Downward monotonicity (San Francisco D7 2020) — BEFORE: Melgar wins¶

Generated from sf_d7_downward_before.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: Melgar

Scenario¶

The real 2020 San Francisco Board of Supervisors election, District 7 (seven candidates), reduced to the final three after four candidates are eliminated and their votes transferred — the preference profile from Graham-Squire & McCune, arXiv:2301.12075, Table 2. Counted by RCV-IRV: Engardio leads Round 1 with 14119 first-choices to Melgar's 11652 and Nguyen's 10855. Nguyen is eliminated; his ballots transfer and Melgar wins the final 18561-16370. This is the BEFORE half of a DOWNWARD-monotonicity pair — Engardio LOSES here. In the AFTER file (sf_d7_downward_after), 800 Engardio>Nguyen>Melgar ballots are shifted DOWN to Nguyen>Engardio>Melgar — giving the loser Engardio LESS first-place support — and Engardio then WINS. Ranking a loser lower makes them win: the downward monotonicity paradox. Companion page: downward_monotonicity_sf.md. Model note: the Round-1 three-way counts (14119 / 11652 / 10855) and the final (Melgar 18561, Engardio 16370) reproduce the paper's published figures exactly; Melgar's own second-preference split (not published in the quoted table) is reconstructed to complete the three-way, chosen consistent with the paper's stated AFTER outcome (Engardio wins once Melgar is eliminated).

Ballots¶

Each row is one voter's ranking, most-preferred first (N: prefix = N identical ballots).

13319:Engardio>Melgar>Nguyen
800:Engardio>Nguyen>Melgar
2500:Melgar>Engardio>Nguyen
3500:Melgar>Nguyen>Engardio
5652:Melgar
6909:Nguyen>Melgar>Engardio
2251:Nguyen>Engardio>Melgar
1695:Nguyen

What the engine says¶

Round-by-round Sankey diagram: each candidate's votes as a band, and where the votes of an eliminated candidate transferred to.

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) ---
  Downward monotonicity (San Francisco D7 2020) — BEFORE: Melgar wins
 Tabulating 36626 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Engardio       14119  Hopeful
Melgar         11652  Hopeful
Nguyen         10855  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Melgar         18561  Elected
Engardio       16370  Rejected
Nguyen             0  Rejected
Blank Votes     1695  Rejected


Winner(s) — RCV / Instant-Runoff Voting (single winner)
  Melgar

--- 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 — 36626 of 36626 ballots still active; majority = 18314
   Nguyen eliminated with 10855:
      → Melgar                 6909
      → Engardio               2251
      → (no continuing ranking)   1695  ← these ballots go inactive

FINAL ROUND — 34931 of 36626 ballots still active (1695 inactive); majority = 17466
   Melgar                18561  (53.1% of the still-active)  ← elected
   Engardio              16370  (46.9% of the still-active)
   Never exhausted, never transferred:
      16370 ballots held by Engardio carried a lower ranking that was never read
      (the count stopped here, so those preferences did nothing).

Inactive ballots at the final round: 1695 of 36626 (4.6%).
   Melgar's 18561 is a majority of the 34931 still active AND of all 36626 cast (50.7%).

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): Melgar
   Outside (2):        Engardio, Nguyen
   One member ⇒ Melgar is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Melgar is INSIDE the Smith set. ✓
      Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
   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/monotonicity/cases/sf_d7_downward_before.yaml

Downward monotonicity (San Francisco D7 2020) — BEFORE: Melgar wins¶

Scenario¶

Ballots¶

What the engine says¶

Full audit — preference matrix, Condorcet, and score distribution¶

See also¶