The rule, exactly. Before an election each citizen chooses: to vote — or to take a payment and not vote in that election. The payment is a percentage of the median income, set by referendum; there is no fixed sum. One ballot is one vote, with no multiplier in the count; the vote is amplified only in that each ballot's share grows as others step out. The budget pays under law; a candidate never pays. Only a referendum of all citizens — simple majority, no quorum — introduces, changes or repeals the rule.
The protocol has been introduced nowhere and no pilot has been run: shares, turnout and outcome figures in the chapters are estimates, and the protocol promises nobody an election victory. If a chapter says otherwise, Exact Answers and the Charter are correct. For a candidate: ten questions and ten steps. For a citizen, a mayor, a finance officer, a donor, a journalist, a scholar, a lawyer: answers by role. Everything in force in one file: llms-full.txt.
Elections as a Measuring Instrument: Comparing "Before" and "After" by Bayes¶
Chapter: 03 — Theoretical Foundations (paired with §13) File: 03_013d · v1 · 19 September 2026 Source: the architect's question "can Bayesian mathematics be applied to AB-EXIT as an analysis or a proof, if one compares current elections with those after AB-EXIT"; his demand to name percentages and to find experiments in which one and the same action is compared free and at a price; two natural experiments (Peru, Switzerland).
1. An analysis, not a proof¶
Bayes' formula describes one thing: how to recompute confidence when new evidence arrives. It does not produce truth out of nothing: with arbitrary starting numbers the conclusion is just as arbitrary, only it looks scientific. So there is no "Bayesian proof of AB-EXIT", and announcing one would be exposing oneself. As an analysis, however, it gives what an argument in words does not: it reduces the whole question to one quantity and shows exactly what must be measured.
2. One quantity¶
An election result is evidence about the quality of the winner. The strength of the evidence is measured by the likelihood ratio:
LR = the probability of winning if the candidate is a good manager, divided by the probability of winning if he is a bad one.
At LR = 1 the result says nothing about quality: it is a lottery. At LR above one, winning is evidence of quality. At LR below one the system selects the worst.
Today. Winning depends on mobilising the indifferent, on name recognition, flattery and handouts (040c.3b) — on things barely connected with the ability to govern. There is independent confirmation that LR today is close to one: serious scholars propose replacing elections with a lottery and expect an improvement (015b.6b). A lottery is LR of exactly 1; if an improvement is expected from it, the present selection is no higher. The reason is that votes are not independent. Condorcet's theorem — "many voters yield a wise decision" — holds for independent judgments; a million and a half people led by one television and one handout are not a million and a half measurements but a few.
After the protocol. Those leave for whom the vote is worth less than the sum. Two things change at once: the average accuracy of the signal among those who stay, and the dependence between votes. That there are fewer voters matters little for Condorcet: six hundred thousand independent judgments with a weak signal tell candidates apart better than a million and a half dependent ones with none.
3. Accumulation over cycles¶
Posterior odds equal prior odds multiplied by LR for each cycle, and this compounds.
| LR per cycle | Shift in odds after 1 cycle | after 3 | after 5 |
|---|---|---|---|
| 1.0 (a lottery) | ×1 | ×1 | ×1 |
| 1.3 | ×1.3 | ×2.2 | ×3.7 |
| 1.5 | ×1.5 | ×3.4 | ×7.6 |
| 2.0 | ×2 | ×8 | ×32 |
The LR values in the table are an illustration, not a measurement. The table shows the mechanics: even a weak signal gives a manifold shift in the composition of government over a few cycles. This is another reading of "x10": not a leap within a year but the accumulation of selection. The fast effect comes from subtraction (019c.6b), the slow one from the change of selection.
4. The assumption and its test: the same action free and at a price¶
Everything rests on one assumption: those who stay choose at least a little more accurately than those who leave. The weak spot is named in 015c: refusing the money speaks of motivation, not competence. The architect proposed a way to test it: find cases where one and the same action — voting — is performed free and at a price, and see who is screened out. Such cases exist, and they have been measured.
