{"path":"listening/2026-10-23-why-independent-reasons-add.md","content":"# Why independent reasons add in log-odds\n\n- **What it is**: a listening walkthrough of about twenty minutes, made the night of 22 to 23 October.\n  His requests, in order: *\"Can you make me a 16-min walkthrough of this, teaching me what we realized\n  today, so I fully understand why we're on the right path now?\"*, then *\"oh I meant to ask, does this\n  new insight contradict modern argumentation theory and what the ppl who built QEM/QBAF or other modern\n  argumentation theory software etc think?\"* and *\"include reflections and research about that in the\n  walkthrough and make it 20 mins\"*, with *\"Take into account what this other session said\"* (the\n  rules-and-reasons session's row on how often an outcome follows). It teaches ledger Q46, ruled the\n  same night, in three groups: the arithmetic of one reason and of two; the real cases and reasons that\n  share a story; the field's view and the outcome-frequency rule.\n- **Covers**: [../research/how-independent-reasons-add.md](../research/how-independent-reasons-add.md)\n  § 0 to § 9; [../research/how-independent-reasons-add/argumentation-builders-on-probability.md](../research/how-independent-reasons-add/argumentation-builders-on-probability.md)\n  (the field report, verbatim); [../research/strength-calculus-literature/computational-argumentation.md](../research/strength-calculus-literature/computational-argumentation.md)\n  § 0, § 2 A and B, D1, D8; [../research/strength-calculus-literature/bayesian-and-informal-logic.md](../research/strength-calculus-literature/bayesian-and-informal-logic.md)\n  § 2.1, § 2.6, § 2.7, § 3.3; [../research/what-relevance-is.md](../research/what-relevance-is.md) § 3f;\n  [2026-09-26-arc-p-the-april-conversation-audited.md](2026-09-26-arc-p-the-april-conversation-audited.md)\n  (what that walk said about QEM and Good's weight of evidence); ledger Q46, Q41, Q42, Q43, AT8\n  ([../research/session26-open-rulings.md](../research/session26-open-rulings.md)).\n- **Chapter list for noting** (rule 33):\n  0. Opening: the question and the map\n  1. What one reason should do: probability as the target?\n  2. When reasons share a story: a claim between for a shared doubt?\n  3. What the field thinks: a sum shows its search?\n  4. How often the outcome follows: rule the revised row?\n- **Registers used** (rule 57): Lucy the spine; his clone on his words of 22 October and four predictions;\n  Elliot on Jeffrey's rule (`bayesian-and-informal-logic.md` § 2.1), I. J. Good's weight of evidence (the\n  September walk), Prakken's three kinds of strength (`computational-argumentation.md` entries 21–22; Prakken\n  2018 in `bayesian-and-informal-logic.md` § 3.5) and Carnap's firmness (§ 3.3 there); Hope on log-odds (the\n  note § 4) and on red sky (AT8); Scotty as a meta-analyst of the early nineties (the note § 5c) and as a\n  critic carrying Potyka and Booth's padding objection (the field report § 4, § 6); Anna on the forecasting\n  studies (the note § 3, § 5b) and on Potyka's own formulas (the field report § 1); Myrddin in every part.\n- **Correction spoken** (rule 37): earlier the same night Claude told him that QEM's squash is what turns a\n  0.9 reason into 0.57. Half of it is the offset: the code feeds QEM the reason's offset from 0.5, and\n  Potyka's QEM on raw strengths gives 0.72 (the note § 0 item 1 and § 9, corrected the same night). Not a\n  correction, an update: the September walk's *QEM strengths are deliberately not calibrated probabilities*\n  described the design then; his aim of 15 October (Q41) changed the design's target.\n- **Numbers kept**: nine-tenths, nine to one and eighty-one to one (the arithmetic is the idea); a tenth\n  becoming a hundredth (the square); seven in ten (Potyka's QEM on raw strength); nine in ten and two in three\n  (the bile-duct tests, published against shipped); four fifths (signs of one process); seven trials; one and\n  a half and almost two (the forecast pairs); twenty years; ten thousand whispers; four weak reasons; ten days,\n  a third, two in three and one in three (red sky); one in six and a little over half (strep).\n- **His words quoted**: 22 October, the last sentence of his ruling of Q46 (*\"I do want to understand this\n  fully.\"*, whole); 22 October, his comment on AT8 (*\"Outcome-tracking definitely makes sense to me, seems\n  bayesian enough...\"*), typed the same night, so the record lookup did not yet find it.