"""Independent reproducibility script - RDCR model on reconciled GE2024 data. Provenance ---------- Vote inputs are aggregated from the House of Commons Library dataset "HoC-GE2024-results-by-constituency.csv" (corrected edition, Record of changes to 5 Jan 2026), researchbriefings.files.parliament.uk, CBP-10009. Transcription was checksum-verified before aggregation: 650 rows; national valid votes exactly 28,809,340; every party's national total equal to the published Library figure; each row's party columns sum to its valid votes. NI note: the Library file folds TUV/PBP/Aontu/independents into an "All other candidates" column. TUV (48,685), PBP (8,438) and Aontu (7,466) are separated using their official national totals (all three stand only in NI); the remaining residual is the Others bucket. The Speaker (25,238, Chorley) is separated in the North West the same way. Scope ----- Reproduces: regional vote layer, central direct-seat scenario at 5% and at the proposed 3% threshold, pure Hamilton anchors, Gallagher indices under both residual conventions, a broadened perturbation stress test, and a Sainte-Lague cross-check. Direct-seat scenarios remain assumptions, not ward-built counterfactual constituencies. This implementation was written from the Green Paper Section 18 prose specification, independently of the Green Paper author's code. """ import math, collections, itertools T_SPEC = {"North East": 26, "North West": 73, "Yorkshire and the Humber": 53, "East Midlands": 48, "West Midlands": 58, "East of England": 62, "London": 85, "South East": 90, "South West": 55, "Scotland": 52, "Wales": 30, "Northern Ireland": 18} C_SPEC = {k: math.ceil(v/2) for k, v in T_SPEC.items()} NON_GROUPINGS = {'Others', 'Independent', 'Speaker', 'PBP', 'Aontu'} REGIONAL_VOTES = { "North East": { "Con": 224584, "Lab": 504569, "LD": 65385, "Reform": 220875, "Green": 66680, "Others": 29447 }, "North West": { "Con": 581099, "Lab": 1361196, "LD": 242662, "Reform": 512115, "Green": 217092, "Speaker": 25238, "Others": 153060 }, "Yorkshire and the Humber": { "Con": 506450, "Lab": 907767, "LD": 158326, "Reform": 371658, "Green": 167514, "Others": 110232 }, "East Midlands": { "Con": 626568, "Lab": 753723, "LD": 136929, "Reform": 403470, "Green": 133447, "Others": 79524 }, "West Midlands": { "Con": 669368, "Lab": 824433, "LD": 214493, "Reform": 439278, "Green": 159140, "Others": 119145 }, "East of England": { "Con": 869447, "Lab": 834896, "LD": 375642, "Reform": 496237, "Green": 195665, "Others": 67432 }, "London": { "Con": 685082, "Lab": 1432622, "LD": 367424, "Reform": 289459, "Green": 335479, "Others": 223916 }, "South East": { "Con": 1332755, "Lab": 1067897, "LD": 951222, "Reform": 609281, "Green": 299665, "Others": 90596 }, "South West": { "Con": 785672, "Lab": 682080, "LD": 686921, "Reform": 384240, "Green": 206780, "Others": 39737 }, "Scotland": { "Con": 307344, "Lab": 851897, "LD": 234228, "Reform": 167979, "Green": 92685, "SNP": 724758, "Others": 35919 }, "Wales": { "Con": 240003, "Lab": 487636, "LD": 85911, "Reform": 223018, "Green": 61662, "Plaid": 194811, "Others": 26035 }, "Northern Ireland": { "Con": 