| Peru, the 2010 election | Switzerland, 26 cantons | |
|---|---|---|
| What was changed | A random part of voters were told of a reduction in the fine for not voting — skipping became "cheaper" | Postal voting was introduced — taking part became cheaper |
| What happened to turnout | A 50 % cut in the fine — turnout −2.6 pp; 75 % — −5.3 pp | Turnout +5 pp |
| Who was screened out or came in | Those who left were in the centre of the political spectrum, less informed, and themselves valued their vote less | Those who came were less educated and knew the ballot propositions less well: the average education and knowledge of those voting fell |
| What else | Aggregate preferences for specific policies did not change; vote buying became rarer and the price of a vote higher | Welfare spending and business taxes fell |
The two experiments look at the same thing from two sides and give a consistent answer: when participation becomes dearer, the less informed leave first; when it becomes cheaper, it is they who come. The price of participation works as a filter on informedness, and this is not theory but measurement. The Peruvian experiment incidentally confirms 019d: as participation becomes dearer, vote buying thins out and the vote becomes dearer.
Outside elections the picture is less clear-cut, and this is worth saying. In an experiment in Zambia a higher price for a water purifier screened out those who used it less; in an experiment in Kenya with anti-malarial bed nets those who paid used them no more often than those who got them free, and demand fell sharply with price (both results from the assistant's memory, unchecked). A price does not always select "the best users". For voting, however, both direct experiments give the same sign.
5. Percentages¶
The architect rightly remarked that the assistant "as always slipped away from percentages". The assistant's estimates, subjective, with what shifted them:
| Statement | Before the two experiments | After |
|---|---|---|
| Those who stay choose more accurately than those who leave (LR after the protocol is above one) | about 60 % | 80–85 % |
| LR per cycle is at least 1.3 | about 35 % | about 50 % |
| Those who stay choose worse (LR below one) | about 20 % | about 10 % |
Why not higher than 85 %. First: the experiments changed the price of participation by a small amount, whereas D is half a minimum pension; at such a price the screening runs not only on informedness but on income, and an informed poor person leaves too. Second: "informed" does not mean "chooses the best manager" — an informed voter may choose in the interests of his own group. Third: a motivated voter may be ideologically blinded. These three objections make up the remaining 15–20 %, and each can be tested: by a survey with a real stake (who takes the money and how accurately he judges the government's results) and then by a pilot.
A fourth objection, separate from the first three: who leaves — the centre or the edges. The architect expects the protocol to remove two-party enmity: the politics of outrage feeds on the indifferent, and they leave with the sum. But the Peruvian experiment of §4 also showed the reverse: when participation becomes dearer, those who leave first are people from the centre of the political spectrum — those without strong convictions — while committed supporters value the vote more and stay. Then the electorate that remains may turn out not calmer but sharper. A familiar analogue is low-turnout party primaries, which are commonly thought to draw the most ideological; direct studies, however, do not confirm this: primary voters turned out no more extreme than other supporters of their party, and primary turnout is not associated with the extremism of the winners. Two arguments from 013e also work in the architect's favour: one who has paid for a vote cheers less and calculates more, and those who stay are more often people with their own money at stake. The assistant's estimate: the probability that the first cycle yields a more polarised body of voters is about 35 %; that from the second or third cycle polarisation falls below today's — about 55 %. It can be tested cheaply and before a pilot: by a survey with a real stake — who refuses the sum, committed supporters or pragmatists.
6. The base rate: why a person must not be checked¶
The same formula closes the question analysed in 019d.4b. Suppose one in fifty of those who refused the sum is a recruit, and the marker "poor and refused" correctly points to a recruit in 90 % of cases and falsely fires on 10 % of non-recruits. Then of a hundred people with the marker about fifteen are recruits and eighty-five are not: checking by the marker hits mainly the innocent. This is the base-rate fallacy, and it makes the rule "an anomaly at a polling station, not suspicion of a person" not only a principle of the protocol but arithmetic. At the level of a polling station the same formula works in favour of a check: a hundred and twenty refusals where twenty were expected leave almost no room for chance.
6b. An analysis of an external text, "The Bayesian Proof of AB-EXIT"¶
The architect brought for checking a text by another model with a ready-made investor slide, "The Bayesian Proof of AB-EXIT". It makes three claims; each has a true core and an overreach that a statistician in the room will spot within a minute.
