Equal & opposite — the equally weighted vote, made runnable¶

The Equal Vote Coalition's "Test of Balance" in one picture: two voters with exact-opposite opinions on every candidate cancel out completely. If a race was tied before their two ballots, it's tied after — neither outweighed the other. That's what an equally weighted vote means, and it's the reason STAR has no forced vote-splitting. This folder makes the demonstration runnable: a base election, then the same election with the two mirror ballots added — the winner never moves. The concept, in full: The Equally Weighted Vote — the Test of Balance.

▶ Live on BetterVoting: base — vote · results ↗ (36f4v2, BV2219) · plus-cancel — vote · results ↗ (q8q9m7, BV2220). Two elections differing only by the two mirror ballots — both elect Comet.

→ Related: the spoiler effect (what an unequal vote causes) · the Equal Vote scorecard (row 1: "spoiler / vote splitting").

The two mirror ballots¶

Six candidates — Astra, Bolt, Comet, Dune, Echo, Flux — on a 0–5 ballot. Two voters disagree on every one; each candidate's two scores sum to 5 (an opposite score is 5 − s):

Candidate	Voter A	Voter B	Sum
Astra	2	3	5
Bolt	1	4	5
Comet	0	5	5
Dune	1	4	5
Echo	5	0	5
Flux	4	1	5

Add both to any election and nothing moves, for two reasons that together are the whole point:

Scoring round: every candidate gains exactly 5 stars (A + B = 5 each). Everyone rises by the same amount, so the ordering — and the top-two finalists — are untouched.
Automatic runoff: whichever finalist Voter A prefers, Voter B prefers the other by the same margin (their scores are opposite). They cancel 1–1.

The demonstration — before and after¶

Before (bv2219_…_base.yaml) — three voters, a decisive STAR winner:

Scoring Round
   Comet  -- 14 -- First place
   Echo   -- 12 -- Second place
   Astra  --  9      Bolt -- 7      Dune -- 3      Flux -- 1
 Comet and Echo advance.
Automatic Runoff
   Comet  -- 2 -- First place   vs   Echo -- 1        → Comet wins

After (bv2220_…_plus_cancel.yaml) — the same three voters plus the two mirror ballots:

Scoring Round
   Comet  -- 19 -- First place        (14 + 5)
   Echo   -- 17 -- Second place       (12 + 5)
   Astra  -- 14   Bolt -- 12   Dune -- 8   Flux -- 6      (each +5)
 Comet and Echo advance.
Automatic Runoff
   Comet  -- 3 -- First place   vs   Echo -- 2        → Comet wins

Every score total rose by exactly 5; the runoff went 3–2 instead of 2–1 — the two ballots put one vote on each side and cancelled. Same winner, Comet. The two voters had maximal, perfectly-opposed opinions, and their combined effect on the outcome was zero. (Full detail in the _tabulated mirrors: base election · with the opposed pair.)

Why a clear-winner base, and not just the two ballots?¶

The source graphic shows the two mirror ballots alone — which produces a perfect six-way tie (every candidate totals 5), decided only by lot. That's the cleanest statement of balance, but a pure tie has no reproducible winner to freeze or test against. So this case pairs the mirror ballots with a small decisive base: the property it proves — "add an exact-opposite pair to any election and the winner is unchanged" — is the same balance, but now deterministic, checkable by the test suite, and safe to freeze against BetterVoting.

The parallel in ranked methods¶

Balance isn't unique to scores. A ranked ballot and its exact reverse also cancel: in every head-to-head pair, one ballot's X > Y is met by the other's Y > X, so the pairwise margin is unchanged. So Ranked Robin passes the Test of Balance too. The method that fails it is Choose-One: a single mark can only add to one candidate, never subtract — there is no ballot anyone can cast to cancel it, which is exactly why plurality splits votes. (RCV-IRV is the subtle one — opposite ballots don't reliably cancel under sequential elimination.)

Files¶

Case	What it shows
base — tabulated report · `.yaml`	the base election — Comet wins 2–1
plus-cancel — tabulated report · `.yaml`	base + two mirror ballots — Comet still wins, 3–2

Source of the demonstration: Equal Vote Coalition, "Equally Weighted Vote" (the Test of Balance, after Mark Frohnmayer). Cast renamed here (Astra…Flux) for a fresh example. Live on BetterVoting as BV2219 (36f4v2) and BV2220 (q8q9m7) — two STAR elections that reproduce the same Comet wins. BetterVoting's own STAR count agrees with the engine on both (Comet, scores 14 and 19); the frozen exports are bv2219_…_base_bv_export.json and bv2220_…_plus_cancel_bv_export.json.