization.
+
+    The primal LP being solved by column generation, with a variable x_P for each feasible panel P:
+
+    maximize z
+    s.t.     Σ_{P : i ∈ P} x_P ≥ z                         ∀ i not in fixed_probabilities
+             Σ_{P : i ∈ P} x_P ≥ fixed_probabilities[i]    ∀ i in fixed_probabilities
+             Σ_P x_P ≤ 1                                   (This should be thought of as equality, and wlog.
+                                                           optimal solutions have equality, but simplifies dual)
+             x_P ≥ 0                                       ∀ P
+
+    We instead solve its dual linear program:
+    minimize ŷ - Σ_{i in fixed_probabilities} fixed_probabilities[i] * yᵢ
+    s.t.     Σ_{i ∈ P} yᵢ ≤ ŷ                              ∀ P
+             Σ_{i not in fixed_probabilities} yᵢ = 1
+             ŷ, yᵢ ≥ 0                                     ∀ i
+
+    Args:
+        new_committee_solver: Solver for finding committees
+        agent_vars: agent variables in the committee solver
+        dual_model: Gurobi model for dual LP
+        dual_agent_vars: agent variables in dual model
+        dual_cap_var: capacity variable in dual model
+        committees: set of committees (modified in-place)
+        fixed_probabilities: probabilities that have been fixed (modified in-place)
+        people: People object with all agents
+        reduction_counter: counter for probability reductions
+        output_lines: list of output messages (modified in-place)
+
+    Returns:
+        tuple of (should_break_outer_loop, updated_reduction_counter)
+    """
+    while True:
+        dual_model.optimize()
+        if dual_model.status != grb.GRB.OPTIMAL:
+            # In theory, the LP is feasible in the first iterations, and we only add constraints (by fixing
+            # probabilities) that preserve feasibility. Due to floating-point issues, however, it may happen that
+            # Gurobi still cannot satisfy all the fixed probabilities in the primal (meaning that the dual will be
+            # unbounded). In this case, we slightly relax the LP by slightly reducing all fixed probabilities.
+            for agent_id in fixed_probabilities:
+                # Relax all fixed probabilities by a small constant
+                fixed_probabilities[agent_id] = max(0.0, fixed_probabilities[agent_id] - 0.0001)
+            dual_model, dual_agent_vars, dual_cap_var = _dual_leximin_stage(
+                people,
+                committees,
+                fixed_probabilities,
+            )
+            logger.debug(f"Status: {dual_model.status} REDUCE PROBS for {reduction_counter}th time.")
+            reduction_counter += 1
+            continue
+
+        # Find the panel P for which Σ_{i ∈ P} yᵢ is largest, i.e., for which Σ_{i ∈ P} yᵢ ≤ ŷ is tightest
+        agent_weights = {agent_id: agent_var.x for agent_id, agent_var in dual_agent_vars.items()}
+        new_committee_solver.set_objective(
+            solver_sum(agent_weights[agent_id] * agent_vars[agent_id] for agent_id in people), SolverSense.MAXIMIZE
+        )
+        new_committee_solver.optimize()
+        new_set = ilp_results_to_committee(new_committee_solver, agent_vars)  # panel P
+        value = new_committee_solver.get_objective_value()  # Σ_{i ∈ P} yᵢ
+
+        upper = dual_cap_var.x  # ŷ
+        dual_obj = dual_model.objVal  # ŷ - Σ_{i in fixed_probabilities} fixed_probabilities[i] * yᵢ
+
+        _add_report_update(report, dual_obj, value, upper, committees)
+        if value <= upper + EPS:
+            # Within numeric tolerance, the panels in `committees` are enough to constrain the dual, i.e., they are
+            # enough to support an optimal primal solution.
+            for agent_id, agent_weight in agent_weights.items():
+                if agent_weight > EPS and agent_id not in fixed_probabilities:
+                    # `agent_weight` is the dual variable yᵢ of the constraint "Σ_{P : i ∈ P} x_P ≥ z" for
+                    # i = `agent_id` in the primal LP. If yᵢ is positive, this means that the constraint must be
+                    # binding in all optimal solutions [1], and we can fix `agent_id`'s probability to the
+                    # optimal value of the primal/dual LP.
+                    # [1] Theorem 3.3 in: Renato Pelessoni. Some remarks on the use of the strict complementarity in
+                    # checking coherence and extending coherent probabilities. 1998.
+                    fixed_probabilities[agent_id] = max(0, dual_obj)
+            return True, reduction_counter  # Break outer loop
+
+        # Given that Σ_{i ∈ P} yᵢ > ŷ, the current solution to `dual_model` is not yet a solution to the dual.
+        # Thus, add the constraint for panel P and recurse.
