Initial commit of MES (#1)

**Context:**

This pull request adds new test cases for the `MethodOfEqualShares` class within the `packages/backend/src/Tabulators/MethodOfEqualShares.ts` file. This includes importing the `fraction.js` package and several testing scenarios such as Basic Example, Influence Budget Redistribution, Random Tiebreaker, Random Tiebreaker with Defined Order, and Valid/Invalid/Under/Bullet Vote Counts.

**Key Changes:**

1. **New test file:**
   - Created a new test file at `packages/backend/src/Tabulators/MethodOfEqualShares.test.ts`.
   - Added comprehensive test cases to validate the functionality of the `MethodOfEqualShares`.

2. **Implementation of MethodOfEqualShares**
   - Added `packages/backend/src/Tabulators/MethodOfEqualShares.ts` to implement the MethodOfEqualShares function.
   - The function calculates election results based on various voting methods and scenarios.
   - It handles tiebreakers, influence budget redistribution, and validates different vote types.

**Testing Instructions:**

- Run the test suite in the `packages/backend/` directory to ensure all new and existing tests pass.

**Motivation:**

- To ensure the reliability and accuracy of the `MethodOfEqualShares` function.
- To handle edge cases and validate the workflow of the election model.

packages/backend/src/Tabulators/MethodOfEqualShares.test.ts

@@ -0,0 +1,136 @@
+import { MethodOfEqualShares } from "./MethodOfEqualShares";
+const Fraction = require("fraction.js");
+
+describe("Method of Equal Shares Tests", () => {
+  test("Basic Example", () => {
+    const candidates = ["Allison", "Bill", "Carmen", "Doug"];
+    const votes = [
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 4, 4, 0],
+      [0, 0, 0, 3],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+    ];
+    const results = MethodOfEqualShares(candidates, votes, 2, [], false, false);
+    expect(results.elected.length).toBe(2);
+    expect(results.elected[0].name).toBe("Allison");
+    expect(results.elected[1].name).toBe("Doug");
+    const weightedScoresRound0 =
+      results.summaryData.weightedScoresByRound[0].map((score) =>
+        parseFloat(score.toString()),
+      );
+    expect(weightedScoresRound0).toStrictEqual([25, 24, 24, 23]);
+    const weightedScoresRound1 =
+      results.summaryData.weightedScoresByRound[1].map((score) =>
+        parseFloat(score.toString()),
+      );
+    expect(weightedScoresRound1).toStrictEqual([0, 0, 16, 23]);
+  });
+
+  test("Influence Budget Redistribution", () => {
+    const candidates = ["Allison", "Bill", "Carmen", "Doug"];
+    const votes = [
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 4, 4, 0],
+      [0, 0, 0, 3],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+    ];
+    const results = MethodOfEqualShares(candidates, votes, 2, [], false, false);
+    expect(results.elected.length).toBe(2);
+    expect(results.elected[0].name).toBe("Allison");
+    expect(results.elected[1].name).toBe("Doug");
+    const weightedScoresRound0 =
+      results.summaryData.weightedScoresByRound[0].map((score) =>
+        parseFloat(score.toString()),
+      );
+    expect(weightedScoresRound0).toStrictEqual([40, 39, 23, 18]);
+    const weightedScoresRound1 =
+      results.summaryData.weightedScoresByRound[1].map((score) =>
+        parseFloat(score.toString()),
+      );
+    expect(weightedScoresRound1).toStrictEqual([0, 9.75, 14.75, 18]);
+  });
+
+  test("Random Tiebreaker", () => {
+    const candidates = ["Allison", "Bill", "Carmen", "Doug"];
+    const votes = [
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 4, 0],
+      [0, 0, 0, 3],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+    ];
+    const results = MethodOfEqualShares(candidates, votes, 2, [], true, false);
+    expect(results.elected.length).toBe(2);
+    expect(results.tied[0].length).toBe(2); // two candidates tied in the first round
+    expect(results.elected[0].name).toBe("Allison"); // random tiebreaker, second place lower index 1
+    expect(results.elected[1].name).toBe("Doug");
+  });
+
+  test("Random Tiebreaker with Defined Order", () => {
+    const candidates = ["Allison", "Bill", "Carmen", "Doug"];
+    const votes = [
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 1, 0],
+      [5, 5, 4, 0],
+      [0, 0, 0, 3],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+      [0, 0, 4, 5],
+    ];
+    const results = MethodOfEqualShares(
+      candidates,
+      votes,
+      2,
+      [4, 3, 2, 1],
+      true,
+      false,
+    );
+    expect(results.elected.length).toBe(2);
+    expect(results.tied[0].length).toBe(2); // two candidates tied in the first round
+    expect(results.elected[0].name).toBe("Bill"); // random tiebreaker, second place lower index 1
+    expect(results.elected[1].name).toBe("Doug");
+  });
+
+  test("Valid/Invalid/Under/Bullet Vote Counts", () => {
+    const candidates = ["Allison", "Bill", "Carmen"];
+    const votes = [
+      [1, 3, 5],
+      [1, 3, 5],
+      [1, 3, 5],
+      [0, 0, 0],
+      [0, 0, 0],
+      [-1, 3, 5],
+      [0, 3, 6],
+      [5, 0, 0],
+      [0, 5, 0],
+      [0, 0, 5],
+    ];
+    const results = MethodOfEqualShares(candidates, votes, 1, [], false, false);
+    expect(results.summaryData.nValidVotes).toBe(8);
+    expect(results.summaryData.nInvalidVotes).toBe(2);
+    expect(results.summaryData.nUnderVotes).toBe(2);
+    expect(results.summaryData.nBulletVotes).toBe(3);
+  });
+});