favorite_betrayal — the worked STAR favorite-betrayal pair¶

The rare construction favorite_betrayal_voting_301.md describes but — until now — never showed with numbers: STAR is not formally FBC-compliant, and its leak lives in the runoff. Your scores don't just support candidates; they pick the two finalists. In a delicately balanced electorate, the score you give your favorite can be exactly what keeps your compromise out of the runoff — and then the only repair is scoring your favorite lower. That's a favorite betrayal, it happens here, and it pays.

This is the repo's concession case. We show STAR's own criterion failure at full volume, with the live elections to click — because the credibility of every center-squeeze page in this repo is bought by pages like this one.

▶ Live on BetterVoting: - Half 1, honest: vote · results ↗ (election 7mckyg, Test ID BV2206) - Half 2, betrayal: vote · results ↗ (election b6xrdr, Test ID BV2207)

BetterVoting agrees with the LH engine on both halves (Clover; Bluebell) — no tiebreaks anywhere.

The electorate¶

A garden club of 57 picks the town flower: Aster, Bluebell, Clover.

Count	Aster	Bluebell	Clover	who they are
9	5	5	0	the double-fans: love Aster, love Bluebell — the betrayers-to-be
6	5	0	0	Aster-only fans
24	0	1	0	the tepid consensus: "Bluebell? …fine."
18	0	0	4	the Clover bloc

Bluebell is the Condorcet winner — she beats Aster head-to-head 24–6 and Clover 33–18. But her support is broad and feeble (twenty-four 1s), and score totals are what pick STAR's finalists.

Half 1 — honest ballots elect Clover¶

[Divergence from STAR]
  STAR                   = Clover
  Choose-One (Plurality) = Bluebell   (differs from STAR)
  RCV-IRV                = Bluebell   (differs from STAR)
  RCV-RR (Condorcet)     = Bluebell   (differs from STAR)
  Note: 9 of 57 ballots (16%) had equal non-zero scores, so their ranks were
        decided by candidate priority order. The RCV-IRV result may be an
        artifact of score-to-rank tie-breaking rather than a deep
        difference.
  Note: Ranked Robin (RCV-RR) sides with RCV-IRV, so STAR is the outlier
        here — STAR need not elect the Condorcet candidate.
  Full round-by-round reports (generated for review):
  RCV-IRV rounds: cases_tabulated/bv2206_7mckyg_fbc_honest_tepid_consensus_RCV-IRV_tabulated.txt
  RCV-RR round-robin: cases_tabulated/bv2206_7mckyg_fbc_honest_tepid_consensus_RCV-RR_tabulated.txt

[Runoff Reversal]
 - Score Round Winner(s) = (Aster)
 - Runoff Round Winner   = (Clover)
  Candidate Aster earned the highest total score, but
  Candidate Clover won the automatic runoff — not a malfunction,
  STAR working as designed: the runoff elects the finalist preferred
  by the majority (of voters with a preference).

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

[STAR Voting]
 Tabulating 57 ballots.
Count × Aster,Bluebell,Clover
   24 ×     0,       1,     0
   18 ×     0,       0,     4
    9 ×     5,       5,     0
    6 ×     5,       0,     0

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Aster         -- 75 -- First place
   Clover        -- 72 -- Second place
   Bluebell      -- 69
 Aster and Clover advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Clover        -- 18 -- First place
   Aster         -- 15
   Equal Support -- 24
 Clover wins.
   Runoff math:
     57  ballots cast
   − 24  Equal Support (no preference between the two finalists)
     ──
     33  voters with a preference  (majority = 17)
           Clover 18 (55%)  ·  Aster 15 (45%)

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

The pairwise matrix behind it (the engine's full view — note Bluebell's row):

                 |   * Aster    |   Bluebell  |  * Clover   |
-------------------------------------------------------------
       * Aster > |     ---      | 6 - 27 - 24 |15 - 24 - 18 |
      Bluebell > | 24 - 27 -  6 |    ---      |33 -  6 - 18 |
      * Clover > | 18 - 24 - 15 |18 -  6 - 33 |    ---      |

[Condorcet Winner]
  Condorcet Winner: Bluebell — STAR elected Clover instead (Bluebell was
  eliminated in the scoring round)

The compromise a majority prefers to everyone misses the runoff by three points. (This half is also a clean Condorcet-winner paradox instance for STAR, alongside BV2156.)