| The text's claim | The true core | Where it overreaches |
|---|---|---|
| Traditional elections are "mathematically incapable of generating trust": the evidence (the election commission's protocol) is produced by the suspect himself, so the probability of seeing it under fraud is 100 % and it carries no information | Evidence produced by the party being checked is indeed worth almost nothing; for a country with captive commissions this is an exact description (048f) | In a working democracy the protocol is not the only evidence: there are observers, party agents, parallel counts, exit polls, recounts and courts. These are independent sources, and forging them all at once is hard. True "where the commission is captive", false "always and mathematically" |
| On receiving money in his account the citizen "instantly updates trust to 100 %", because a bank transfer cannot be forged more cheaply than honoured | A transfer really is evidence that is hard to forge: it is strong evidence that the payment was made | "I was paid" does not imply "the system is honest". A transfer says nothing about how the votes of those who stayed were counted, whether the median in the formula is right, or whether others were paid. The real value of payments for verification lies elsewhere: every recipient can check his own entry, the sum of recipients and voters is bounded by the register, and ballot stuffing runs into double entry (048f.3, 048i). This is strong evidence about turnout, not about the honesty of everything |
| The "money" button is a perfect filter: the noise leaves and "only pure signal" remains in the ballot box, because refusing the sum is a costly signal | The concept is well chosen: refusing the sum is a costly signal, and experiments show that a price of participation screens out above all the less informed (§4) | "Only pure signal" is an overreach: a costly signal says how much a person values the vote, not how well he chooses (015c). The assistant's estimate is 80–85 % that those who stay choose more accurately, not 100 % (§5). And the words "the weak, easily pressured" about those who leave are a ready-made quotation for an opponent (040c.3b) |
The conclusion for a presentation. A slide titled "Proof" must not be made, for the reason named in §1: there is no Bayesian proof, and the phrase "we prove the system mathematically" wrecks trust in everything else. The honest slide is titled "What Bayes says" and holds three statements, each of which survives a question from the floor: evidence created by the party being checked is worth nothing, whereas a payment creates evidence that every recipient checks; a price of participation screens out the less informed — this has been measured in two countries; a weak but positive signal gives a manifold shift over a few cycles (§3). And as a fourth line — what could refute us. For an investor who can count, this is more convincing than the word "proof". The sum "$1,500" in the text is an illustration; by the formula the order for the United States is about 780 dollars (033c.9c). 🟡
6c. A correction: what "independent evidence" is really worth¶
In the first row of the table above the assistant objected to the external text: a working democracy has observers, a parallel count and courts. The architect, who has worked as an observer, replied: "observers are no answer at all. You need to eat, you need the toilet, and even if you sit and watch you still will not see a carousel. Stuffing is easy for five organised members of a precinct commission, even with two observers present. You cannot draw everything, but adding and stuffing 10–15 % is very easy." A point-by-point analysis shows that he is right and the assistant's objection was overstated.
| Evidence | What it catches | What it does not catch | Weight |
|---|---|---|---|
| Observers | What happens in plain sight, at this station, during these hours | A carousel (different people each voting once), home and early voting, multi-day voting, collusion by the commission at the moment the observer steps away; stations with no observer — which are the majority | Measured. In Moscow in 2011 observers were randomly assigned to 156 of 3,164 polling stations: at those stations the ruling party got 36 %, at the rest 47 %. A difference of eleven points |
| Copies of protocols and a parallel count | Rewriting of results between the station and the higher commission | Stuffing: stuffed ballots are honestly counted and honestly entered in the protocol | Catches one kind of forgery out of several |
| Exit polls | A large discrepancy when answers are free | Half or fewer respond; under fear people answer "as required" (048i.3) | Weak |
| Statistical analysis | Anomalies in the distribution of turnout and votes, the nationwide volume of additions | Who, where and how; not accepted in court; understood by a handful (048f) | Strong for a researcher, nil for annulling a result |
| Recounts and courts | Arithmetic errors, gross breaches of procedure | A stuffed ballot is indistinguishable from a real one in a recount; a court demands proof of effect on the outcome | Works in rare cases |
The Moscow experiment deserves to be read twice. It proves that an observer has an effect — and with the very same number proves that where there is none, eleven points are added without difficulty. That is almost exactly the architect's estimate of "10–15 %", which he obtained from inside a polling station. Observers stood at five per cent of stations; the other ninety-five carried on as usual. Studies in other countries also show displacement: additions move from observed stations to neighbouring ones.
So the first row of the table in §6b is corrected as follows. The external text's overreach remains an overreach: "everything can be drawn" is false, and the architect himself says so. But the assistant's objection is false too: the set of evidence limits forgery not "to zero" but to ten to fifteen points — and most elections are decided by a margin smaller than that. By Bayes this means that a protocol with a gap of up to fifteen points says almost nothing about who really won. Trust in stable democracies rests not on the checks listed but on two other things: on commissions composed of rival parties who profit from catching one another, and on the fact that the government loses from time to time — there is no better evidence that the count does not decide the outcome. Where the commission is made up of insiders and the government never loses, everything else is scenery.
