BV2163 — Nurmi Example 16 (2 of 2): 17 voters rank ONLY their favorite — and do better

▶ Live on BetterVoting: vote · results ↗ (election 74j6vv).

The same election as BV2162 with one change, ceteris paribus: the 17 D>C>B>A voters truncate and rank only D. Result: RCV-IRV now elects B — whom those voters prefer to A, the winner their full rankings had produced. Ranking less of the ballot bought a better outcome: the Truncation paradox, live on BetterVoting.

Source

Dan S. Felsenthal, "Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected", University of Haifa / LSE, revised 26 May 2010; Appendix §A6, Example 16, due to Nurmi (1999: 63).

The one changed datum

No. of voters    BV2162 (full)         BV2163 (truncated)
     33          A > B > C > D         A > B > C > D
     29          B > A > C > D         B > A > C > D
     24          C > B > A > D         C > B > A > D
     17          D > C > B > A   →→→   D                (only the favorite)

D is eliminated first in both worlds — but here the 17 truncated ballots exhaust instead of transferring to C. So C (24) is eliminated instead of B, C's transfers flow to B, and B wins. The truncators' sincere ordering was D>C>B>A: they prefer B to A, so silence served them better than honesty — the Truncation paradox. (It also accidentally repairs BV2162's Condorcet failure: B, the pairwise champion, now wins the IRV race too.)

STAR (truncated ballots score only D: 329/373/244/171) and Ranked Robin (B still wins every head-to-head: 53–33 among voters with a preference, 62–24, 86–17) elect B in both worlds — pairwise and score counting give these 17 voters no truncation incentive; the elimination order is what their truncation exploits.

Agreement

Election	Race	BetterVoting	LH engine	Agree?
BV2162 full	RCV-IRV	A	A	✓
BV2163 truncated	RCV-IRV	B	B	✓
BV2162 / BV2163	STAR	B / B	B / B	✓
BV2162 / BV2163	Ranked Robin	B / B	B / B	✓

Files: star · irv · rr · frozen export · mirrors: star, irv, rr · Part 1: BV2162.