\n- **Predictions**, from `listening_context.py --prepare --said` and `mannaminne --said`: part 1 from his words\n  of 15 October (ledger Q41, *the strength in the world*) and of 31 March (*a proper rational Bayesian\n  probabilistic argument graph*); part 2 from Q42's own reading and his question quoted in that row, on how many\n  independent reasons can sit under a claim; part 3 from the September walk's participation point and the\n  weight ruled 22 October; part 4 from his comment on AT8.\n- **Not covered, no decision raised**: recommendations 3, 5 and 6 of the note (the *partly one story*\n  overlap, shrinking machine relevance, odds factors on screen) beyond a line; the resident clause on Q38's\n  line, still proposed; the vote weight removed the same night (AS3); the field report's software survey.\n- **The dry run's notes, read and left**: the quote of AT8's comment not found (typed the same night); one\n  sentence flagged as speaking for him is Anna's about Potyka (*Later he wrote another formula*); number words\n  over three a part, none a tally.\n- **Rendered**: 21.7 minutes (forecast 19:44 to 22:09; 146 words a minute while speaking, 102 overall),\n  5,634 voice credits, six chapter marks; audio in `.private/local-only/listening-audio/`.\n- **Status**: snapshot of 23 October. Q46 ruled and unbuilt; AT8 revised by its session and open; Q41's R1,\n  Q42 and Q43 open.\n- Method: [how-to-write-for-listening.md](how-to-write-for-listening.md).\n\n---\n# Why independent reasons add in log-odds\n\n[[scene Lucy opens a late walk for Fredrik at the end of 22 October. Tonight he ruled that independent reasons add in log-odds, and asked to learn why afterwards. She is calm and clear, a teacher who enjoys the subject.]]\n\nWhy is adding independent reasons in log-odds the right path?\n\n[[pause 5]]\n\nHere is the short answer first. It is what probability says. It came closest on nearly every real case we tried. And the field that built the old formula already holds it, as a formula of its own.\n\nThe silences are deliberate. They are room to think.\n\n[[pause 4]]\n\nNo chapter notes from this evening's walk have reached me yet.\n\nTonight you ruled, and asked to learn afterwards. In your words:\n\n[[voice fredrik]]\n\n[earnest] I do want to understand this fully.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nThe map has three groups. First, what a single reason does, and what a pair does. Second, the real cases, and reasons that share a story. Third, what the field thinks, and how often an outcome follows.\n\n---\n\n# Part one. What one reason should do\n\n[[scene Lucy takes the part that decides the others: what a strong reason passes to its claim, and what two independent reasons do together. Elliot brings Richard Jeffrey and I. J. Good. Hope asks what log-odds means. Myrddin speaks briefly. Mood: patient and exact.]]\n\nA claim has a single reason. The reason is nine-tenths sure, and it fully decides the claim. How sure is the claim?\n\n[[pause 5]]\n\nMost people say: as sure as its reason. Probability agrees.\n\nThe site says barely more than even.\n\n[[pause 4]]\n\nHere is why. Since September, a link carries its reason's strength, scaled by its relevance. Relevance is how much the reason bears on the claim.\n\n[[pause 4]]\n\nTake a reason by itself, that way. The claim moves from its start toward the reason's strength, as far as relevance allows. I will call the result the reason's alone value.\n\n[[pause 4]]\n\nA fully relevant reason gives an alone value equal to its own strength. Exactly what common sense said.\n\n[[pause 4]]\n\n[[voice elliot]]\n\nThe philosopher Richard Jeffrey asked this in the sixties. How should you update on evidence you are not sure of? His answer was a weighted mixture. Belief moves toward what the evidence would show, as far as you trust the evidence.\n\n[[pause 4]]\n\nYour factors are his rule, term for term.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nSo the factors were right all along. What went wrong came after them. The code measured each reason from the middle, so a strong reason entered as a small push. Then it squared the push, through a curve called the quadratic energy model. A push of a tenth becomes a hundredth. So a lone strong reason barely moves its claim.\n\n[[pause 4]]\n\nThat is my correction. Earlier tonight I blamed the curve alone. Nico Potyka's own model, given the reason's full strength, lifts that claim to about seven in ten. The near-silence came from our small pushes, squared.