Successive elimination Ex.9 — two D voters stay home and get a better result¶

Generated from succ_elim_ex9_noshow.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: Ranked Robin (RCV-RR / Copeland) · 1 seat · Expected winner: A

Scenario¶

The no-show variant of Felsenthal's Example 9. Source: Dan S. Felsenthal (2010), Appendix A4, Example 9 — see succ_elim_ex9_pareto.yaml for the full 11-voter profile and the other three paradoxes it carries. The same electorate with two of the five D>A>B>C voters ABSENT: 9 voters. Their absence breaks the cycle, A becomes the Condorcet winner outright, and the procedure elects A from any agenda whatever — under D vs A, winner vs C, winner vs B the rounds run A beats D 5:4, A beats C 6:3, A beats B 9:0. With all 11 present the same agenda elects B. Both absent voters rank A second and B third, so staying home got them a strictly better outcome than voting did: the no-show paradox. Nothing about anyone's preferences changed — only the turnout. Note what makes this readable: once two D ballots are gone the profile has a Condorcet winner, and successive elimination is Condorcet-consistent, so the agenda stops mattering. All of Example 9's pathology lives in the cycle. Labels are Felsenthal's own, capitalized, so the case can be read beside the paper's table. Tabulated as Ranked Robin for the pairwise matrix the agenda consumes pair by pair; Ranked Robin also elects A, as any Condorcet method must here. Run the procedure with tools_adam/pref_voting_tabulation_engine/successive_elimination_report.py.

Ballots¶

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

3:A>B>C>D
2:C>A>B>D
1:C>D>A>B
3:D>A>B>C

What the engine says¶

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

--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 9 ballots (ranked ballots).

Ballots:
     3 × A > B > C > D
     2 × C > A > B > D
     1 × C > D > A > B
     3 × D > A > B > C

Round-Robin — every pair, head-to-head (For – Against):
   A  beats B   9 – 0
   A  beats C   6 – 3
   A  beats D   5 – 4
   B  beats C   6 – 3
   B  beats D   5 – 4
   C  beats D   6 – 3

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
      |     A     |    B     |    C     |    D     |
----------------------------------------------------
  A > |    ---    |9 - 0 - 0 |6 - 0 - 3 |5 - 0 - 4 |
  B > | 0 - 0 - 9 |   ---    |6 - 0 - 3 |5 - 0 - 4 |
  C > | 3 - 0 - 6 |3 - 0 - 6 |   ---    |6 - 0 - 3 |
  D > | 4 - 0 - 5 |4 - 0 - 5 |3 - 0 - 6 |   ---    |

Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by total margin, then lot order):
    #  Candidate  W–L–T  Copeland  Margin  Beats
    1  A          3–0–0         3     +13  B, C, D
    2  B          2–1–0         2      -5  C, D
    3  C          1–2–0         1      -3  D
    4  D          0–3–0         0      -5  —

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

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 4): A
   Outside (3):        B, C, D
   One member ⇒ A is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner A is INSIDE the Smith set. ✓
      Guaranteed: Ranked Robin (Copeland) is Smith-efficient — every member of
      the set outscores every outsider, so the top of the win–loss table is
      always inside the set, however the tie among them is then broken.
   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/succ_elim_ex9_noshow.yaml

Successive elimination Ex.9 — two D voters stay home and get a better result¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