+        assert new_set not in committees
+        committees.add(new_set)
+        dual_model.addConstr(grb.quicksum(dual_agent_vars[agent_id] for agent_id in new_set) <= dual_cap_var)
+
+
+def _solve_leximin_primal_for_final_probabilities(
+    committees: set[frozenset[str]], fixed_probabilities: dict[str, float]
+) -> list[float]:
+    """Solve the final primal problem to get committee probabilities from fixed agent probabilities.
+
+    The previous algorithm computed the leximin selection probabilities of each agent and a set of panels such that
+    the selection probabilities can be obtained by randomizing over these panels. Here, such a randomization is found.
+
+    Args:
+        committees: set of committees
+        fixed_probabilities: fixed probabilities for each agent
+
+    Returns:
+        list of normalized probabilities for each committee
+    """
+    primal = grb.Model()
+    # Variables for the output probabilities of the different panels
+    committee_vars = [primal.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0) for _ in committees]
+    # To avoid numerical problems, we formally minimize the largest downward deviation from the fixed probabilities.
+    eps = primal.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0)
+    primal.addConstr(grb.quicksum(committee_vars) == 1)  # Probabilities add up to 1
+    for agent_id, prob in fixed_probabilities.items():
+        agent_probability = grb.quicksum(
+            comm_var for committee, comm_var in zip(committees, committee_vars, strict=False) if agent_id in committee
+        )
+        primal.addConstr(agent_probability >= prob - eps)
+    primal.setObjective(eps, grb.GRB.MINIMIZE)
+    primal.optimize()
+
+    # Bound variables between 0 and 1 and renormalize, because numpy.random.choice is sensitive to small deviations here
+    probabilities = numpy.array([comm_var.x for comm_var in committee_vars]).clip(0, 1)
+    return list(probabilities / sum(probabilities))
+
+
+def _run_leximin_main_loop(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    committees: set[frozenset[str]],
+    people: People,
+    report: RunReport,
+) -> dict[str, float]:
+    """Run the main leximin optimization loop that fixes probabilities iteratively.
+
+    The outer loop maximizes the minimum of all unfixed probabilities while satisfying the fixed probabilities.
+    In each iteration, at least one more probability is fixed, but often more than one.
+
+    Args:
+        new_committee_solver: Solver for finding committees
+        agent_vars: agent variables in the committee solver
+        committees: set of committees (modified in-place)
+        people: People object with all agents
+        output_lines: list of output messages (modified in-place)
+
+    Returns:
+        dict mapping agent_id to fixed probability
+    """
+    fixed_probabilities: dict[str, float] = {}
+    reduction_counter = 0
+
+    while len(fixed_probabilities) < len(people):
+        logger.debug(f"Fixed {len(fixed_probabilities)}/{len(people)} probabilities.")
+
+        dual_model, dual_agent_vars, dual_cap_var = _dual_leximin_stage(
+            people,
+            committees,
+            fixed_probabilities,
+        )
+
+        # Run column generation inner loop
+        should_break, reduction_counter = _run_leximin_column_generation_loop(
+            new_committee_solver,
+            agent_vars,
+            dual_model,
+            dual_agent_vars,
+            dual_cap_var,
+            committees,
+            fixed_probabilities,
+            people,
+            reduction_counter,
+            report,
+        )
+        if should_break:
+            break
+
+    return fixed_probabilities
+
+
+def find_distribution_leximin(
+    features: FeatureCollection,
+    people: People,
+    number_people_wanted: int,
+    check_same_address_columns: list[str],
+    solver_backend: str = "highspy",
+) -> tuple[list[frozenset[str]], list[float], RunReport]:
+    """Find a distribution over feasible committees that maximizes the minimum probability of an agent being selected
+    (just like maximin), but breaks ties to maximize the second-lowest probability, breaks further ties to maximize the
+    third-lowest probability and so forth.
+
+    Args:
+        features: FeatureCollection with min/max quotas
+        people: People object with pool members
+        number_people_wanted: desired size of the panel
+        check_same_address_columns: Address columns for household identification, or empty
+                                    if no address checking to be done.
+        solver_backend: solver backend to use ("highspy" or "mip") for committee discovery.
+                        Note: The dual LP still uses Gurobi.