Half 2 — nine voters demote their favorite, and it pays¶

The nine double-fans see the standings. Notice what they cannot do: raise Bluebell. She's already at 5 on their ballots — STAR let them equal-top the compromise for free, and it wasn't enough, because the problem is Aster's own total keeping Bluebell out of the runoff. The only move left is scoring their true favorite lower — Aster 5 → 4, strictly below Bluebell. That is the definition of favorite betrayal.

[Divergence from STAR]
  STAR     = Bluebell
  Approval = Clover   (differs from STAR)

[Runoff Reversal]
 - Score Round Winner(s) = (Clover)
 - Runoff Round Winner   = (Bluebell)
  Candidate Clover earned the highest total score, but
  Candidate Bluebell won the automatic runoff — not a malfunction,
  STAR working as designed: the runoff elects the finalist preferred
  by the majority (of voters with a preference).

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

[STAR Voting]
 Tabulating 57 ballots.
Count × Aster,Bluebell,Clover
   24 ×     0,       1,     0
   18 ×     0,       0,     4
    9 ×     4,       5,     0
    6 ×     5,       0,     0

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Clover        -- 72 -- First place
   Bluebell      -- 69 -- Second place
   Aster         -- 66
 Clover and Bluebell advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Bluebell      -- 33 -- First place
   Clover        -- 18
   Equal Support --  6
 Bluebell wins.
   Runoff math:
     57  ballots cast
   −  6  Equal Support (no preference between the two finalists)
     ──
     51  voters with a preference  (majority = 26)
           Bluebell 33 (65%)  ·  Clover 18 (35%)

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

The runoff pairing flips from Aster-vs-Clover to Clover-vs-Bluebell, and the Condorcet winner wins it 33–18. The nine turned their outcome from Clover (their 0) into Bluebell (their 5) by lowering their favorite. STAR failed the Favorite Betrayal Criterion, exactly as its ❌ on the criteria chart says it can.

Why this is a lab specimen, not a strategy¶

The 301 page claims STAR's FBC failures are "fragile and unactionable." This case demonstrates the fragility rather than asserting it:

It takes 7 of the 9. Each betrayer moves Aster down one point. Seven or more: the flip works. Exactly six: Aster and Bluebell tie at 69 for the last runoff seat and the outcome falls to a tie-break. Five or fewer: nothing changes — Clover still wins, and the betrayers gave up score-support for their favorite for free.
It needs the standings to 3 points. The whole construction balances on Aster 75 / Clover 72 / Bluebell 69. Real electorates don't publish their totals in advance; polling error alone swamps a 3-point gap in a 57-voter race.
It needs the compromise pre-maxed. If the nine had any room to raise Bluebell instead, that honest, non-betrayal repair would come first — STAR's equal-top is free. The betrayal is only forced because the honest fix is already spent.

Measured across thousands of random elections, betrayals that actually pay are the ~2% tail in STAR — the other ~98% backfire (fbc_simulation.py). This page is what one of the 2% looks like: engineered, coordinated, knife-edged. Compare the RCV-IRV failure mode — the center squeeze — which is systematic, arrives in ordinary competitive three-way races, and gives a whole political wing a standing reason to betray (Alaska 2022, worked on the 301 page).

Reading this fairly¶

Both sides of the honesty ledger, in one breath: STAR fails FBC — this pair is the proof, concede it without a number attached. And the failure needed a 3-point knife edge, a pre-maxed compromise, and 7-of-9 coordination to appear, while the same electorate under RCV-IRV rules would have been an ordinary center-squeeze setup. Neither method is betrayal-proof; the theorem says something had to give (no method satisfies both Favorite Betrayal and Later-No-Harm). What differs is whether the failure is a lab specimen or a repeating pattern.

Run it yourself¶

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 01_STAR/03_Criteria/favorite_betrayal/cases/bv2206_7mckyg_fbc_honest_tepid_consensus.yaml
python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 01_STAR/03_Criteria/favorite_betrayal/cases/bv2207_b6xrdr_fbc_betrayal_pays.yaml

Sources: bv2206_7mckyg_fbc_honest_tepid_consensus.yaml · bv2207_b6xrdr_fbc_betrayal_pays.yaml. Full mirrors: honest ballots · betrayal pays.

Where this comes from. Ballots and cast are this repo's own, built to instantiate the finalist-pairing mechanism described in favorite_betrayal_voting_301.md §5 ("your scores can change which two candidates are finalists"). Related: runoff reversal (the benign face of the same score-vs-runoff two-step) · residual vote splitting (the other runoff-born edge case) · monotonicity (STAR's clean bill on the raise direction).