3) — the compromise a majority prefers, squeezed out four ways¶

▶ Live on BetterVoting: vote · results ↗ (election pp2q4q, Test ID BV2170).

The textbook "two poles and a compromise" electorate: 100 voters, three candidates — Avery on the left, Blake on the right, and Casey the broadly-liked centrist. Both poles rank Casey second. It is the classic profile from the ranked-ballot literature (a Condorcet winner with almost no first-choice support), and it is perfectly symmetric between the two poles — which is what makes it such a sharp teaching case: the same 100 ballots elect Casey, one of the two poles, or nobody-in-particular, depending only on the counting method.

Casey is the Condorcet winner: a majority prefers Casey head-to-head over each rival (Casey beats Avery 53–47 and beats Blake 53–47). Yet Casey holds only 6 first-choice votes. The methods that look only at first choices — RCV-IRV and Choose-One — throw Casey out immediately, and because the electorate is a mirror image, the two poles then deadlock in an exact tie. The methods that look at the whole ballot — STAR and Ranked Robin — elect Casey.

The ballots¶

# voters	1st	2nd	3rd	reading
47	Avery	Casey	Blake	left pole, centrist second
47	Blake	Casey	Avery	right pole, centrist second
3	Casey	Avery	Blake	centrist, leans left
3	Casey	Blake	Avery	centrist, leans right

First choices: Avery 47, Blake 47, Casey 6. Pairwise: Casey 53–47 over each pole; Avery 50–50 Blake.

One electorate, four counts¶

Race (BV)	Method	Winner	Determinate?
Symmetric centrist — STAR	STAR	Casey	Yes (winner). Score round Casey 312 vs Avery/Blake 294; runoff Casey 53–47.
Symmetric centrist — Ranked Robin	RankedRobin (Copeland)	Casey	Yes. Casey 2–0, the Condorcet winner.
Symmetric centrist — RCV-IRV	IRV	tie 50–50	No — random. BV drew Blake; LH's seeded tiebreak lands on Avery.
Symmetric centrist — Choose-One	Plurality	tie 47–47	No — random. BV drew Blake.

STAR and Ranked Robin agree on Casey. IRV and Choose-One eliminate the centrist first and end in a genuine pole tie. On BetterVoting both ties resolved to Blake this run (frozen in the export), but they are true 50–50 / 47–47 coin flips: a re-tally could land on Avery. That non-determinism is not a defect of the example — the deadlock of the two poles, once the candidate a majority actually prefers has been squeezed out, is the whole lesson.

On freezability: STAR (Casey) and Ranked Robin (Casey) are deterministic and reproduce exactly in the LH engine. The IRV and Choose-One winners are random tiebreaks and are not freezable — the frozen export records this run's draw (Blake), while LH's IRV, which breaks the tie with its own stable seed rather than the published lot, records Avery. Same profile, same conclusion (a symmetric pole tie); only the coin lands differently.

LH engine reports (View 2)¶

STAR — Casey (the Condorcet winner)¶

[Divergence from STAR]
  STAR                   = Casey
  Choose-One (Plurality) = Blake   (differs from STAR)
  RCV-IRV                = Avery   (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/bv2170_pp2q4q_star_RCV-IRV_tabulated.txt

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

[STAR Voting]
 Tabulating 100 ballots.
Count × Avery,Blake,Casey
   47 ×     5,    1,    3
   47 ×     1,    5,    3
    3 ×     3,    1,    5
    3 ×     1,    3,    5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Casey         -- 312 -- First place
   Avery         -- 294 -- Tied for second place
   Blake         -- 294 -- Tied for second place
 Casey advances, but there's a two-way tie for second.

[STAR Voting: Scoring Round: First tiebreaker]
 The candidate preferred in the most head-to-head matchups advances.
   Avery         -- 50 -- Tied for second place
   Blake         -- 50 -- Tied for second place
   Equal Support --  0
 There's still a two-way tie for second.

[STAR Voting: Scoring Round: Second tiebreaker]
 The candidate with the most votes of score 5 advances.
   Avery         -- 47 -- Tied for second place
   Blake         -- 47 -- Tied for second place
 There's still a two-way tie for second.

*(Ties are resolved by choosing the tied candidate with the highest-priority official lot number.)*
    Lot-number priority order: ['Blake', 'Casey', 'Avery']

[Tiebreaker: Lot Number Priority]
  Tie among: ['Avery', 'Blake']
  Resolved: ['Blake'] (selected by lot-number priority).

[Lot-decided tie — rare]
  ⚠ The ballots did not break this tie: the deterministic rungs
    (pairwise / score, then five-star) all came back equal, so the
    pre-published LOT order chose among the tied candidates — the
    result here was set by lot, not by the votes. Usually the
    "dead rung": no tied candidate held a score-5 vote (five-star
    counts fives, not fours). Verify the tied candidates' 5-counts.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Casey         -- 53 -- First place
   Blake         -- 47
   Equal Support --  0
 Casey wins.
   Runoff math:
     100  ballots cast
   −   0  Equal Support (no preference between the two finalists)
     ───
     100  voters with a preference  (majority = 51)
           Casey 53 (53%)  ·  Blake 47 (47%)

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

Ranked Robin — Casey (2–0)¶

Round-Robin — every pair, head-to-head (For – Against):
   Casey  beats Avery   53 – 47
   Avery  ties  Blake   50 – 50
   Casey  beats Blake   53 – 47

Win–loss record — Copeland score = wins + ½·ties:
    #  Candidate  W–L–T  Copeland  Margin  Beats
    1  Casey      2–0–0         2     +12  Avery, Blake
    2  Avery      0–1–1       0.5      -6  —
    3  Blake      0–1–1       0.5      -6  —

Winner — Ranked Robin (RCV-RR): Casey
   beats every opponent head-to-head — the Condorcet winner.

RCV-IRV — the centrist eliminated, poles deadlock 50–50¶

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Avery             47  Hopeful
Blake             47  Hopeful
Casey              6  Rejected      <- Condorcet winner, fewest first choices

FINAL RESULT (Casey's 6 split 3/3 to the poles)
Avery             50  Elected   (LH seeded tiebreak)
Blake             50  Rejected

A genuine 50–50 tie. LH's IRV breaks it with a stable seed → Avery; BetterVoting broke it at random → Blake this run. Not freezable.

Choose-One (Plurality) — poles tie 47–47¶

   Avery         -- 47 -- Tied for first place
   Blake         -- 47 -- Tied for first place
   Casey         --  6
 There's a two-way tie for first.  (BV random draw → Blake; LH lot → Blake)

Files¶

Race	YAML	`_tabulated` mirror
STAR (lead)	page · bv2170_pp2q4q_star.yaml	txt
RCV-IRV	page · bv2170_pp2q4q_irv.yaml	txt
Ranked Robin	page · bv2170_pp2q4q_ranked_robin.yaml	txt
Choose-One	page · bv2170_pp2q4q_plurality.yaml	txt

Frozen BetterVoting export (Election + Ballots + Results): bv2170_pp2q4q_bv_export.json.

BetterVoting result screenshots (View 1) can be dropped into img/ as img/pp2q4q_<what>.png and linked here.