+
+    Returns:
+        tuple of (committees, probabilities, output_lines)
+        - committees: list of feasible committees (frozenset of agent IDs)
+        - probabilities: list of probabilities for each committee
+        - output_lines: list of debug strings
+
+    Raises:
+        RuntimeError: If Gurobi is not available
+    """
+    if not GUROBI_AVAILABLE:
+        msg = "Leximin algorithm requires Gurobi solver which is not available"
+        raise RuntimeError(msg, "gurobi_not_available", {})
+
+    report = RunReport()
+    report.add_message_and_log("using_leximin_algorithm", logging.INFO)
+    grb.setParam("OutputFlag", 0)
+
+    # Set up an ILP that can be used for discovering new feasible committees
+    new_committee_solver, agent_vars = setup_committee_generation(
+        features, people, number_people_wanted, check_same_address_columns, solver_backend
+    )
+
+    # Find initial committees that cover every possible agent
+    committees, covered_agents, initial_report = generate_initial_committees(
+        new_committee_solver, agent_vars, 3 * len(people)
+    )
+    report.add_report(initial_report)
+
+    # Run the main leximin optimization loop to fix agent probabilities
+    fixed_probabilities = _run_leximin_main_loop(new_committee_solver, agent_vars, committees, people, report)
+
+    # Convert fixed agent probabilities to committee probabilities
+    probabilities_normalised = _solve_leximin_primal_for_final_probabilities(committees, fixed_probabilities)
+
+    return list(committees), probabilities_normalised, report
diff --git a/src/sortition_algorithms/committee_generation/op1_leximin.py b/src/sortition_algorithms/committee_generation/op1_leximin.py
new file mode 100644
index 0000000..3e1933a
--- /dev/null
+++ b/src/sortition_algorithms/committee_generation/op1_leximin.py
@@ -0,0 +1,250 @@
+# ABOUTME: Leximin algorithm for committee generation.
+# ABOUTME: Maximizes minimum probability, breaking ties by second-lowest, third-lowest, etc.
+# Option 1: The "Rebuilding the World" Bottleneck
+
+import logging
+from typing import Any
+
+import numpy
+
+try:
+    import gurobipy as grb
+
+    GUROBI_AVAILABLE = True
+except ImportError:
+    GUROBI_AVAILABLE = False
+    grb = None
+
+from sortition_algorithms.committee_generation.common import (
+    EPS,
+    generate_initial_committees,
+    ilp_results_to_committee,
+    setup_committee_generation,
+)
+from sortition_algorithms.committee_generation.solver import Solver, SolverSense, solver_sum
+from sortition_algorithms.features import FeatureCollection
+from sortition_algorithms.people import People
+from sortition_algorithms.utils import RunReport, logger
+
+
+def _setup_dual_model(
+    people: People,
+    committees: set[frozenset[str]],
+) -> tuple:
+    """Sets up the initial Gurobi model for the dual LP exactly once."""
+    if not GUROBI_AVAILABLE:
+        msg = "Leximin algorithm requires Gurobi solver which is not available"
+        raise RuntimeError(msg, "gurobi_not_available", {})
+
+    assert len(committees) != 0
+
+    model = grb.Model()
+    
+    # Variables: yᵢ for each agent, and ŷ (cap_var)
+    agent_vars = {agent_id: model.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0) for agent_id in people}  
+    cap_var = model.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0)  
+
+    # Initial constraint: Σ yᵢ = 1 
+    # (Since no probabilities are fixed yet, all agents have coefficient 1)
+    sum_constr = model.addConstr(
+        grb.quicksum(agent_vars[agent_id] for agent_id in people) == 1,
+        name="sum_unfixed"
+    )
+
+    # Initial committee constraints
+    for committee in committees:
+        model.addConstr(grb.quicksum(agent_vars[agent_id] for agent_id in committee) <= cap_var)
+
+    # Initial objective: minimize ŷ (cap_var)
+    model.setObjective(cap_var, grb.GRB.MINIMIZE)
+
+    # Change Gurobi configuration to encourage strictly complementary ("inner") solutions.
+    model.setParam("Method", 2)  # optimize via barrier only
+    model.setParam("Crossover", 0)  # deactivate cross-over
+
+    return model, agent_vars, cap_var, sum_constr
+
+
+def _update_dual_model(
+    model: Any,
+    agent_vars: dict[str, Any],
+    cap_var: Any,
+    sum_constr: Any,
+    fixed_probabilities: dict[str, float],
+    people: People
+):
+    """Updates the persistent dual LP in-place without rebuilding it from scratch."""
+    # 1. Update the sum constraint coefficients.
+    for agent_id in people:
+        if agent_id in fixed_probabilities:
+            model.chgCoeff(sum_constr, agent_vars[agent_id], 0.0)
+        else:
+            model.chgCoeff(sum_constr, agent_vars[agent_id], 1.0)
+
+    # 2. Update the objective function
+    model.setObjective(
+        cap_var - grb.quicksum(
+            fixed_probabilities[agent_id] * agent_vars[agent_id]
+            for agent_id in fixed_probabilities
+        ),
+        grb.GRB.MINIMIZE
+    )
+
+
+def _add_report_update(
+    report: RunReport, dual_obj: float, value: float, upper: float, committees: set[frozenset[str]]
+) -> None:
+    at_most = f"{dual_obj - upper + value:.2%}"
+    dual_obj_str = f"{dual_obj:.2%}"
+    gap_str = f"{value - upper:.2%}"
+    report.add_message_and_log(
+        "leximin_is_at_most",
+        log_level=logging.DEBUG,
+        at_most=at_most,
+        dual_obj_str=dual_obj_str,
+        num_committees=len(committees),
+        gap_str=gap_str,
+    )
+
+
+def _run_leximin_column_generation_loop(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    dual_model: Any,  
+    dual_agent_vars: dict[str, Any],  
+    dual_cap_var: Any,  
+    sum_constr: Any, 
+    committees: set[frozenset[str]],
+    fixed_probabilities: dict[str, float],
+    people: People,
+    reduction_counter: int,
+    report: RunReport,
+) -> tuple[bool, int]:
+    """Run the column generation inner loop for leximin optimization."""
