Coombs Ex.20 — District II: 7 voters, B wins outright¶

Generated from coombs_ex20_district2.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: B

Scenario¶

District II of Felsenthal's Coombs reinforcement example. Source: Dan S. Felsenthal (2010), Appendix A7, Example 20. Seven voters, three candidates: 1×(A>B>C), 6×(B>A>C). B is ranked first by 6 of 7 — an absolute majority on the first count — so Coombs elects B immediately and never reaches its deletion step. No paradox here; this is the second clean district whose combination with the first produces one. The source prints this district as "6 voters" while listing 7, and its amalgamated table sums to 41, which only works with 7. We take the tables as authoritative and flag the typo rather than quietly choosing. District I (coombs_ex20_district1.yaml) also elects B. Together they elect A (coombs_ex20_amalgamated.yaml) — the reinforcement paradox. Labels are Felsenthal's own A/B/C so the case can be read side by side with the paper's table. Tabulated as RCV-IRV, the mirror-image count Coombs inverts; with a first-round majority both methods elect B by the same step. For the Coombs count run tools_adam/pref_voting_tabulation_engine/coombs_report.py.

Ballots¶

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

1:A>B>C
6:B>A>C

What the engine says¶

The count, step by step — the rounds and how the winner is reached:

--- RCV / Instant-Runoff Voting (single winner) ---
  Coombs Ex.20 — District II: 7 voters, B wins outright
 Tabulating 7 ballots (ranked ballots).

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
B                  6  Elected
A                  1  Rejected
C                  0  Rejected


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

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): B
   Outside (2):        A, C
   One member ⇒ B is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner B 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/felsenthal_paradoxes/cases/coombs_ex20_district2.yaml

See also¶

Glossary · all cases by method