Skip to content

"One person, one vote" — the legal principle, and the reformer's stronger claim

Two different ideas wear the same four words, and conflating them causes half the arguments about voting methods. One is settled constitutional law; the other is a method-design criterion. This page keeps them apart — because "RCV upholds one person, one vote" and "RCV fails the equal vote" can both be true, and are.

→ Companions: The Equally Weighted Vote (Test of Balance) · RCV-IRV fails the Equal Vote · exhausted ballots. Glossary: equally weighted vote.

"One person, one vote" is a constitutional apportionment rule from the 1960s reapportionment cases. The Supreme Court coined the phrase in Gray v. Sanders (1963) and applied it in Wesberry v. Sanders (1964, congressional districts) and Reynolds v. Sims (1964, state legislatures): the weight of each citizen's vote must, as nearly as practicable, be equal — no one's vote may be diluted by living in an over-populated district.

Crucially, this is about districting and vote-counting equality, not about which tabulation method you use. A method satisfies it when every voter casts one ballot and every ballot is counted on equal terms. By that bar, Choose-One, RCV-IRV, and STAR all pass — and courts have specifically upheld RCV-IRV against one-person-one-vote challenges (the "exhausted ballots disenfranchise voters" argument has lost in court). So if the question is "is this voting method legal / constitutional?", the answer for all of them is yes.

Sense 2 — the reformer's "equally weighted vote" (a stronger, different bar)

Voting-reform advocates — especially the Equal Vote Coalition — use the same phrase for a stronger, mathematical idea: the Equal Vote / cancellation criterion, the "Test of Balance." It asks: for any ballot one voter casts, can another voter cast an exact-opposite ballot so the two together change nothing? If yes, no voter's ballot can outweigh another's.

This is a property of the tabulation, not a legal standard — and the methods split on it:

Legal OPOV (Sense 1) Test of Balance (Sense 2)
Choose-One (Plurality) ✅ passes ❌ fails (a mark can only add, never cancel)
RCV-IRV ✅ passes ❌ fails (opposite ballots don't cancel under sequential elimination)
Ranked Robin (Condorcet) ✅ passes ✅ passes (opposites cancel in the pairwise matrix)
Score / STAR / Approval ✅ passes ✅ passes (opposite scores cancel in the sum)

Note what that table shows: the balance failure is not "ranked ballots are worse than scored ones" — Ranked Robin is ranked and passes. It's specific to methods whose count is a sequential elimination (or a single mark), where only the top of each ballot drives the result. See the worked, runnable example: balanced ballots flip the RCV-IRV winner.

Why the two get tangled — and how to keep them straight

The confusion runs both directions:

  • Reform critics hear that RCV-IRV "fails one person, one vote" and picture illegal — some voters literally getting extra ballots. That's not the claim; RCV-IRV is legal and every voter casts one ballot. The reformer claim is about whose later preferences get counted once elimination starts — a design shortfall, not a legal one.
  • Reform defenders (e.g. FairVote's essay, "Enhancing Voter Equality") answer the legal charge — and win it — but that defends RCV-IRV against Choose-One, not against the Test of Balance. Both can be true at once: RCV-IRV upholds the constitutional standard and fails the balance criterion.

The honest caveats (stated out loud)

  • The balance criterion isn't neutral. It's promoted mainly by cardinal-method advocates, and cardinal methods pass it essentially by construction; even its formalizer notes it may not fully capture the informal intent. So "RCV-IRV fails our criterion" carries method-favoring flavor — it's largely the spoiler / center-squeeze critique in equal-vote language, not a wholly separate defect. (Ranked Robin passing it is the reminder that it isn't a scores-only trophy.)
  • The legal principle is genuinely settled and shouldn't be waved away either. "One person, one vote" as the courts mean it is a real, hard-won standard; every reform on this site clears it.

So the precise sentence is: all these methods give one person one vote in the legal sense; they differ on whether every voter's vote carries equal weight through the count, which is the reformers' bar — and there, Choose-One and RCV-IRV fall short while Score, STAR, Approval, and Ranked Robin hold up.

A third sense, from the theory side — and it explains the 0–5 cap

There's a version of this principle that neither sense above quite reaches, and it answers a question score-ballot skeptics ask fairly: why cap the ballot at 5? Why not let a voter who really cares say 100?

Because the theory says a cap and equal weight are the same thing. In the distortion literature, results are proved under unit-sum normalization — every voter's utilities sum to the same total (on a 0–5 ballot: everyone gets the same amount of ink). Procaccia & Rosenschein's Proposition 3 proves that model equivalent to one where utilities are unconstrained but each voter is weighted by their own total. The two are interchangeable, which means the converse is exact: an uncapped ballot is a weighted vote, and a voter's weight is whatever they claim to feel. Drop the constraint and the worst-case loss is unbounded at three voters.

That's the equally weighted vote argument arriving from computational social choice rather than from reform advocacy — worth having, since Sense 2's provenance is the caveat above. It also marks the limit of the analogy honestly: this is a statement about utility scales, not about districting or ballot counting, so it settles neither of the two senses above. It settles the design question they don't reach.

Sources