The count and cameras. The architect added from the same experience: "only cameras can prevent stuffing. And then there is the counting procedure itself, during which you cannot even blink: it is simply a matter of adding a hundred papers — like the market swindlers' scheme where one distracts. And you arrive as an observer at seven in the morning, while the count may finish at four at night. Can one keep watch in that state?" This closes the last illusion of the table. The count is a separate and perhaps the main point: a bundle is slipped onto the table once the ballots are already out of the box, and after that it is indistinguishable from the rest; two people and one second of someone's inattention suffice. And by that second the observer has spent twenty-one hours on his feet. A verification system that demands superhuman attention from a volunteer at exactly the moment when it is physically impossible is not a verification system.
Cameras really are stronger than an observer: they do not tire and do not step away. But they have three weaknesses known from practice. Someone has to watch the recording — thousands of stations at twenty hours each; access to it is granted by the same government that is being checked and can be closed; and a ceiling camera sees the counting table poorly. A camera shifts the problem from "failed to keep watch" to "did not look" and "was not allowed to look".
So the section's argument is not that checks are useless but where the ceiling moves. All the methods listed catch forgery at the moment it is committed and require somebody's attention. Double entry catches it arithmetically and afterwards: however many bundles are slipped in, the number of ballots cannot exceed the number of those who did not take the sum, and that number is known to each recipient about himself and to the treasury about everyone.
Competition is not a complete cure. The assistant named commissions made up of rival parties as the support of trust. The architect refined this: "yes, if the parties are rivals there are more eyes. But under competition every vote matters, and the value of stuffing rises still further; and any party can stuff while the other is not looking. As for autocrats, there is nothing to discuss." The refinement is correct and symmetrical: rivalry increases the number of watching eyes and at the same time the price of every slipped-in ballot — in a race decided by one per cent a hundred papers are worth more than in a race decided in advance. The history of stable democracies bears this out: the loudest disputes over counting occurred precisely in the closest races. Rivalry turns forgery from systemic into episodic, but does not abolish it.
The upshot of this point, in the architect's words: "I wanted to show that elections and their technology are outdated, and also that AB-EXIT gives even this rusty locomotive a chance to run more honestly than now." This is an exact formula for what the first stage of the protocol does. It does not replace the paper ballot, the polling station or the commission — the election mechanism at the first stage stays as it is (048h.2). It adds to it what it has never had: an arithmetic ceiling that depends neither on an observer's attention, nor on the commission's honesty, nor on whether parties compete. The locomotive is the same; it has acquired a pressure gauge.
What the protocol changes, and this is no longer rhetoric but arithmetic. Stuffing feeds on "dead souls" — those who are on the roll but did not come to the station: today that is forty to fifty per cent of the roll, and each of them is a ballot that can be cast on his behalf. After the protocol most non-voters have taken the sum, and that is a treasury entry each recipient sees for himself: a ballot cast in his name creates a conflict between two registers (048f.3, 056e.3). The reserve for stuffing shrinks to those who neither took the sum nor turned up — at a sum of half a pension, a few per cent of the roll. And a vote cast through the open verifiable channel (048i) cannot be stuffed at all. The observer no longer needs to sit twelve hours without food: the ceiling on stuffing is set not by his attention but by the size of the remainder in the register. 🟡
7. Weak point of the section¶
LR values have not been measured for any country; the table in §3 is mechanics, not a forecast. The estimates in §5 are the assistant's subjective probabilities: they honestly show the direction and size of the shift from evidence, but another person with other starting numbers will get others. Both experiments in §4 concern small changes in the price of participation in working democracies; carrying them over to a sum of half a pension and to a poor country is extrapolation. The main thing the section gives is not numbers but the question in measurable form: is the accuracy of a person's choice connected with his decision to stay. 🟡
Related: 013 (game theory) · 015c (a change of sign; the weak spot on motivation and competence) · 015b.6b (the thermostat, the lower bound — a coin) · 019d (the market price of a vote; the line "a station, not a person") · 019c.6b (fast and slow effect) · 040c.3b (flattering the voter) · 040b.2b (two sensors)