+    while True:
+        dual_model.optimize()
+        if dual_model.status != grb.GRB.OPTIMAL:
+            for agent_id in fixed_probabilities:
+                # Relax all fixed probabilities by a small constant
+                fixed_probabilities[agent_id] = max(0.0, fixed_probabilities[agent_id] - 0.0001)
+            
+            # Update persistent model instead of rebuilding
+            _update_dual_model(dual_model, dual_agent_vars, dual_cap_var, sum_constr, fixed_probabilities, people)
+            
+            logger.debug(f"Status: {dual_model.status} REDUCE PROBS for {reduction_counter}th time.")
+            reduction_counter += 1
+            continue
+
+        agent_weights = {agent_id: agent_var.x for agent_id, agent_var in dual_agent_vars.items()}
+        new_committee_solver.set_objective(
+            solver_sum(agent_weights[agent_id] * agent_vars[agent_id] for agent_id in people), SolverSense.MAXIMIZE
+        )
+        new_committee_solver.optimize()
+        new_set = ilp_results_to_committee(new_committee_solver, agent_vars)  
+        value = new_committee_solver.get_objective_value()  
+
+        upper = dual_cap_var.x  
+        dual_obj = dual_model.objVal  
+
+        _add_report_update(report, dual_obj, value, upper, committees)
+        if value <= upper + EPS:
+            for agent_id, agent_weight in agent_weights.items():
+                if agent_weight > EPS and agent_id not in fixed_probabilities:
+                    fixed_probabilities[agent_id] = max(0, dual_obj)
+            return True, reduction_counter  
+
+        assert new_set not in committees
+        committees.add(new_set)
+        # Add the new constraint directly to the persistent model
+        dual_model.addConstr(grb.quicksum(dual_agent_vars[agent_id] for agent_id in new_set) <= dual_cap_var)
+
+
+def _solve_leximin_primal_for_final_probabilities(
+    committees: set[frozenset[str]], fixed_probabilities: dict[str, float]
+) -> list[float]:
+    """Solve the final primal problem to get committee probabilities from fixed agent probabilities."""
+    primal = grb.Model()
+    committee_vars = [primal.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0) for _ in committees]
+    eps = primal.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0)
+    primal.addConstr(grb.quicksum(committee_vars) == 1)  
+    for agent_id, prob in fixed_probabilities.items():
+        agent_probability = grb.quicksum(
+            comm_var for committee, comm_var in zip(committees, committee_vars, strict=False) if agent_id in committee
+        )
+        primal.addConstr(agent_probability >= prob - eps)
+    primal.setObjective(eps, grb.GRB.MINIMIZE)
+    primal.optimize()
+
+    probabilities = numpy.array([comm_var.x for comm_var in committee_vars]).clip(0, 1)
+    return list(probabilities / sum(probabilities))
+
+
+def _run_leximin_main_loop(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    committees: set[frozenset[str]],
+    people: People,
+    report: RunReport,
+) -> dict[str, float]:
+    """Run the main leximin optimization loop that fixes probabilities iteratively."""
+    fixed_probabilities: dict[str, float] = {}
+    reduction_counter = 0
+
+    # Build the model exactly ONCE
+    dual_model, dual_agent_vars, dual_cap_var, sum_constr = _setup_dual_model(people, committees)
+
+    while len(fixed_probabilities) < people.count:
+        logger.debug(f"Fixed {len(fixed_probabilities)}/{people.count} probabilities.")
+
+        # Update the math before running the inner loop
+        _update_dual_model(dual_model, dual_agent_vars, dual_cap_var, sum_constr, fixed_probabilities, people)
+
+        should_break, reduction_counter = _run_leximin_column_generation_loop(
+            new_committee_solver,
+            agent_vars,
+            dual_model,
+            dual_agent_vars,
+            dual_cap_var,
+            sum_constr, 
+            committees,
+            fixed_probabilities,
+            people,
+            reduction_counter,
+            report,
+        )
+        if should_break:
+            break
+
+    return fixed_probabilities
+
+
+def find_distribution_leximin(
+    features: FeatureCollection,
+    people: People,
+    number_people_wanted: int,
+    check_same_address_columns: list[str],
+    solver_backend: str = "highspy",
+) -> tuple[list[frozenset[str]], list[float], RunReport]:
+    """Find a distribution over feasible committees that maximizes the minimum probability of an agent being selected."""
