↩ SocioRhetoric · A New Catalogue of Speech Acts
sociorhetoric · a speech act
A lie only works while it's believed — and belief survives only while lies are rare. Assert what you take to be false, to mislead, and you spend something you did not make. The question is colder than morality: when do words stop carrying information at all, so that a channel of communication dies?
The striking thing about a lie is how much it still honours the truth. A liar does not walk away from the territory; he draws a careful map of it and then inverts one road. The referent still governs the act — you cannot lie about a thing without knowing what the honest claim would have been, and you cannot succeed unless your listener trusts the map enough to walk on it. The lie is parasitic, living on the credit of a mostly-honest channel: every believed lie is a small withdrawal from an account that only honest speech deposits into.
Which means the lie is self-limiting in a way a threat or an insult is not. Push the interests of speaker and listener apart, or push the sheer rate of lying up, and a rational receiver does the only sensible thing: he stops believing. The words do not become false — they become empty. Cheap-talk theorists call the empty state babbling: a channel on which the message and the world have gone statistically independent, so that hearing the message tells you nothing about the state. The instrument below is a real sender–receiver model. It lets you widen the interest gap until credible speech collapses to a single indistinct noise, and raise the lie rate until a listener's trust — and the information in every message — goes dark.
the honest instrument
Two coupled models, both computed live in your browser — no stored numbers. The first is a Crawford–Sobel cheap-talk game: as interest-bias grows, the states the sender can credibly distinguish coarsen until only one remains. The second is a Bayesian receiver who watches a sender lie and updates his trust. Drag anything; every count, bit, and trajectory recomputes from the equations.
The lie, as an information channel
alignment → credible talk · repeated deception → trust
A · alignment sets the ceiling — Crawford & Sobel
The world is a hidden state on [0,1], drawn uniformly. The sender's ideal action sits a distance b above the receiver's — that gap is interest-misalignment. In equilibrium the sender can only be believed when he groups states into intervals coarse enough that he doesn't want to lie about which interval he's in. Raise b and the credible partition coarsens; past b = 0.25 only one interval survives — babbling.
B · repeated trust — a Bayesian receiver
Now the sender lies at rate λ. The receiver doesn't know it; he entertains two hypotheses — a reliable source (lies ~5% of the time) versus an unreliable one (lies at rate λ₁) — and updates the odds after every caught lie or confirmed truth. Below a threshold lie-rate his trust climbs to certainty; above it, trust collapses to zero and each message stops moving his beliefs. A "boy who cried wolf" run, drawn from a fixed seed so it's reproducible.
the lie needs an honest channel
A lie is not the opposite of communication; it is a specialised use of it. To abandon the map entirely — to emit sounds with no relation to the world — is not lying but babbling, and it fools no one, because no one is listening for meaning in the first place. The liar needs the opposite condition: a listener who is reading the map as reliable, so that a single inverted road sends him confidently the wrong way. The whole efficacy of the act rests on the background assumption that assertions are, by default, true. In SocioRhetoric's terms the lie stays keyed to reality — it still points at the territory — while its motive turns manipulative: the effect depends on the inversion not being disclosed.
That dependency is also the trap. Every believed lie draws down a shared reserve — the base rate of honesty that makes any assertion worth attending to. One liar in a sea of honest speakers is nearly free; his lie is cheap precisely because it is rare. But the trick does not scale. As lies become common, listeners rationally discount, and the discount falls on every speaker, the honest included. The manipulator is thus in the position of a counterfeiter: profitable while notes are trusted, self-defeating the moment enough counterfeit circulates that people stop taking notes at all. Panel B makes this literal — watch the receiver's trust, and with it the information carried by each message, fall to nothing once the lie-rate crosses its threshold.
what to try
In Panel A, drag interest bias b from left to right. Watch the credible-message count fall — 8, 5, 3, 2 — and the partition strip coarsen into fewer, wider bands. Cross b = 0.25 and it snaps to a single band: mutual information hits exactly 0.00 bits. Even a perfectly honest sender can transmit nothing once his interests diverge far enough. Alignment, not virtue, sets the ceiling.
In Panel B, raise the lie-rate λ past the threshold marked on the chart (~0.26). The trust trajectory, which had been climbing toward 1, bends over and collapses toward 0. Push λ to 0.5 and trust is gone within a dozen rounds — the classic cried-wolf cliff. Note the readout: info per message falls from ~0.71 bits to ~0.03.
Hold λ fixed and instead lower prior trust τ₀, or raise bad-type rate λ₁ so the suspected liar looks more like a coin-flip. The receiver grows harder to convince and quicker to abandon. Manipulation is easiest against a trusting audience and self-defeating against a burned one — the reserve, once spent, does not refill on command.
alignment sets the ceiling on credible talk
Crawford and Sobel's 1982 result is the quiet counterweight to every theory of persuasion. It says that how much a speaker can credibly convey is fixed by the alignment of his interests with the listener's. Eloquence and honesty cannot overcome misaligned incentives. Their model is spare: the sender privately observes a state; he and the receiver both want the receiver's action to land somewhere, but the sender's preferred landing sits a fixed distance b above the receiver's. The sender speaks; the receiver acts. Because talk is cheap — free, unverifiable — the receiver believes a message only when the sender has no incentive to have said something else.