553, "Green": 8692, "DUP": 172058, "SF": 210891, "SDLP": 86861, "UUP": 94779, "Alliance": 117191, "TUV": 48685, "PBP": 8438, "Aontu": 7466, "Others": 24226 } } ACTUAL_WINNERS = { "North East": { "Lab": 26, "Con": 1 }, "North West": { "Lab": 65, "Independent": 1, "LD": 3, "Con": 3, "Speaker": 1 }, "Yorkshire and the Humber": { "Lab": 43, "Con": 9, "Independent": 1, "LD": 1 }, "East Midlands": { "Lab": 29, "Reform": 2, "Con": 15, "Independent": 1 }, "West Midlands": { "Con": 15, "Lab": 38, "Independent": 1, "Green": 1, "LD": 2 }, "East of England": { "Con": 23, "Lab": 27, "LD": 7, "Reform": 3, "Green": 1 }, "London": { "Lab": 59, "Con": 9, "LD": 6, "Independent": 1 }, "South East": { "Lab": 36, "Con": 30, "LD": 24, "Green": 1 }, "South West": { "LD": 22, "Lab": 24, "Con": 11, "Green": 1 }, "Scotland": { "SNP": 9, "Lab": 37, "Con": 5, "LD": 6 }, "Wales": { "Lab": 27, "LD": 1, "Plaid": 4 }, "Northern Ireland": { "DUP": 5, "SF": 7, "SDLP": 2, "Alliance": 1, "TUV": 1, "Independent": 1, "UUP": 1 } } GP_CENTRAL_SCENARIO = { "North East": { "Lab": 13 }, "North West": { "Lab": 33, "Con": 1, "LD": 2, "Speaker": 1 }, "Yorkshire and the Humber": { "Lab": 21, "Con": 5, "LD": 1 }, "East Midlands": { "Lab": 14, "Con": 9, "Reform": 1 }, "West Midlands": { "Lab": 19, "Con": 9, "LD": 1 }, "East of England": { "Lab": 14, "Con": 13, "LD": 3, "Reform": 1 }, "London": { "Lab": 35, "Con": 5, "LD": 3 }, "South East": { "Lab": 17, "Con": 15, "LD": 12, "Green": 1 }, "South West": { "Lab": 12, "Con": 5, "LD": 11 }, "Scotland": { "Lab": 16, "SNP": 4, "Con": 3, "LD": 3 }, "Wales": { "Lab": 12, "Plaid": 2, "LD": 1 }, "Northern Ireland": { "SF": 4, "DUP": 2, "SDLP": 1, "Alliance": 1, "UUP": 1 } } def hamilton(counts, target, votes=None): """Largest-remainder compression; ties by remainder then regional votes.""" total = sum(counts.values()) quota = {p: target*n/total for p, n in counts.items()} base = {p: math.floor(q) for p, q in quota.items()} left = target - sum(base.values()) order = sorted(counts, key=lambda p: (quota[p]-base[p], (votes or counts).get(p, 0), p), reverse=True) for p in order[:left]: base[p] += 1 return {p: n for p, n in base.items() if n} def allocate(T, C, votes, direct, threshold): """Green Paper s.18: qualifying groupings >= threshold of regional valid votes; F = direct seats of non-qualifying entities; targets over T-F; T-C regional seats to the largest deficit, ties by raw votes.""" total = sum(votes.values()) qual = [p for p in votes if p not in NON_GROUPINGS and votes[p]/total >= threshold] F = sum(n for p, n in direct.items() if p not in qual) Q = sum(votes[p] for p in qual) target = {p: (T-F)*votes[p]/Q for p in qual} seats = collections.Counter(direct) for _ in range(T-C): deficit = {p: target[p]-seats[p] for p in qual} best = max(deficit.values()) tied = [p for p, d in deficit.items() if abs(d-best) < 1e-12] seats[max(tied, key=lambda p: votes[p])] += 1 return target, {p: n for p, n in seats.items() if n} def sainte_lague(T, C, votes, direct, threshold): total = sum(votes.values()) qual = [p for p in votes if p not in NON_GROUPINGS and votes[p]/total >= threshold] seats = collections.Counter(direct) for _ in range(T-C): pick = max(qual, key=lambda p: votes[p]/(2*seats[p]+1)) seats[pick] += 1 return {p: n for p, n in seats.items() if n} def gallagher(votes, seats, T, drop_others=False): tot = sum(v for p, v in votes.items() if not (drop_others and p == 'Others')) parties = set(votes) | set(seats) if drop_others: parties -= {'Others'} return math.sqrt(sum((votes.get(p, 0)/tot*100 - seats.get(p, 0)/T*100)**2 for p in parties)/2) def perturbations(votes, direct, C, actual, radius=2, l1max=4, min_share=0.08): """Vary every grouping with >= min_share regional vote share, a scenario seat, or an actual 2024 seat (superset of the Green Paper test, which varied 2024 winners only). Non-grouping direct seats held fixed.""" total = sum(votes.values()) var = [p for p in votes if p not in NON_GROUPINGS and (votes[p]/total >= min_share or direct.get(p, 0) > 0 or actual.get(p, 0) > 0)] special = {p: n for p, n in direct.items() if p in NON_GROUPINGS} tgt = C - sum(special.values()) ranges = [range(max(0, direct.get(p, 0)-radius), min(C, direct.get(p, 0)+radius)+1) for p in var] for vals in itertools.product(*ranges): if sum(vals) != tgt: continue if sum(abs(v-direct.get(p, 0)) for p, v in zip(var, vals)) > l1max: continue d = {p: v for p, v in zip(var, vals) if v} d.update(special) yield d if __name__ == '__main__': assert sum(sum(v.values()) for v in REGIONAL_VOTES.values()) == 28_809_340 assert sum(T_SPEC.values()) == 650 and sum(C_SPEC.values()) == 327 for th, label in [(0.05, '5% threshold'), (0.03, '3% threshold (proposal)')]: nat = collections.Counter() for r, votes in REGIONAL_VOTES.items(): tgt, fin = allocate(T_SPEC[r], C_SPEC[r], votes, GP_CENTRAL_SCENARIO[r], th) if th == 0.05: print(r, 'targets=', {p: round(t, 3) for p, t in tgt.items()}, 'final=', fin) nat.update(fin) assert sum(nat.values()) == 650 print(label, '->', dict(sorted(nat.items(), key=lambda x: -x[1])), '\n') print('Hamilton anchors:') for r in REGIONAL_VOTES: print(' ', r, hamilton(ACTUAL_WINNERS[r], C_SPEC[r], REGIONAL_VOTES[r])) print('\nPerturbation envelopes (broadened test):') lo = collections.Counter(); hi = collections.Counter() for r, votes in REGIONAL_VOTES.items(): finals = [allocate(T_SPEC[r], C_SPEC[r], votes, d, 0.05)[1] for d in perturbations(votes, GP_CENTRAL_SCENARIO[r], C_SPEC[r], ACTUAL_WINNERS[r])] parties = set().union(*(f.keys() for f in finals)) rng = {p: (min(f.get(p, 0) for f in finals), max(f.get(p, 0) for f in finals)) for p in parties} for p, (a, b) in rng.items(): lo[p] += a; hi[p] += b print(' ', r, {p: v for p, v in rng.items() if v[0] != v[1]} or 'INVARIANT') print('National envelope:', {p: (lo[p], hi[p]) for p in sorted(hi, key=lambda x: -hi[x])}) natSL = collections.Counter(); nat5 = collections.Counter() for r, votes in REGIONAL_VOTES.items(): natSL.update(sainte_lague(T_SPEC[r], C_SPEC[r], votes, GP_CENTRAL_SCENARIO[r], 0.05)) nat5.update(allocate(T_SPEC[r], C_SPEC[r], votes, GP_CENTRAL_SCENARIO[r], 0.05)[1]) print('Sainte-Lague delta vs greedy-deficit:', {p: natSL.get(p, 0)-nat5.get(p, 0) for p in set(natSL) | set(nat5) if natSL.get(p, 0) != nat5.get(p, 0)})