ocaml: phase 5.1 majority_vote.ml baseline (Boyer-Moore majority, [3;3;4;2;4;4;2;4;4] = 4)

O(n) time / O(1) space majority vote algorithm:

  let majority xs =
    let cand = ref 0 in
    let count = ref 0 in
    List.iter (fun x ->
      if !count = 0 then begin
        cand := x;
        count := 1
      end else if x = !cand then count := !count + 1
      else count := !count - 1
    ) xs;
    !cand

The candidate is updated to the current element whenever count
reaches zero. When a strict majority exists, this guarantees the
result.

  majority [3;3;4;2;4;4;2;4;4] = 4   (5 of 9, > n/2)

97 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -51,6 +51,7 @@
   "json_pretty.ml": 24,
   "kadane.ml": 6,
   "lambda_calc.ml": 7,
+  "majority_vote.ml": 4,
   "levenshtein.ml": 11,
   "memo_fib.ml": 75025,
   "mortgage.ml": 1073,

lib/ocaml/baseline/majority_vote.ml

@@ -0,0 +1,15 @@
+let majority xs =
+  let cand = ref 0 in
+  let count = ref 0 in
+  List.iter (fun x ->
+    if !count = 0 then begin
+      cand := x;
+      count := 1
+    end else if x = !cand then count := !count + 1
+    else count := !count - 1
+  ) xs;
+  !cand
+
+;;
+
+majority [3; 3; 4; 2; 4; 4; 2; 4; 4]

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-09 Phase 5.1 — majority_vote.ml baseline (Boyer-Moore
+  majority, [3;3;4;2;4;4;2;4;4] → 4). O(n) time / O(1) space:
+  candidate-and-count refs; on match increment, on mismatch
+  decrement and replace candidate when count reaches zero.
+  Demonstrates the classical streaming algorithm. 97 baseline
+  programs total.
 - 2026-05-09 Phase 5.1 — adler32.ml baseline (Adler-32 checksum of
   "Wikipedia" = 300286872 = 0x11E60398). Two running sums modulo
   65521; final checksum is `b * 65536 + a`. Used by zlib for stream