\n\n[[pause 4]]\n\n[inhales] Now add a second reason, just as strong. It is independent: it reaches the claim by a different route.\n\nHow do they share the credit? Averaging would say: no change. The second reason would add nothing.\n\n[[pause 4]]\n\nAveraging is the rule for a single piece of evidence counted twice. Separate routes are different. Nine-tenths means odds of nine to one. Independent evidence multiplies odds. Twice over, that is eighty-one to one: near certainty.\n\n[[pause 5]]\n\n[[voice hope]]\n\nOdds? I would just add the percentages. Why multiply?\n\n[[voice lucy]]\n\nBecause percentages run out of room near the top. Odds do not. Each independent reason multiplies the odds by its own factor. Take the logarithm, and every multiplication becomes an addition. That scale is called log-odds. [slowly] On it, independent evidence simply adds.\n\n[[pause 4]]\n\nSo each reason contributes the same: half the evidence, a ninefold change in the odds. In percentage points the second looks small. Only because probability flattens near certainty.\n\n[[pause 4]]\n\n[[voice elliot]]\n\nThe statistician I. J. Good called that sum the weight of evidence. A walk in September said the site's sum rhymed with his. The curve after it broke the rhyme.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nThat walk also described a claim's strength as deliberately not a probability.\n\nIn October you set a different aim: a claim's strength should say how likely it is in the world. Tonight's ruling is the arithmetic that aim needs.\n\n[[pause 4]]\n\nMy take. Nothing ruled about the factors changes. Only the curve after them goes.\n\n[[voice myrddin]]\n\nEvidence is weighed in odds, not in points. Near certainty, each honest addition sounds small. It is the same size it always was.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nThe decision is the row underneath all of this. Should a claim's strength aim at its probability, given the record? The weight beside it was ruled tonight.\n\n[[pause 5]]\n\nMy prediction.\n\n[[voice fredrik]]\n\n[firmly] Yes, rule it. I want a stranger to trust a claim's strength as its strength in the world. The weight beside it says how much of the world was looked at.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nToday, a strong reason moves its claim barely past even on the site. Built, a claim would say what its record supports. And a stranger could read each reason as a factor on the odds.\n\n---\n\n# Part two. When reasons share a story\n\n[[scene Lucy turns to the real cases tested tonight, and to reasons that one story explains. Scotty borrows the voice of a confident meta-analyst from the early nineties. Anna brings the forecasting studies. Myrddin speaks briefly. His clone gives the prediction. Mood: grounded, a little sober.]]\n\nTwo medical tests both come back positive. Should they count twice?\n\n[[pause 5]]\n\nTonight we tried each rule on cases whose answer was published. Children with a suspected blocked bile duct had both tests. When both were positive, the published answer was a little over nine in ten.\n\n[[pause 4]]\n\nLog-odds came within a few points of it. The site's code said about two in three. That is further off than either test alone.\n\n[[pause 4]]\n\nOn every case, the site's code was the worst rule. Reasons with different mechanisms added almost exactly. Signs of a single process, like the symptoms of a sore throat, kept about four fifths of their sum.\n\n[[pause 4]]\n\n[takes a slow breath] And then the failures. Every overclaim we collected came from adding reasons that share a single story.\n\n[[voice scotty]]\n\n[confidently] Seven small trials of magnesium after a heart attack. Every trial points the same way. Pool them, and the benefit is large and certain. Who needs a big trial?\n\n[[voice lucy]]\n\n[[pause 4]]\n\nThose were my words, in a meta-analyst's manner. A few years later, a trial far larger than all of them combined found no benefit at all.\n\n[[pause 4]]\n\nThe shared story was this. Small trials that found a benefit got published. Small trials that found none mostly did not.\n\n[[pause 4]]\n\nSo tonight's ruled question comes in. Suppose the claim is false. What most likely explains each reason? Is it the same explanation? For the magnesium trials, yes. For separate coin flips, no.\n\n[[pause 4]]\n\n[[voice anna]]\n\nElection forecasting shows the middle ground. Graefe and colleagues combined several methods. Polls and models together were worth about one and a half methods, because the models feed on the polls. Prediction markets and experts were worth almost two.