Restrictive sincerity — bullet voting, truncation, down-voting¶

Level: 201 · for voters

One of the four kinds of insincere vote. Restrictive sincerity is the downward erasure: you keep your favorite where they belong and push everyone else lower than you honestly rate them — usually all the way to zero, or off the ballot entirely.

You have probably done it. It's the most common insincere vote in the world, and it rarely feels like strategy:

Bullet voting — score or approve only your favorite, everyone else 0.
Truncation — on a ranked ballot, rank one or two and stop.
Down-voting — the milder version: your honest 3 becomes a 1, so the rival gets "less oxygen."

All three say the same false thing: "I am indifferent among everyone who isn't my favorite." You aren't. You'd much rather have your friendly second choice than the candidate you can't stand, and a restricted ballot hides exactly that.

Why voters do it — the fear is real, so start by conceding it¶

The reasoning is sound as far as it goes: scoring your second choice supports them, and they might beat your favorite with it. That's not paranoia — it's a named criterion failure. STAR, Approval, Score, and Ranked Robin all fail later-no-harm: a mark you make lower down can cost your favorite the win. (RCV-IRV is the method that keeps later-no-harm, and it pays for that by not reading your lower ranks at all until your higher ones are gone — the same property from the other side.)

So the honest question isn't "could scoring my second choice ever hurt?" It's "which risk is bigger — my second choice beating my favorite, or my last choice beating both?" For almost every voter in almost every race, the second risk is much bigger, and restrictive sincerity is aimed at the smaller one.

What it costs, worked: four fans bullet-vote and elect the candidate they scored 0¶

A club books a speaker. Ari's four fans genuinely like Bree too — honest ballot Ari 5, Bree 3, Cash 0. The night before, one of them argues: scoring Bree helps Ari's rival — zero her, and Ari walks in. All four bullet vote.

Honest ballots elect Bree, the compromise — a result Ari's fans rate a 3:

[Divergence from STAR]
  STAR                   = Bree
  Choose-One (Plurality) = Ari   (differs from STAR)
  RCV-IRV                = Cash   (differs from STAR)
  Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine
        method difference, not a tie-breaking artifact.
  Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone
        outlier — the classic center-squeeze signature.
  Full round-by-round reports (generated for review):
  RCV-IRV rounds: cases_tabulated/ex06_bullet_honest_RCV-IRV_tabulated.txt

--- STAR Voting Method (single winner) ---

[STAR Voting]
 Tabulating 9 ballots.
Count × Ari,Bree,Cash
    4 ×   5,   3,   0
    4 ×   0,   2,   5
    1 ×   0,   5,   1

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Bree          -- 25 -- First place
   Cash          -- 21 -- Second place
   Ari           -- 20
 Bree and Cash advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Bree          -- 5 -- First place
   Cash          -- 4
   Equal Support -- 0
 Bree wins.
   Runoff math:
     9  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     9  voters with a preference  (majority = 5)
           Bree 5 (56%)  ·  Cash 4 (44%)

[STAR Voting: Winner — STAR Voting Method (single winner)]
 Bree

Now the four fans zero Bree out. Nothing else changes:

[Divergence from STAR]
  STAR                   = Cash
  Choose-One (Plurality) = Ari   (differs from STAR)
  Approval               = Ari   (differs from STAR)

--- STAR Voting Method (single winner) ---

[STAR Voting]
 Tabulating 9 ballots.
Count × Ari,Bree,Cash
    4 ×   5,   0,   0
    4 ×   0,   2,   5
    1 ×   0,   5,   1

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Cash          -- 21 -- First place
   Ari           -- 20 -- Second place
   Bree          -- 13
 Cash and Ari advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Cash          -- 5 -- First place
   Ari           -- 4
   Equal Support -- 0
 Cash wins.
   Runoff math:
     9  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     9  voters with a preference  (majority = 5)
           Cash 5 (56%)  ·  Ari 4 (44%)

[STAR Voting: Winner — STAR Voting Method (single winner)]
 Cash

Cash wins — the candidate all four scored 0. Their 12 points of honest support were the only thing holding Bree above Cash in the scoring round; withdrawing it didn't promote Ari, it promoted the person they liked least into the runoff, where Ari lost. The plan had a hidden precondition — Ari must actually be able to reach the top two — and it was false.

Full exercise, with the parts worked one at a time: Exercise 6 — Bullet voting backfires (both halves are live on BetterVoting, and each also carries RCV-IRV and Ranked Robin races).

The same move, by method¶

Method	What restricting looks like	What it costs you
STAR	score only your favorite	you keep your full voice in the runoff only if your favorite is in it; otherwise you've flattened the two people the runoff is actually between — the case above
Score / Range	same	strictly worse: there is no runoff to rescue you, so a bullet vote is simply a smaller ballot
Approval	approve only your favorite	the sharpest version, because Approval has no canonical sincere ballot — the threshold is a free parameter, so "insincere" is genuinely arguable. See Approval's honest limits §3 and is Approval's outcome arbitrary?
RCV-IRV	rank one and stop	your ballot exhausts when your candidate is eliminated and stops counting entirely — exhausted ballots
Ranked Robin	rank one and stop	you sit out every pairwise matchup among the candidates you didn't rank — the matchups most likely to decide the race
Proportional STAR	bullet-vote your slate	it doesn't protect your share — the PR FAQ answers this directly

The version that hurts a whole side: a coalition bullet-votes itself apart¶

STAR ends forced vote-splitting — it can't stop a coalition from splitting itself by refusing to use the scale. Ada and Ben are on the same side (60 of 100 voters); Cara is the opposition (40). Ada's fans give Ben a 0, Ben's fans give Ada a 0, purely tribally. Scores: Ada 175, Ben 125, Cara 200 — Cara takes a finalist slot off a split field and wins the runoff, against a 60% majority that preferred her side.

The cure is entirely in the voters' hands, and it's small: scoring the ally even a 3 elects the majority side. Both halves, with the full write-up: residual vote-splitting · the bullet-voting half.

When restricting is honest¶

Two cases, both real:

You genuinely don't support anyone else. A 0 that reflects a real 0 is not a strategy, it's an opinion, and STAR is built to record it. Same for leaving a candidate blank — see abstention vs. zero vs. NOTA.
Two candidates really are equal to you. Equal scores are a feature; the runoff reports them as Equal Support rather than inventing a preference you never stated.

What makes a restricted ballot insincere is flattening people you can actually rank — and the price of that is paid in the round where your flattening leaves you with nothing to say.

The rule of thumb¶

Use the whole scale, top to bottom. A 5 for your favorite and a 3 for the ally you can live with is a stronger ballot than a lone 5 — it keeps your favorite's support intact and keeps you in the runoff if your favorite doesn't make it. The mirror-image mistake, flattening people upward, is expansive sincerity, and it fails for the same structural reason.

file: restrictive_sincerity.md¶