Simplify and make Kemeny voting implementation faster.

PiperOrigin-RevId: 596618517
Change-Id: I9156c7a7cda417337b616d9ec9d84ca4e597af12

open_spiel/python/voting/kemeny_young.py

@@ -33,38 +33,43 @@ def name(self) -> str:
 
   def _score(
       self,
-      alternatives: List[base.AlternativeId],
       pref_mat: np.ndarray,
       perm: Tuple[int, ...],
-  ) -> Tuple[List[base.AlternativeId], int, np.ndarray]:
+  ) -> np.ndarray:
     # The score of alternative a_i in a ranking R is defined to be:
     #      KemenyScore(a_i) = sum_{a_j s.t. R(a_i) >= R(a_j)} N(a_i, a_j)
     # The score of ranking R is then sum_i KemenyScore(a_i).
     num_alts = len(perm)
     scores = np.zeros(num_alts, dtype=np.int32)
-    ranking = []
     for i in range(num_alts):
-      alt_idx_i = perm[i]
       for j in range(i+1, num_alts):
-        alt_idx_j = perm[j]
-        value = pref_mat[alt_idx_i, alt_idx_j]
-        scores[i] += value
-      ranking.append(alternatives[alt_idx_i])
-    return (ranking, scores.sum(), scores)
+        scores[i] += pref_mat[perm[i], perm[j]]
+    return scores
+
+  def _permutation_to_ranking(
+      self,
+      alternatives: List[base.AlternativeId],
+      permutation: Tuple[base.AlternativeId, ...]) -> List[base.AlternativeId]:
+    assert len(permutation) == len(alternatives)
+    return [alternatives[permutation[i]] for i in range(len(alternatives))]
 
   def run_election(self, profile: base.PreferenceProfile) -> base.RankOutcome:
     assert self.is_valid_profile(profile)
     pref_mat = profile.pref_matrix()
     alternatives = profile.alternatives
     m = profile.num_alternatives()
-    # ranking info is tuples of (ranking, total_score, scores list)
-    best_ranking_info = (None, 0, [])
-    for perm in itertools.permutations(range(m)):
-      # perm is a permutation of alternative indices
-      ranking_info = self._score(alternatives, pref_mat, perm)
-      if ranking_info[1] > best_ranking_info[1]:
-        best_ranking_info = ranking_info
-    outcome = base.RankOutcome(rankings=best_ranking_info[0],
-                               scores=list(best_ranking_info[2]))
+    best_permutation = None
+    best_score = -1
+    best_score_array = None
+    for permutation in itertools.permutations(range(m)):
+      scores = self._score(pref_mat, permutation)
+      total_score = scores.sum()
+      if total_score > best_score:
+        best_score = total_score
+        best_score_array = scores
+        best_permutation = permutation
+    best_ranking = self._permutation_to_ranking(alternatives, best_permutation)
+    outcome = base.RankOutcome(rankings=best_ranking,
+                               scores=list(best_score_array))
     return outcome