Skip to content

The Fidelity Ladder — converting between scores and ranks

Every time you turn a score ballot into a ranked one (or vice versa), the conversion either drops information or invents it. This page ranks the common conversions by how much they fabricate — which turns out to explain why Ranked Robin is clean, why RCV-IRV is fragile, and why Borda is a leap.

→ Companions: scores vs. ranks · strict vs. weak ranks · Borda · Glossary: scores vs ranks

The one idea: scores contain ranks; ranks don't contain scores

A score ballot says how much you like each candidate — and that automatically contains the order. A ranked ballot says only the order — it never contained the intensities. So the two directions are not symmetric, and a conversion is only as honest as the amount it has to make up.

The ladder

# Conversion Used by Drops Invents
1 score → weak rank Ranked Robin intensity nothing — ties stay ties (A=B)
2 score → strict rank RCV-IRV (Hare) intensity a tie-break order (A=B forced to A>B)
3 rank → score Borda — the entire intensity (the spacing)

Read it top to bottom and the fabrication grows:

  • Rung 1 — score → weak rank (Ranked Robin). A score ballot A5 B3 C3 D0 becomes A > B=C > D. You lose the intensity, but the ties survive (B and C stay tied, because weak ranks allow it). Nothing is invented — RR's pairwise count reads exactly the equal- preference structure the voter gave. This is the honest reduction.
  • Rung 2 — score → strict rank (RCV-IRV). IRV needs a strict order and cannot represent a tie, so it must turn B=C into either B > C or C > B using an arbitrary rule (candidate priority / lot). That invented order is real input to the count — and it's exactly why an IRV result can be fragile: flip the tiebreak and the manufactured order flips, which can change who's eliminated.
  • Rung 3 — rank → score (Borda). Starting from a bare ranking A > B > C, there are no intensities to recover, so Borda invents all of them by assuming a spacing (even gaps: 2, 1, 0). It's a defensible convention, but it's pure fabrication of a dimension the ballot never had.

One ballot, all three conversions

Voter #1 from the random-sweep record 0, a score ballot A3 B3 C0 D2 E4 F3:

scores:                A3 B3 C0 D2 E4 F3

rung 1  (RR, weak):    E > A=B=F > D > C          ← ties kept; nothing invented
rung 2  (IRV, strict): E > A > B > F > D          ← A=B=F forced to A>B>F; C dropped (0=unranked)
rung 3  (Borda, if you ONLY had a ranking): assign 5,4,3,2,1,0 by position — invents the gaps

Same ballot; the more strictness or intensity the method demands, the more it has to make up.

Why this matters in practice

  • You can hand STAR scores to Ranked Robin or RCV-IRV (derive ranks) — but you cannot run STAR on ranked ballots, because there are no scores to add. The richer object only flows downhill.
  • RCV-IRV's fragility is rung 2 in action — the tie-break it's forced to invent. See center squeeze and the RR-vs-Condorcet side-by-side, which shows rung 1 and rung 2 on the same ballot.
  • STAR's ballot sits above the whole ladder — it carries the intensity natively, so it never has to drop or invent anything to be itself; it only converts downward when compared against ranked methods.