\n\n\n[[voice lucy]]\n\n[[pause 4]]\n\nMy take. Independence is where the real work sits.\n\n[[voice myrddin]]\n\nAgreement is cheap when it comes from a single source. Ask of every chorus how many throats it has.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nThe decision. When the check finds a single story, the reasons could go under a claim of their own. That claim supports the conclusion once. The trials would sit under: small trials found fewer deaths with magnesium. And under that link: these trials were not selectively published. Should that be ruled?\n\n[[pause 5]]\n\nMy prediction.\n\n[[voice fredrik]]\n\n[curious] Yes. Then the shared story sits on the map, where someone can attack it, instead of hiding in a strength. And a crowd of reasons right under a claim tells me a claim is missing in between.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nToday, every reason on the site adds, shared story or not. Built, the check would ask the rival question of each pair. And a pile of echoes would count once.\n\n---\n\n# Part three. What the field thinks\n\n[[scene Lucy turns to the researchers who build argument-strength formulas, and asks whether tonight's ruling breaks with them. Anna reads the builders' own papers. Scotty argues for the other side, in a borrowed voice. Elliot brings Henry Prakken's kinds of strength. Myrddin speaks. His clone gives the prediction. Mood: curious and fair to the other side.]]\n\nDoes tonight's ruling break with modern argumentation theory?\n\n[[pause 5]]\n\nNo. It picks a formula the field already has. And it answers the field's main worry in its own way.\n\n[[pause 4]]\n\nFor about twenty years, researchers have built formulas for how strong an argument is, given its supporters and attackers. They call them gradual semantics, and judge them by principles. Supporters raise a claim. Attackers lower it.\n\n[[pause 4]]\n\nProbability is not among those principles. Most authors treat a claim's strength as a measure of the debate. Leila Amgoud and colleagues keep probability out of the result. Where it enters at all, it enters as the starting weight.\n\n[[pause 4]]\n\n[[voice anna]]\n\nNico Potyka built the quadratic energy model in 2018, to fix two faults. In an older formula, an argument at full strength made all the others irrelevant. In another, attacks and supports pulled unequally.\n\n[[pause 4]]\n\nLater he wrote another formula, reading a neural network as an argument graph. There, a claim's log-odds is its starting log-odds plus a weighted sum of its supporters, minus its attackers.\n\n[[pause 4]]\n\nThat is tonight's rule, nearly term for term. Potyka did not claim the Bayesian reading himself. He chose it for its simple reading, and found it met the field's principles almost perfectly.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nSo the change is smaller than it sounds. We moved from a formula of Potyka's to another of his.\n\n[[voice scotty]]\n\n[irreverent] Fine. But add enough weak reasons, and your claim climbs without limit. Potyka and Booth warned about exactly that. Ten thousand whispers make a shout.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nThose were my words, in a critic's manner. The worry is fair, and even the logistic formula fails their test. It has two halves.\n\nWhispers from a single story count once. That is the check from part two.\n\n[[pause 4]]\n\nTruly independent whispers should add. Godden and Zenker give four weak reasons for a claim. None alone makes it likelier than not. Together they do.\n\n[[pause 4]]\n\nWe found no published formula that pairs log-odds with an independence check. That pairing is ours.\n\n[[voice elliot]]\n\nHenry Prakken asked what strength even means. He separates three kinds. The strength of an inference. How well an argument stands against its attackers. And how persuasive it is.\n\n[[pause 4]]\n\nTonight's ruling is about the first kind. For that kind, Prakken himself used probability. He also warned that reasons may not be independent. The ruling agrees, and checks first.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nMy take. The field never said a claim's strength must not be a probability. It said: state what it means. Potyka and Booth call the comparison with probability an open question. Deliberus is answering it.