The consequence is that credible speech comes in intervals. The sender cannot reliably say "the state is 0.42"; if he could gain by nudging the receiver upward, he'd always claim a higher number, and the receiver, knowing this, would ignore him. What he can do is commit to coarse bins — "somewhere in the lower third" — bins wide enough that shading the truth within one isn't worth the risk of tipping into the next. As the bias b grows, those bins must grow wider to stay incentive-compatible, so their number falls. Panel A computes the finest equilibrium partition for each b exactly: the interval lengths form an arithmetic sequence rising by 4b, and the count drops step by step — until, past b = 1/4, no partition finer than a single interval survives. That terminal state is babbling: the sender still talks, the receiver still listens, and the mutual information between them is zero. This ceiling is reached by well-meaning speakers too. Divergent interests, not dishonesty, are enough to empty the words.
model
Panel A. The state is uniform on [0,1]; the sender's bias is b. A partition into N intervals is an equilibrium when each boundary type is indifferent between the two actions it could induce, which yields the recursion ai+1 = 2ai − ai−1 + 4b — interval lengths in arithmetic progression, each 4b longer than the last. Summing to 1 fixes the first length at (1 − 2b·N(N−1)) / N, which stays positive only while N(N−1) < 1/2b; the largest such N (capped by your state-granularity slider) is the credible-message count. The receiver's action in each interval is its midpoint, so his action is a deterministic function of which interval the state fell in, and the mutual information between state and action is just the entropy of the interval-length distribution, −Σ dᵢ log₂ dᵢ. Channel noise ε mixes each message into a uniform draw with probability ε; the readout then reports the true mutual information of that noisy channel, which falls to 0 as ε → 1.
Panel B. The receiver holds two hypotheses about the sender: reliable (lies at base rate 0.05) and unreliable (lies at rate λ₁). Starting from prior trust τ₀, he updates the log-odds after every observation by the Bayesian increment log[ P(obs | reliable) / P(obs | unreliable) ]. The sender in fact lies at rate λ, drawn round by round from a fixed-seed generator, so the plotted run is real and reproducible. Whether trust climbs or collapses is decided by the sign of the expected per-round increment, which flips at the threshold λ* = log[(1−l₀)/(1−l₁)] / ( log[(1−l₀)/(1−l₁)] − log[l₀/l₁] ) — about 0.258 for the default rates. The reported information per message is the trust-weighted channel capacity τ·(1−H(l₀)) + (1−τ)·(1−H(l₁)) in bits: roughly 0.71 when trust is intact, roughly 0.03 when it has collapsed. Treat all of this as a toy model — the mechanism is exact; the parameters are illustrative.
the act ↔ the model
| The act | The model |
|---|---|
| the state | what the speaker privately knows — the truth of the matter the words are about. |
| interest bias b | how far the speaker's preferred outcome diverges from the listener's; the misalignment the lie exploits. |
| a credible message | a distinction the listener will actually believe — a bin coarse enough that the speaker won't shade it. |
| babbling | words emptied of information: message and world gone independent, mutual information zero. |
| the trust posterior | how much a message still moves belief — the receiver's live credence that the source is reliable. |
| trust collapse | the channel's death: once trust hits zero, further messages carry ~0 bits and cannot revive it. |
how this act misfires
misfire · manipulation
The catalogue's named misfire for this act. Manipulation works by not being disclosed — but disclosure is exactly what repetition forces. Each believed lie erodes the base rate of honesty that made assertions worth trusting, so a channel of habitual liars carries nothing: the very trust the lie feeds on is the trust it consumes. The counterfeiter prospers only while the notes are scarce. Past the threshold in Panel B, the manipulator has spent his listeners' credence entirely, and now even his true statements move no one — the punishment for lying too often is that you can no longer be believed when it matters.
misfire · the model idealizes
Both panels assume a coldly rational Bayesian receiver with the sender's bias known and two neat hypotheses in hand. Actual listeners are nothing so tidy: they over-trust charismatic or in-group speakers long past the point the math would abandon them, and they under-trust — writing off honest sources on a single stumble. Motivated reasoning, sunk credence, and the sheer cost of re-checking all bend the real thresholds. So read the numbers as structure, not forecast: the direction of every effect (more bias → coarser talk; more lies → collapse) is robust; the exact crossover point is a property of this toy, not a measurement of any particular conversation.
A lie spends the trust that makes it legible; spend enough and the words go dark.
can you use it?
RECOGNITION — Which is the lie? A: a vendor who knows the shipment is late says “it shipped on time.” B: a vendor with no idea when it shipped says “it shipped on time.” C: a vendor who knows it is late says “logistics have been brutal industry-wide.”
A. A lie asserts what the speaker takes to be false, to mislead — the map is known and one road inverted. B never consults the map at all; C says something true to mislead, which is the palter's territory.
THE NEAREST NEIGHBOR — What single criterion separates a lie from babbling?
Dependence on the truth. The liar knows the honest claim and needs a listener who trusts the channel; babbling has gone statistically independent of the world, so it carries nothing and fools no one.
PRODUCTION — A colleague pads status reports about half the time. Using Panel B, predict what happens to his accurate warnings, then check.
λ ≈ 0.5 sits far above the ≈ 0.26 threshold: trust collapses, each message falls toward 0 bits, and his true warnings move no one. Yours works if the damage lands on the listener's discount — and on every future message.