Topic: Participation (can showing up to vote ever hurt you?)¶
Topic hub — a cross-method view. The Participation criterion: adding sincere ballots that prefer X over Y must never change the winner from X to Y. A method that fails it has the no-show paradox — an electorate where some voters get a better result by staying home than by casting an honest ballot. Read forward, the same failure is the Twin paradox: new voters who agree with you exactly arrive, and your group's outcome gets worse.
The one idea to take away: "vote — it can only help your side" is a promise a voting method can keep or break. Pure score-summing methods keep it structurally; every method with an elimination or runoff stage — RCV-IRV, Coombs, plurality-runoff, and STAR — plus every Condorcet-consistent method (Moulin's theorem) can break it in some electorate. The differences are how often and how visibly.
The three-candidate exception. Moulin's theorem needs ≥ 4 candidates. Restricted to exactly three, Brandt, Dong & Peters (2024) prove there is a no-show-immune family of Condorcet extensions — the refinements of maximin (leximin, Nanson), and uniquely so among homogeneous rules. The escape hatch closes again at four candidates. See Condorcet-Consistent Choice Among Three Candidates.
The live demonstration — one electorate, told twice (BV2174 / BV2175)¶
The centerpiece pair: 8 voters who love April (sincere ranking April > Bruno > Celia) decide whether to show up. Same three candidates, same everyone-else, three races on each election — and the methods split:
| Method | 8 fans stay home (BV2174 ↗) | 8 fans vote (BV2175 ↗) | Showing up… |
|---|---|---|---|
| Choose-One | Celia | April | ✅ helped — last choice → favorite |
| STAR | Bruno | April | ✅ helped — favorite wins (more sincere support moved the result their way) |
| RCV-IRV | Bruno | Celia | ❌ HURT — 2nd choice replaced by LAST choice |
| Ranked Robin (LH) | Celia | April | ✅ helped (LH-only — see below) |
The IRV mechanism, in one sentence: the 8 extra April-first ballots keep April alive past round one, which gets Bruno — the 8 voters' own fallback — eliminated instead, and Bruno's transfers elect Celia, their last choice, 38–24. Their honest votes for their favorite bought their worst outcome; staying home (BV2174) keeps Bruno. Case pages with full engine reports: baseline · show-up.
Two footnotes on the pair, both deliberate:
- Both electorates are a Condorcet cycle (April > Bruno > Celia > April) — that's the soil no-show paradoxes grow in, and it's why there is no Ranked Robin race on BetterVoting: a Copeland three-way tie resolves by random draw there (not freezable), while the LH engine's margin tiebreak resolves it deterministically (Celia before, April after — see the
_tabulatedmirrors, and LH vs BV on RR ties). - BV2174's STAR count is a Runoff Reversal — Celia tops the scores 136/122/120, Bruno wins the runoff 34–20. One pair, two lessons.
Which methods can punish participation — and where each is treated¶
| Method | Participation? | Notes | Full treatment |
|---|---|---|---|
| Score / Approval | ✅ immune | a sincere added ballot only adds support where the voter intends — summation can't backfire | scoring methods vs ranked |
| Choose-One (Plurality) | ✅ immune | more votes for your favorite never hurts your favorite | plurality |
| STAR | ❌ rare | the runoff stage costs the formal guarantee — live flip: BV2165→BV2166 (Coombs Ex.19), shown honestly | STAR's honest limits |
| Ranked Robin / all Condorcet methods | ❌ provably | Moulin's theorem: Condorcet consistency ⇒ no-show paradoxes exist; see also Edelman's join-consistency argument | Edelman, tabulated |
| RCV-IRV / plurality-runoff / Coombs | ❌ readily | the elimination machinery — same root as non-monotonicity | no-show paradox |
The honest scorecard, spelled out: this page's live pair shows IRV failing while STAR passes — but on other electorates STAR fails too (BV2165/66: two abstainers do better under STAR's runoff as well as Coombs'). No elimination-or-runoff method — and no Condorcet method — carries a participation guarantee. The structural difference: STAR's failures need a finalist to flip and the runoff to reverse (rare, constructed), IRV's need only an elimination-order flip (the everyday center-squeeze machinery). Only pure summation (Score, Approval) and Choose-One are immune outright — and they pay for it elsewhere (what makes a good winner?).
The paradox catalog & the theory¶
- The No-Show paradox — when staying home beats voting (and its Twin) — the Felsenthal-taxonomy page: BV2150/51 (plurality-runoff, 11 voters) and the STAR flip BV2165/66.
- Edelman's "Myth of the Condorcet Winner," tabulated — Young's join-consistency theorem (two groups both choose C; combined they choose B) and why the no-show family is inherent to Condorcet consistency.
- Reading these fairly — the honest-limits framing: every method fails something; the question is which failures, how often, how visibly.
Glossary: no-show paradox.
This is a topic hub (cross-method index). The authoritative write-ups live in the per-method folders and the paradox catalog linked above. See the topics index for the other topic hubs.