Prefer high-performing distractors

api/QuestionsApi/Models/ChoicePoolSelector.cs

@@ -0,0 +1,65 @@
+namespace QuestionsApi.Models;
+
+public static class ChoicePoolSelector
+{
+    private const int PresentedChoiceCount = 5;
+    private const double MaximumRateMultiplier = 5.0;
+
+    public static List<string> SelectChoiceIds(
+        Question question,
+        IReadOnlyDictionary<string, int>? liveSelectionPercentages = null,
+        Random? random = null)
+    {
+        random ??= Random.Shared;
+        var rates = liveSelectionPercentages is { Count: > 0 }
+            ? liveSelectionPercentages
+            : question.ChoiceSelectionPercentages;
+        var correct = question.Choices.FirstOrDefault(choice => choice.Id == question.CorrectChoiceId);
+        var remaining = question.Choices
+            .Where(choice => choice.Id != question.CorrectChoiceId)
+            .ToList();
+        var selected = new List<QuestionChoice>();
+
+        while (selected.Count < PresentedChoiceCount - 1 && remaining.Count > 0)
+        {
+            var totalWeight = remaining.Sum(choice => Weight(choice.Id, rates));
+            var threshold = random.NextDouble() * totalWeight;
+            var cumulative = 0.0;
+            var selectedIndex = remaining.Count - 1;
+            for (var index = 0; index < remaining.Count; index++)
+            {
+                cumulative += Weight(remaining[index].Id, rates);
+                if (threshold < cumulative)
+                {
+                    selectedIndex = index;
+                    break;
+                }
+            }
+            selected.Add(remaining[selectedIndex]);
+            remaining.RemoveAt(selectedIndex);
+        }
+
+        if (correct is not null)
+            selected.Add(correct);
+        else
+            selected = question.Choices.Take(PresentedChoiceCount).ToList();
+
+        Shuffle(selected, random);
+        return selected.Select(choice => choice.Id).ToList();
+    }
+
+    private static double Weight(string choiceId, IReadOnlyDictionary<string, int>? rates)
+    {
+        var rate = Math.Clamp(rates?.GetValueOrDefault(choiceId, 0) ?? 0, 0, 100);
+        return 1.0 + MaximumRateMultiplier * rate / 100.0;
+    }
+
+    private static void Shuffle<T>(IList<T> items, Random random)
+    {
+        for (var index = items.Count - 1; index > 0; index--)
+        {
+            var replacement = random.Next(index + 1);
+            (items[index], items[replacement]) = (items[replacement], items[index]);
+        }
+    }
+}

api/QuestionsApi/Models/QuestionResponse.cs

@@ -33,7 +33,7 @@ public class QuestionResponse
         int questionElo = 1000,
         bool includeChoicePool = true)
     {
-        var choices = includeChoicePool ? question.Choices : SelectLegacyChoices(question);
+        var choices = includeChoicePool ? question.Choices : SelectLegacyChoices(question, liveChoiceSelectionPercentages);
         var choiceIds = choices.Select(choice => choice.Id).ToHashSet(StringComparer.Ordinal);
         var percentages = BuildChoiceSelectionPercentages(question, liveChoiceSelectionPercentages);
         return new QuestionResponse
@@ -87,20 +87,17 @@ public class QuestionResponse
         return response;
     }
 
-    private static List<QuestionChoice> SelectLegacyChoices(Question question)
+    private static List<QuestionChoice> SelectLegacyChoices(
+        Question question,
+        IReadOnlyDictionary<string, int>? liveChoiceSelectionPercentages)
     {
         if (question.Choices.Count <= 5)
             return question.Choices;
 
-        var correct = question.Choices.First(choice => choice.Id == question.CorrectChoiceId);
-        var distractors = question.Choices
-            .Where(choice => choice.Id != question.CorrectChoiceId)
-            .OrderBy(_ => Random.Shared.Next())
-            .Take(4)
-            .Append(correct)
-            .OrderBy(_ => Random.Shared.Next())
+        var selectedIds = ChoicePoolSelector.SelectChoiceIds(question, liveChoiceSelectionPercentages);
+        return selectedIds
+            .Select(id => question.Choices.First(choice => choice.Id == id))
             .ToList();
-        return distractors;
     }
 
     public static Dictionary<string, int> BuildChoiceSelectionPercentages(Question question, Dictionary<string, int>? liveChoiceSelectionPercentages)