The 50 percent cliff

Four comparative-fault rules, one comparison operator between two of them, and a $50,000 discontinuity at a single point. Worked on a $100,000 award. 9 August 2026.

When a plaintiff is partly at fault for their own injury, the damages award gets reduced. Every US negligence system agrees on that much and then diverges, and the divergence is not a matter of degree — it is a matter of where, and whether, the recovery function has a discontinuity in it. This note works the four rules out arithmetically on a single $100,000 award, locates the cliffs, and shows what they do to the value of a claim before the fault share is known, which is the state anyone actually makes decisions in.

Nothing here is a statement about which jurisdiction applies which rule. That is a question about current statute and case law in a specific state, it changes, and it is not something arithmetic can answer. This is the mechanics only.

The four rules

Write the plaintiff's fault share as f and the gross award as G.

Pure comparative       net = G * (1 - f)                     always
Modified, 50% bar      net = G * (1 - f)  if f <  0.50, else 0
Modified, 51% bar      net = G * (1 - f)  if f <= 0.50, else 0
Contributory           net = G            if f == 0,    else 0

The two modified rules differ by a single character: < against <=. Their conventional names describe the bar from the other side — under the 50% rule you are barred at 50% or more, under the 51% rule you are barred only once you exceed 50%, which is to say at 51% and above when fault is found in whole percentage points. Both descriptions name the same operator.

The implementation above was checked against all 28 worked rows of the source dataset before anything below was computed; every row agrees exactly.

The grid

Net recovery on a $100,000 gross award:

Three shapes are visible. Pure comparative is a straight line from G to zero — continuous everywhere, no cliff, and a plaintiff 99% at fault still recovers 1%. The two modified rules follow that line and then fall off it. Contributory is not really a reduction rule at all: it is a switch, and it is off everywhere except at exactly zero fault.

Where the cliffs are

The interesting region is one point wide. Here is the same table at 49.99%, 50% and 50.01%:

At exactly 50%, the two modified rules return $0 and $50,000 for identical facts. Both cliffs are the same height — the limit of G * (1 - f) as f approaches one half, which is $50,000, half the award — and the two rules disagree about exactly one point: whether the midpoint itself sits on the paying side or the barred side. Everywhere else they are the same function.

Put the marginal cost of fault next to it. Under a continuous rule, one basis point of additional fault costs one basis point of the award. At the bar, it costs everything still on the table:

The second column is the same for every rule by construction, since all four share the same linear term; the third is the largest single step anywhere on a 0.01% grid. Under contributory the worst step is at the very first increment of fault above zero and costs the entire award, which is why the rule is usually described as harsh rather than as a reduction at all. Under the modified rules the worst step is at the bar and costs about half the award, because the plaintiff loses in one step the whole of what the linear reduction had left them.

Why the discontinuity is the whole story

A fault share is not an input. It is a finding, made after the fact, by a jury or an adjuster, out of the same evidence that could have supported a somewhat different number. Nobody deciding whether to accept an offer knows f; they know roughly where it will land.

So model it that way. Take the fault finding as uniform over a band and compute the expected recovery — the honest value of the claim at the moment of deciding:

Read the middle row. A claim whose fault finding is somewhere in the 45–55% band is worth $50,000 under pure comparative and $26,250 under either modified rule — 52% of it, because half the distribution lands past the bar and pays nothing. The expected value has fallen by far more than the expected fault share has moved. That is the practical content of the discontinuity: near the bar, the value of a claim is dominated not by how much fault is found but by which side of one number it falls on.

Note also what the two modified columns do here: nothing. They are identical in every band, exactly, because they differ on a single point and a single point has no probability. The operator that is worth $50,000 in the knife-edge case is worth precisely zero in expectation. That is a fair description of most threshold litigation — the rule that looks decisive on paper matters only in the case where the finding lands exactly on the line, and it is the distance to the line, not the rule's tie-breaking convention, that carries the value.

Two consequences follow, and they are the reason the arithmetic is worth doing explicitly rather than intuiting.

• Variance stops being neutral. Away from the bar, an uncertain fault finding is roughly as likely to help as to hurt and the expectation tracks the midpoint. Near the bar it does not: the downside is truncated at zero and the upside is capped by the linear rule, so uncertainty is pure loss. Two claims with the same expected fault share can be worth materially different amounts if one of them has a wider band.
• Small factual disputes carry disproportionate weight. An argument that moves the likely finding from 52% to 48% is worth a few thousand dollars of linear reduction and the entire remainder of the claim on top. The same argument moving 32% to 28% is worth only the few thousand. Identical movement, different value, purely because of position relative to the bar.

The general point about threshold rules

Any rule of the form continuous below a threshold, zero above it behaves this way, and legal thresholds are far from the only place it shows up: benefit cliffs in means testing, tax bracket edges with non-marginal effects, coverage limits, eligibility scores. The arithmetic below the threshold is easy and reassuring, so attention goes there, and the entire behaviour of the system lives in a neighbourhood of one point that the smooth formula never mentions. When you build a calculator over a rule like this, the single most useful thing it can do is not produce a point estimate. It is to show the user where the cliff is relative to where they think they are standing.

That is the design principle behind the settlement estimator I work on at worthmyclaim.com, which shows a range and the arithmetic that produced it rather than a single confident figure.