+    if not GUROBI_AVAILABLE:
+        msg = "Leximin algorithm requires Gurobi solver which is not available"
+        raise RuntimeError(msg, "gurobi_not_available", {})
+
+    report = RunReport()
+    report.add_message_and_log("using_leximin_algorithm", logging.INFO)
+    grb.setParam("OutputFlag", 0)
+
+    new_committee_solver, agent_vars = setup_committee_generation(
+        features, people, number_people_wanted, check_same_address_columns, solver_backend
+    )
+
+    committees, covered_agents, initial_report = generate_initial_committees(
+        new_committee_solver, agent_vars, 3 * people.count
+    )
+    report.add_report(initial_report)
+
+    fixed_probabilities = _run_leximin_main_loop(new_committee_solver, agent_vars, committees, people, report)
+
+    probabilities_normalised = _solve_leximin_primal_for_final_probabilities(committees, fixed_probabilities)
+
+    return list(committees), probabilities_normalised, report
\ No newline at end of file
diff --git a/src/sortition_algorithms/committee_generation/op2_leximin.py b/src/sortition_algorithms/committee_generation/op2_leximin.py
new file mode 100644
index 0000000..5fa2acd
--- /dev/null
+++ b/src/sortition_algorithms/committee_generation/op2_leximin.py
@@ -0,0 +1,273 @@
+# ABOUTME: Leximin algorithm for committee generation.
+# ABOUTME: Maximizes minimum probability, breaking ties by second-lowest, third-lowest, etc.
+# Option 2: Fixing the "Batch" Heuristic
+
+import logging
+from typing import Any
+
+import numpy
+
+try:
+    import gurobipy as grb
+
+    GUROBI_AVAILABLE = True
+except ImportError:
+    GUROBI_AVAILABLE = False
+    grb = None
+
+from sortition_algorithms.committee_generation.common import (
+    EPS,
+    generate_initial_committees,
+    ilp_results_to_committee,
+    setup_committee_generation,
+)
+from sortition_algorithms.committee_generation.solver import Solver, SolverSense, solver_sum
+from sortition_algorithms.features import FeatureCollection
+from sortition_algorithms.people import People
+from sortition_algorithms.utils import RunReport, logger
+
+
+def _dual_leximin_stage(
+    people: People,
+    committees: set[frozenset[str]],
+    fixed_probabilities: dict[str, float],
+) -> tuple:
+    if not GUROBI_AVAILABLE:
+        msg = "Leximin algorithm requires Gurobi solver which is not available"
+        raise RuntimeError(msg, "gurobi_not_available", {})
+
+    assert len(committees) != 0
+
+    model = grb.Model()
+    agent_vars = {agent_id: model.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0) for agent_id in people}  
+    cap_var = model.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0)  
+    model.addConstr(
+        grb.quicksum(agent_vars[agent_id] for agent_id in people if agent_id not in fixed_probabilities) == 1
+    )
+    for committee in committees:
+        model.addConstr(grb.quicksum(agent_vars[agent_id] for agent_id in committee) <= cap_var)
+    model.setObjective(
+        cap_var
+        - grb.quicksum(fixed_probabilities[agent_id] * agent_vars[agent_id] for agent_id in fixed_probabilities),
+        grb.GRB.MINIMIZE,
+    )
+
+    model.setParam("Method", 2)  
+    model.setParam("Crossover", 0)  
+
+    return model, agent_vars, cap_var
+
+
+def _add_report_update(
+    report: RunReport, dual_obj: float, value: float, upper: float, committees: set[frozenset[str]]
+) -> None:
+    at_most = f"{dual_obj - upper + value:.2%}"
+    dual_obj_str = f"{dual_obj:.2%}"
+    gap_str = f"{value - upper:.2%}"
+    report.add_message_and_log(
+        "leximin_is_at_most",
+        log_level=logging.DEBUG,
+        at_most=at_most,
+        dual_obj_str=dual_obj_str,
+        num_committees=len(committees),
+        gap_str=gap_str,
+    )
+
+
+def _run_leximin_heuristic_for_additional_committees(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    dual_model: Any,
+    dual_agent_vars: dict[str, Any],
+    dual_cap_var: Any,
+    committees: set[frozenset[str]],
+    people: People,
+    agent_weights: dict[str, float],
+    upper: float,
+    value: float,
+) -> int:
+    """Run heuristic to find additional committees to reduce outer loop calls."""
