Favorite betrayal (RCV-IRV) — HONEST: Left voters rank their favorite first, and their WORST wins¶
Generated from bv2227_3xgkck_honest_irv.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.
Method: RCV-IRV (Instant Runoff) · 1 seat · Expected winner: Right
▶ Live on BetterVoting: vote · results ↗ (election 3xgkck · test BV2227).
Scenario¶
The plainest form of the favorite-betrayal incentive, the one RCV voters keep asking about ("is it smart to rank my favorite second?"). Three candidates on a spectrum: Left, Center, Right. 34 voters. The 12 Left voters vote honestly — Left > Center > Right. But Center, everyone's second choice and the Condorcet winner, has the FEWEST first-choices (9) and is eliminated first; Center's ballots split, and RIGHT wins the final 18-16. The Left voters' sincere ballots elected their LEAST-favorite candidate. See the companion fb_irv_betray (2 of those Left voters rank Center first and Center wins) and fb_star_honest (STAR/Ranked Robin elect Center from these same honest preferences — no betrayal needed). Concept: favorite_betrayal_voting_301.md.
Ballots¶
Each row is one voter's ranking, most-preferred first (N: prefix = N identical ballots).
12:Left>Center>Right
5:Center>Right>Left
4:Center>Left>Right
13:Right>Center>Left
What the engine says¶
Where the votes went. Band thickness is votes; a band leaving an eliminated candidate lands on whoever that ballot ranked next, or on inactive if it ranked nobody who was left.
The count, step by step — the rounds and how the winner is reached:
--- RCV / Instant-Runoff Voting (single winner) ---
Favorite betrayal (RCV-IRV) — HONEST: Left voters rank their favorite first, and their WORST wins
Tabulating 34 ballots (ranked ballots).
ROUND 1
Candidate Votes Status
----------- ------- --------
Right 13 Hopeful
Left 12 Hopeful
Center 9 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Right 18 Elected
Left 16 Rejected
Center 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Right
--- Transfers and inactive ballots (what the round tables leave out) ---
The tables above give each candidate's round total but not where a
transferred vote came FROM, nor how many ballots stopped counting.
Both are recomputed from the ballots, using the eliminations the
count above actually made.
ROUND 1 — 34 of 34 ballots still active; majority = 18
Center eliminated with 9:
→ Right 5
→ Left 4
FINAL ROUND — 34 of 34 ballots still active; majority = 18
Right 18 (52.9% of the still-active) ← elected
Left 16 (47.1% of the still-active)
Never exhausted, never transferred:
16 ballots held by Left carried a lower ranking that was never read
(the count stopped here, so those preferences did nothing).
Inactive ballots at the final round: 0 of 34 (0.0%).
Right's 18 is a majority of the 34 still active AND of all 34 cast (52.9%).
Full audit — preference matrix, Condorcet, and score distribution¶
--- Smith Set (the generalized Condorcet winner) ---
The smallest group whose every member beats every candidate outside it —
the honest answer to "who is even in contention?".
Smith set (1 of 3): Center
Outside (2): Left, Right
One member ⇒ Center is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Right is OUTSIDE the Smith set. ✗
Every member of the set (Center) beats Right head-to-head, yet
RCV-IRV elected Right anyway. RCV-IRV is not Smith-efficient (nor
Condorcet-efficient) — this is the shape a center squeeze leaves behind.
More: 07_Concepts/topics/smith_set.md
Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).
Run it yourself:
python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/favorite_betrayal_irv/cases/bv2227_3xgkck_honest_irv.yaml
See also¶
More cases in this set: bv2227_3xgkck_honest_star · bv2228_bgcmxx_betray_irv