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PVSI — the Pivotal Voter Strategic Incentive

VSE asks "does this method pick a good winner?" PVSI asks the other half of the question: "does this method reward you for lying on your ballot?" It is VSE's companion metric, introduced in the same peer-reviewed paper, and it's the number behind claims like "in STAR, strategy is as likely to backfire as to work."

Level: 301 · deep dive Source: Wolk, Quinn & Ogren (2023) — peer-reviewed, open access, and claim-checked here (the authors are STAR advocates; lean disclosed).

The one-line definition

PVSI is the average gain a pivotal voter gets from voting strategically instead of honestly, expressed as a percentage of the utility gap between that voter's favorite and an average candidate.

PVSI Reading
~0% strategy essentially never pays — honesty is the safe default
negative strategy backfires more often than it works
high positive strategy is genuinely rewarded, so expect voters to use it
100% (the ceiling) a tactical vote would be guaranteed to swap an average winner for your favorite

The scale matters: Plurality's ~14% is not "14% of voters strategize" — it means the decisive voter's expected payoff from strategizing is 14% of the way from an average candidate to their favorite. That's a large, reliable incentive.

How it's measured — the pivotal-voter idea

Take a faction that would like to run a particular strategy. Order its members by who stands to gain most, then flip them to the strategic ballot one at a time until the outcome actually changes. The voter who tips it is the pivotal voter, and PVSI measures the utility change from their perspective. Simulation runs where the outcome never changes count as zero.

Formally, averaged over many simulated elections:

PVSI = ( U(strategic winner) − U(honest winner) ) ÷ ( U(favorite) − U(average candidate) )

evaluated for the pivotal voter. A "random faction" is defined by picking two candidates at random and taking the voters who prefer the first.

Why pivotal? Because strategy only matters when it changes something. The overwhelming majority of strategic ballots change no outcome at all; averaging over those would drown the signal. Isolating the decisive voter measures the incentive a voter actually faces when their vote can matter — which is exactly the moment strategy is tempting.

The strategies tested

Strategy What the voter does
Favorite Betrayal rate the allied frontrunner above your true favorite
Burial rate the enemy frontrunner below candidates you actually like less
Bullet voting support only your favorite, nobody else
Inclusive / Exclusive (Approval) lower or raise your approval threshold
Polarized Inclusive / Exclusive (STAR) score every candidate either 5 or 0
Honest Inflation / Deflation (STAR) exaggerate — 5, 4, 1, 0 — to boost an ally or block an enemy, keeping your honest order

What the numbers say

Most-incentivized strategy per method, on the paper's clustered-spatial model (6 candidates):

Method PVSI The strategy that pays
Plurality ~14% Favorite Betrayal — "vote for the lesser of two evils"
Approval ~10% set your threshold between the two frontrunners (Exclusive 10.1%; FB 9.8%)
RCV-IRV ~3% Favorite Betrayal — a positive incentive here means ranking your favorite first can backfire
Approval Top Two ~3% threshold-setting, much damped by the runoff
STAR ~2% exaggerate your scores while keeping honest preference order
Smith/Minimax disincentivized across the board —

Two findings do more work than the individual numbers:

  1. In STAR, Approval Top Two and Smith/Minimax, every strategy that gives less than full support to your favorite is disincentivized. That is the measurable version of "vote your conscience": favorite betrayal, burial and bullet voting are all strongly disincentivized in STAR.
  2. STAR's only surviving incentive is honesty-preserving. The ~2% rewards exaggerating magnitudes (5s and 0s rather than 4s and 1s), not reordering your preferences. Your honest ranking still decides the runoff — so the residual strategy doesn't corrupt the information the method relies on.

Note the direction of the IRV result: because IRV's most-rewarded strategy is favorite betrayal, the method that's marketed as letting you "vote your heart" measurably rewards not doing so. See favorite betrayal and center squeeze for the mechanism.

How PVSI relates to VSE

They measure different axes, and a method can do well on one and badly on the other:

  • VSE — accuracy: how good is the winner, in voter-satisfaction terms?
  • PVSI — incentive: how much pressure is there to misrepresent your preferences?

VSE also degrades because of strategy, so the two interact: a method with a high PVSI will tend to see more strategic ballots, which feeds back into a worse real-world VSE. That coupling is the paper's core argument for judging methods on both at once rather than on a pass/fail checklist.

The "backfire ratio" chart — get the attribution right

The widely-shared figures STAR 1:1 · Approval 2.6:1 · RCV-IRV 2.7:1 · Plurality 17.8:1 are a works : backfires restatement produced by the Equal Vote Coalition from the VSE simulator — not numbers printed in the paper. The paper reports PVSI percentages (the table above). Same underlying simulation, two presentations: cite the ratios to the infographic and the percentages to the journal article. (A 1:1 ratio and a ~2% PVSI are saying the same thing about STAR from different angles: strategy is roughly a coin flip, so it isn't worth running.)

Run the cousin in this library

fbc_simulation.py computes a works : backfires ratio by exhaustive ballot search — every possible betrayal ballot for every voter. That is a different and broader measurement than PVSI's realistic strategic-faction model, so the magnitudes are not directly comparable; only the direction (STAR less rewardingly manipulable than IRV, and both far less than Plurality) is shared. It's a useful independent sanity check precisely because it's built differently.

The honest limits

  • Model-dependent. The headline figures come from one clustered-spatial electorate model; Appendix B checks robustness across parameters, and the ordering holds up better than the exact values. Never quote a PVSI without its model — the standing rule for every simulated number here (election simulation models, the spatial model).
  • It assumes decent polling. Every viability-aware strategy depends on knowing who the frontrunners are. Real polls carry error (the paper models 5% noise); worse information makes strategy riskier than PVSI suggests.
  • A live running tally is a perfect poll — and that cuts the other way. The measured figures assume noisy pre-election polling. Show voters the tally as they vote and you have removed the uncertainty that makes strategy risky, so the real incentive rises above the number in the table. Add the ability to change a ballot before close and it rises further: a faction can watch, see its candidate trailing, and switch together in the final minutes. The published incentives are therefore a floor for a zero-information election, not a constant — which is why running a serious election with live results and editable ballots quietly forfeits much of the strategy resistance the method was chosen for. (Both settings are common on online platforms; see BetterVoting's own warning.)
  • It's a marginal measure, not a coordination cost. PVSI describes the single decisive voter, and deliberately says nothing about how hard it is to organize a whole faction to strategize in unison — which in practice is the bigger barrier.
  • Low is the goal; zero is impossible. Gibbard–Satterthwaite guarantees every method with 3+ candidates is manipulable, so STAR's ~2% is small, not nil — see STAR's honest limits.
  • Advocate-authored. The metric is sound and the code is published, but it was introduced by STAR proponents; on their own data a Condorcet method (Smith/Minimax) beats STAR on this very metric — which the claim-check reports rather than buries.