+    counter = 0
+    new_set = None
+
+    for _ in range(10): # Try to harvest up to 10 extra committees
+        if new_set is not None:
+            for agent_id in new_set:
+                # Penalize agents in the last found committee so it finds different ones
+                agent_weights[agent_id] *= (upper / value) if value > EPS else 0.5
+
+        sum_weights = sum(agent_weights.values())
+        if sum_weights < EPS:
+            break
+        for agent_id in agent_weights:
+            agent_weights[agent_id] /= sum_weights
+        upper /= sum_weights
+
+        new_committee_solver.set_objective(
+            solver_sum(agent_weights[agent_id] * agent_vars[agent_id] for agent_id in people),
+            SolverSense.MAXIMIZE,
+        )
+        new_committee_solver.optimize()
+        new_set = ilp_results_to_committee(new_committee_solver, agent_vars)
+        value = sum(agent_weights[agent_id] for agent_id in new_set)
+
+        if value <= upper + EPS or new_set in committees:
+            break
+
+        committees.add(new_set)
+        dual_model.addConstr(grb.quicksum(dual_agent_vars[agent_id] for agent_id in new_set) <= dual_cap_var)
+        counter += 1
+
+    return counter
+
+
+def _run_leximin_column_generation_loop(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    dual_model: Any,  
+    dual_agent_vars: dict[str, Any],  
+    dual_cap_var: Any,  
+    committees: set[frozenset[str]],
+    fixed_probabilities: dict[str, float],
+    people: People,
+    reduction_counter: int,
+    report: RunReport,
+) -> tuple[bool, int]:
+    while True:
+        dual_model.optimize()
+        if dual_model.status != grb.GRB.OPTIMAL:
+            for agent_id in fixed_probabilities:
+                fixed_probabilities[agent_id] = max(0.0, fixed_probabilities[agent_id] - 0.0001)
+            dual_model, dual_agent_vars, dual_cap_var = _dual_leximin_stage(
+                people,
+                committees,
+                fixed_probabilities,
+            )
+            logger.debug(f"Status: {dual_model.status} REDUCE PROBS for {reduction_counter}th time.")
+            reduction_counter += 1
+            continue
+
+        agent_weights = {agent_id: agent_var.x for agent_id, agent_var in dual_agent_vars.items()}
+        new_committee_solver.set_objective(
+            solver_sum(agent_weights[agent_id] * agent_vars[agent_id] for agent_id in people), SolverSense.MAXIMIZE
+        )
+        new_committee_solver.optimize()
+        new_set = ilp_results_to_committee(new_committee_solver, agent_vars)  
+        value = new_committee_solver.get_objective_value()  
+
+        upper = dual_cap_var.x  
+        dual_obj = dual_model.objVal  
+
+        _add_report_update(report, dual_obj, value, upper, committees)
+        if value <= upper + EPS:
+            for agent_id, agent_weight in agent_weights.items():
+                if agent_weight > EPS and agent_id not in fixed_probabilities:
+                    fixed_probabilities[agent_id] = max(0, dual_obj)
+            return True, reduction_counter  
+
+        assert new_set not in committees
+        committees.add(new_set)
+        dual_model.addConstr(grb.quicksum(dual_agent_vars[agent_id] for agent_id in new_set) <= dual_cap_var)
+
+        # --- NEW HEURISTIC TRICK INJECTED HERE ---
+        counter = _run_leximin_heuristic_for_additional_committees(
+            new_committee_solver,
+            agent_vars,
+            dual_model,
+            dual_agent_vars,
+            dual_cap_var,
+            committees,
+            people,
+            agent_weights,
+            upper,
+            value
+        )
+        if counter > 0:
+            logger.debug(f"Heuristic added {counter} extra committees.")
+
+
+def _solve_leximin_primal_for_final_probabilities(
+    committees: set[frozenset[str]], fixed_probabilities: dict[str, float]
+) -> list[float]:
+    primal = grb.Model()
+    committee_vars = [primal.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0) for _ in committees]
+    eps = primal.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0)
+    primal.addConstr(grb.quicksum(committee_vars) == 1)  
+    for agent_id, prob in fixed_probabilities.items():
+        agent_probability = grb.quicksum(
+            comm_var for committee, comm_var in zip(committees, committee_vars, strict=False) if agent_id in committee
+        )
+        primal.addConstr(agent_probability >= prob - eps)
+    primal.setObjective(eps, grb.GRB.MINIMIZE)
+    primal.optimize()
+
+    probabilities = numpy.array([comm_var.x for comm_var in committee_vars]).clip(0, 1)
+    return list(probabilities / sum(probabilities))
+
+
+def _run_leximin_main_loop(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    committees: set[frozenset[str]],
+    people: People,
+    report: RunReport,
+) -> dict[str, float]:
+    fixed_probabilities: dict[str, float] = {}
+    reduction_counter = 0
+
+    while len(fixed_probabilities) < people.count:
+        logger.debug(f"Fixed {len(fixed_probabilities)}/{people.count} probabilities.")
