The Truncation paradox — when ranking less gets you more

The Truncation paradox (preference-truncation): a voter obtains a better outcome by ranking only some of the candidates than by revealing their full, sincere ordering. (A conditional paradox in Felsenthal's taxonomy: the one changed datum is how much of the ballot a group of voters fills in.)

→ Glossary: truncation · Felsenthal's taxonomy: README

The live demonstration (a pair of elections)

Nurmi's example (Felsenthal 2010, §A6, Example 16), run for real: BV2162 — 103 voters rank all four candidates and RCV-IRV elects A (missing the Condorcet winner B). BV2163 — the 17 D>C>B>A voters rank only D; their exhausted ballots change the elimination order and B wins, whom they prefer to A. Honesty cost them; silence paid.

The paradox strikes other counting families too, each through its own machinery: Borda — BV2160 (Fishburn's example), where truncating a rival denies them points (worked on paper; no Borda tabulator on BV/LH); successive elimination — Example 12's worked table; and it lurks in BV2159 (Brams' IRV sampler).

Where it comes from

Truncation is powerful wherever a ballot's lower ranks can hurt its upper ranks. Under RCV-IRV a lower preference becomes a live vote once transfers reach it — in BV2162 the 17 voters' second choice (C) soaked up their transfers and thereby shielded A from elimination-order justice; withholding it let C die early. Under Borda every listed rival collects points from your ballot, so leaving a strong rival unranked is a direct attack. Pairwise (Ranked Robin) and score (STAR) counting are far more truncation-resistant — on the Nurmi pair both elect B with full and truncated ballots — though no ranked method is perfectly immune in all profiles.

Why it matters

"Rank as many as you like — more information helps" is the standard advice on ranked ballots. A method where the strategically savvy shorten their ballots turns ballot completion into a sucker's move, and it biases outcomes toward factions with better strategic coordination. Note the practical on-screen report: real RCV-IRV elections show heavy truncation, and this paradox says some of it may be rational.