\n\n[[pause 4]]\n\nOne difference stays, owed to the build. In probability, news about a conclusion flows back to its reasons. Our graph sends strength forward only.\n\n[[voice myrddin]]\n\nA formula is a promise about what its strengths mean. Keep the promise, and the formula follows from it.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nA worry stays, and the September walk named it. A claim where only its supporters have shown up still climbs. Probability given the record is only as good as the record.\n\n[[pause 4]]\n\nSo the weight sits beside the strength. And the open row goes further. Beside a sum, it shows how many independent reasons the sum is worth, and how the search went on each side. The case against, never sought. Should it be ruled?\n\n[[pause 5]]\n\nMy prediction.\n\n[[voice fredrik]]\n\n[earnest] Yes. A sum without its search is the participation problem all over again. Show me what nobody looked for.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nToday, the site uses the quadratic formula. Built, it would use the field's own logistic formula, with the independence check that Prakken's principles ask for.\n\n---\n\n# Part four. How often the outcome follows, and how often it would anyway\n\n[[scene Lucy takes the rule another session proposed tonight, and the one thing it needs from this ruling. Hope tries a sentence about red sky. Elliot gives Carnap's distinction. His clone reads his comment from tonight and the prediction. Myrddin closes. Mood: light, a small discovery.]]\n\nMost people who take vitamin C are over their cold within ten days. Is that a reason to take it?\n\n[[pause 5]]\n\nNo. Most colds are over by then anyway.\n\n[[pause 4]]\n\nAnother session proposed a rule tonight. In a case, a link's relevance is the rule's strength, times how often its outcome follows. The example is red sky: about a third of red-sky mornings bring rain.\n\nYou wrote, tonight:\n\n[[voice fredrik]]\n\n[warmly] Outcome-tracking definitely makes sense to me, seems bayesian enough...\n\n[[voice lucy]]\n\n[[pause 4]]\n\nIt is a subtraction short. A reason's relevance is how much more often the outcome follows when the reason holds, than when it does not.\n\n[[pause 4]]\n\nHere is what the gap does under tonight's arithmetic. Start rain today at even, knowing nothing. The rule as written lifts it to about two in three. Yet the rule itself says one in three.\n\n[[pause 4]]\n\nUnder the old curve the error stayed hidden. Under log-odds it shows.\n\n[[pause 4]]\n\n[[voice hope]]\n\nI heard: about a third of red-sky mornings bring rain. So red sky means rain is likely?\n\n[[voice lucy]]\n\nOnly if rain is rarer on other mornings. If rain comes as often on any morning, red sky tells you nothing.\n\n[[pause 4]]\n\nNow a real case where the lift is large. Among adults with a sore throat, about one in six has strep. With all four signs of the clinical score, a little over half do. Half is not a high chance. It is a big lift.\n\n[[pause 4]]\n\n[[voice elliot]]\n\nRudolf Carnap drew this distinction in the sixties. He found two meanings hiding in the word confirm. Firmness: how probable a claim is, given the evidence. And increase in firmness: how much the evidence raised it.\n\n[[pause 4]]\n\nA stated proportion is firmness. A reason's relevance is the increase. Vitamin C has firmness without increase. The sore-throat signs have modest firmness and a large increase.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nSo my take. The stated proportion sets the case's alone value, and relevance is whatever moves the start there. Below the start, the link becomes an attack.\n\n[[pause 4]]\n\nThe comparison is the claim's start: the base rate, wherever one is known. Rules with named exceptions need no change.\n\n[[voice myrddin]]\n\nA sign is worth what it adds to what you already expected. The rest is the weather.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nThe row's own session revised it with this repair, just after midnight. It is open.\n\nThe decision. Should the rule, as revised, be ruled?\n\n[[pause 5]]\n\nMy prediction.\n\n[[voice fredrik]]\n\n[thoughtful] Yes, rule it. That's what I meant by outcome-tracking. How much more often it follows, not just how often.\n\n[[voice lucy]]\n\n[[pause 4]]\n\nToday, no rule claim in the graph carries a proportion yet. Built, the pass that writes a rule would also bring the claim's start.\n\n---\n\n[[scene Lucy closes the walk, brief and warm.]]\n\nThat is the walk. One word a chapter, if you have one: muddled, agreed, or disagreed and why.\n"}