+
+        dual_model, dual_agent_vars, dual_cap_var = _dual_leximin_stage(
+            people,
+            committees,
+            fixed_probabilities,
+        )
+
+        should_break, reduction_counter = _run_leximin_column_generation_loop(
+            new_committee_solver,
+            agent_vars,
+            dual_model,
+            dual_agent_vars,
+            dual_cap_var,
+            committees,
+            fixed_probabilities,
+            people,
+            reduction_counter,
+            report,
+        )
+        if should_break:
+            break
+
+    return fixed_probabilities
+
+
+def find_distribution_leximin(
+    features: FeatureCollection,
+    people: People,
+    number_people_wanted: int,
+    check_same_address_columns: list[str],
+    solver_backend: str = "highspy",
+) -> tuple[list[frozenset[str]], list[float], RunReport]:
+    if not GUROBI_AVAILABLE:
+        msg = "Leximin algorithm requires Gurobi solver which is not available"
+        raise RuntimeError(msg, "gurobi_not_available", {})
+
+    report = RunReport()
+    report.add_message_and_log("using_leximin_algorithm", logging.INFO)
+    grb.setParam("OutputFlag", 0)
+
+    new_committee_solver, agent_vars = setup_committee_generation(
+        features, people, number_people_wanted, check_same_address_columns, solver_backend
+    )
+
+    committees, covered_agents, initial_report = generate_initial_committees(
+        new_committee_solver, agent_vars, 3 * people.count
+    )
+    report.add_report(initial_report)
+
+    fixed_probabilities = _run_leximin_main_loop(new_committee_solver, agent_vars, committees, people, report)
+
+    probabilities_normalised = _solve_leximin_primal_for_final_probabilities(committees, fixed_probabilities)
+
+    return list(committees), probabilities_normalised, report
\ No newline at end of file
diff --git a/src/sortition_algorithms/committee_generation/op4_leximin.py b/src/sortition_algorithms/committee_generation/op4_leximin.py
new file mode 100644
index 0000000..6c119e0
--- /dev/null
+++ b/src/sortition_algorithms/committee_generation/op4_leximin.py
@@ -0,0 +1,213 @@
+# ABOUTME: Leximin algorithm for committee generation.
+# ABOUTME: Maximizes minimum probability, breaking ties by second-lowest, third-lowest, etc.
+# Option 4: Heuristic Pricing (The "Good Enough" Approach)
+
+import logging
+from typing import Any
+
+import numpy
+
+try:
+    import gurobipy as grb
+
+    GUROBI_AVAILABLE = True
+except ImportError:
+    GUROBI_AVAILABLE = False
+    grb = None
+
+from sortition_algorithms.committee_generation.common import (
+    EPS,
+    generate_initial_committees,
+    ilp_results_to_committee,
+    setup_committee_generation,
+)
+from sortition_algorithms.committee_generation.solver import Solver, SolverSense, solver_sum
+from sortition_algorithms.features import FeatureCollection
+from sortition_algorithms.people import People
+from sortition_algorithms.utils import RunReport, logger
+
+
+def _dual_leximin_stage(
+    people: People,
+    committees: set[frozenset[str]],
+    fixed_probabilities: dict[str, float],
+) -> tuple:
+    if not GUROBI_AVAILABLE:
+        msg = "Leximin algorithm requires Gurobi solver which is not available"
+        raise RuntimeError(msg, "gurobi_not_available", {})
+
+    assert len(committees) != 0
+
+    model = grb.Model()
+    agent_vars = {agent_id: model.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0) for agent_id in people}  
+    cap_var = model.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0)  
+    model.addConstr(
+        grb.quicksum(agent_vars[agent_id] for agent_id in people if agent_id not in fixed_probabilities) == 1
+    )
+    for committee in committees:
+        model.addConstr(grb.quicksum(agent_vars[agent_id] for agent_id in committee) <= cap_var)
+    model.setObjective(
+        cap_var
+        - grb.quicksum(fixed_probabilities[agent_id] * agent_vars[agent_id] for agent_id in fixed_probabilities),
+        grb.GRB.MINIMIZE,
+    )
+
+    # ---> OPTION 4 SPEEDUP: Let Gurobi use its default Simplex method <---
+    # We are commenting out Paul's forced Barrier method.
+    # model.setParam("Method", 2)  # optimize via barrier only
+    # model.setParam("Crossover", 0)  # deactivate cross-over
+
+    return model, agent_vars, cap_var
+
+
+def _add_report_update(
+    report: RunReport, dual_obj: float, value: float, upper: float, committees: set[frozenset[str]]
+) -> None:
+    at_most = f"{dual_obj - upper + value:.2%}"
+    dual_obj_str = f"{dual_obj:.2%}"
+    gap_str = f"{value - upper:.2%}"
+    report.add_message_and_log(
+        "leximin_is_at_most",
+        log_level=logging.DEBUG,
+        at_most=at_most,
+        dual_obj_str=dual_obj_str,
+        num_committees=len(committees),
+        gap_str=gap_str,
+    )
+
+
+def _run_leximin_column_generation_loop(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    dual_model: Any,  
+    dual_agent_vars: dict[str, Any],  
+    dual_cap_var: Any,  
+    committees: set[frozenset[str]],
+    fixed_probabilities: dict[str, float],
+    people: People,
+    reduction_counter: int,
+    report: RunReport,
+) -> tuple[bool, int]:
+    while True:
+        dual_model.optimize()
+        if dual_model.status != grb.GRB.OPTIMAL:
+            for agent_id in fixed_probabilities:
+                fixed_probabilities[agent_id] = max(0.0, fixed_probabilities[agent_id] - 0.0001)
+            dual_model, dual_agent_vars, dual_cap_var = _dual_leximin_stage(
+                people,
+                committees,
+                fixed_probabilities,
+            )
+            logger.debug(f"Status: {dual_model.status} REDUCE PROBS for {reduction_counter}th time.")
+            reduction_counter += 1
+            continue
+
+        agent_weights = {agent_id: agent_var.x for agent_id, agent_var in dual_agent_vars.items()}
+        new_committee_solver.set_objective(
+            solver_sum(agent_weights[agent_id] * agent_vars[agent_id] for agent_id in people), SolverSense.MAXIMIZE
+        )
+        new_committee_solver.optimize()
+        new_set = ilp_results_to_committee(new_committee_solver, agent_vars)  
+        value = new_committee_solver.get_objective_value()  
+
+        upper = dual_cap_var.x  
+        dual_obj = dual_model.objVal  
+
+        _add_report_update(report, dual_obj, value, upper, committees)
+        if value <= upper + EPS:
+            for agent_id, agent_weight in agent_weights.items():
+                if agent_weight > EPS and agent_id not in fixed_probabilities:
+                    fixed_probabilities[agent_id] = max(0, dual_obj)
+            return True, reduction_counter  
+
+        assert new_set not in committees
+        committees.add(new_set)
+        dual_model.addConstr(grb.quicksum(dual_agent_vars[agent_id] for agent_id in new_set) <= dual_cap_var)
+
+
+def _solve_leximin_primal_for_final_probabilities(
+    committees: set[frozenset[str]], fixed_probabilities: dict[str, float]
+) -> list[float]:
+    primal = grb.Model()
+    committee_vars = [primal.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0) for _ in committees]
+    eps = primal.addVar(vtype=grb.GRB.CONTINUOUS, lb=0.0)
+    primal.addConstr(grb.quicksum(committee_vars) == 1)  
+    for agent_id, prob in fixed_probabilities.items():
+        agent_probability = grb.quicksum(
+            comm_var for committee, comm_var in zip(committees, committee_vars, strict=False) if agent_id in committee
+        )
+        primal.addConstr(agent_probability >= prob - eps)
+    primal.setObjective(eps, grb.GRB.MINIMIZE)
+    primal.optimize()
+
+    probabilities = numpy.array([comm_var.x for comm_var in committee_vars]).clip(0, 1)
+    return list(probabilities / sum(probabilities))
+
+
+def _run_leximin_main_loop(
+    new_committee_solver: Solver,
+    agent_vars: dict[str, Any],
+    committees: set[frozenset[str]],
+    people: People,
+    report: RunReport,
+) -> dict[str, float]:
+    fixed_probabilities: dict[str, float] = {}
+    reduction_counter = 0
+
+    while len(fixed_probabilities) < people.count:
+        logger.debug(f"Fixed {len(fixed_probabilities)}/{people.count} probabilities.")
+
+        dual_model, dual_agent_vars, dual_cap_var = _dual_leximin_stage(
+            people,
+            committees,
+            fixed_probabilities,
+        )
+
+        should_break, reduction_counter = _run_leximin_column_generation_loop(
+            new_committee_solver,
+            agent_vars,
+            dual_model,
+            dual_agent_vars,
+            dual_cap_var,
+            committees,
+            fixed_probabilities,
+            people,
+            reduction_counter,
+            report,
+        )
+        if should_break:
+            break
+
+    return fixed_probabilities
+
+
+def find_distribution_leximin(
+    features: FeatureCollection,
+    people: People,
+    number_people_wanted: int,
+    check_same_address_columns: list[str],
+    solver_backend: str = "highspy",
+) -> tuple[list[frozenset[str]], list[float], RunReport]:
+    if not GUROBI_AVAILABLE:
+        msg = "Leximin algorithm requires Gurobi solver which is not available"
+        raise RuntimeError(msg, "gurobi_not_available", {})
+
+    report = RunReport()
+    report.add_message_and_log("using_leximin_algorithm", logging.INFO)
+    grb.setParam("OutputFlag", 0)
+
+    new_committee_solver, agent_vars = setup_committee_generation(
+        features, people, number_people_wanted, check_same_address_columns, solver_backend
+    )
+
+    # We keep our Option 3 win here (capped at 100)
+    committees, covered_agents, initial_report = generate_initial_committees(
+        new_committee_solver, agent_vars, 100
+    )
+    report.add_report(initial_report)
+
+    fixed_probabilities = _run_leximin_main_loop(new_committee_solver, agent_vars, committees, people, report)
+
+    probabilities_normalised = _solve_leximin_primal_for_final_probabilities(committees, fixed_probabilities)
+
+    return list(committees), probabilities_normalised, report
\ No newline at end of file