{"path":"research/what-if-and-lenses/outside-reading-formal.md","content":"# What-if view and worldview lenses: outside reading, formal and computational side\n\nDate: 2026-10-22\n\nScope: outside reading for the what-if view and worldview lenses. Read depth is stated per source.\n\n## How to read this file\n\nRead-depth labels:\n\n- Full: I fetched the whole text and read it. I skipped proofs.\n- Part: I fetched part of the text. The item says which part.\n- Abstract: abstract or summary page only.\n- Excerpts: only the passages a search tool showed me.\n- Not read: known from other papers' citations, or from memory.\n\nNumbers in square brackets point to the source list at the end. Most text is my paraphrase. Where a point is my own reading and not the source's, I write \"My reading\".\n\n## Summary\n\n1. The hinge clamp is an intervention in Pearl's sense. It overrides a claim's strength and ignores what supports or attacks that claim (I checked `deliberus/hinge.py`, read-only). A what-if view built on it can say \"if this were settled, the conclusion would stand at X\". It cannot say \"if this is true, X is likely\", because the strength calculation only flows forward. The view should list the supporters and attackers the grant set aside.\n2. The closest formal model of a lens is value-based argumentation (Bench-Capon 2003; Bench-Capon, Doutre and Dunne 2007). An audience is a ranking of a few named values. A conclusion is then accepted under every ranking, under some, or under none. That gives a ready three-way readout, and it shows which single priority decides a contested conclusion. Facts stay outside the ranking.\n3. The same authors say a ranking of values cannot be an input fixed in advance. It comes out of reasoning in a context. Modgil's extended frameworks let \"this outweighs that\" be a claim that others can argue for or attack. That fits the rule that a lens is made of the holder's own contributions.\n4. Do not merge lenses. Judgement-aggregation results show that combining views premise by premise can give a group outcome whose reasons do not support its conclusion. Show lenses side by side. For each claim show whether they agree, disagree, or reach the same result by different premises.\n5. Horty's reasons-as-defaults gives the words for the normative trial: triggered, defeated, excluded, and several equally good outcomes when rules conflict without a priority. Catala turns the same logic into code. Two equally ranked exceptions that both apply raise a conflict error, and no rule applying gives an empty result. A number-valued semantics hides such conflicts. The trial should report them.\n6. The hinge is one of several known ways to credit a claim for a result. Removal, gradient and Shapley-style scores each fail a different sensible test (Kampik et al. 2024). One failure matters here: when many independent supporters carry a conclusion, each scores near zero alone. Add a group version or a sampled Shapley score. Counterfactual methods such as CE-QArg answer the better reader question: what is the smallest change that flips the verdict.\n7. Existing tools do less than the idea asks. Kialo's Perspectives redraws votes by person, group or a made-up persona, and recomputes nothing. Its impact vote mixes truth and relevance in one number. Carneades is the nearest working what-if: an audience is a set of assumptions plus weights, and accepted statements hold whatever the arguments say. Polis, Community Notes, Consider.it and the Habermas Machine find what groups agree on. None derives what follows.\n8. Bridging has known limits. Community Notes rests on a one-dimensional learned axis, publishes about one note in ten, and in simulation a small bad minority can suppress good notes. A bridging score favours what both sides already accept. A hinge ranking favours what the conclusion rests on. Claims that rank high on the hinge and split across lenses are the ones worth showing.\n9. Policy what-if tools mostly refuse to predict. OpenFisca says outright that it is a static model with no behavioural response. RAND's robust decision making and assumption-based planning sweep many assumptions, find where a policy fails, and list the load-bearing assumptions to watch. This supports the consequence trial's duty to name which behavioural rules it holds fixed.\n10. The literature warns against the \"mind-meld\" framing. A what-if shows what follows from stated premises and weights. It does not show the other person's reasons or background. People confuse a claim's starting weight with its final standing (Oren and Yun). Granting a premise may change how a person sees the link itself, and a clamp cannot show that. \"Holds under all lenses\" covers only the lenses entered.\n\n---\n\n## 1. Audiences, values and preferences\n\n### 1.1 Bench-Capon 2003: value-based argumentation frameworks [1]\n\n**Says.** Start from Dung's abstract frameworks: arguments and attacks. Add values: each argument promotes one value. An audience is a ranking of the values. For an audience, an attack succeeds unless the attacked argument's value ranks higher. An argument is objectively acceptable if it is accepted under every ranking. It is subjectively acceptable if accepted under some ranking. It is indefensible if accepted under none. When no cycle uses a single value, each ranking gives exactly one result, and it is cheap to compute. Checking all rankings costs a factorial in the number of values, so the method wants few values, often two. Facts are handled as a special value that outranks all others for every audience. Uncertain facts create two-argument cycles and give several results per ranking. For persuasion under uncertainty, an argument must hold across the factual possibilities too. Bench-Capon advises settling factual disputes before arguing about values. A worked moral example (using another person's insulin to save a life) shows arguments that hold under every ranking and others that flip with it. A section on \"lines of argument\" says which chains of arguments, with which values, can change an argument's status.\n\n**Read.** Full. The text was about 56,000 characters. I read the abstract, introduction, definitions of defeat and acceptance, the single-value-cycle results, the worked example, the facts-and-uncertainty section and the conclusion. I skimmed the proofs.\n\n**For us.** The three-way readout (every lens, some lenses, no lens) is directly usable. So is the \"which priority decides it\" analysis. My reading: the factual and the value-weighted parts of a disagreement are different operations, so they should be different controls. Granting a factual premise is a supposition. Choosing weights is a lens. Warnings: the method needs a small set of named values, and one value per argument (see 1.6 for the extension). \"Accepted under all rankings\" only quantifies over rankings of the values listed. A concern that is not on the list is invisible.\n\n### 1.2 Bench-Capon, Doutre and Dunne 2007: audiences in argumentation frameworks [2]\n\n**Says.** An audience is a partial order on values. A specific audience is a full ordering that fits it. The universal audience is the empty order, which fits every ordering. Three results hold even for the universal audience or two values: is the argument accepted under some compatible ordering (NP-complete), under every one (coNP-complete), and are two audiences at issue over it (D^p-complete). Two audiences have \"grounds for agreement\" over an argument when each has a compatible ordering that accepts it, or neither does. The disagreement may sit in value orders that do not affect that argument. The paper names three features of practical reasoning. It is situated in a context. Rational disagreement is always possible. And the priority among aims is a product of practical reasoning, not an input to it. The paper then gives a dialogue in which preferences over values emerge, with soundness and completeness results.\n\n**Read.** Excerpts: abstract, definitions 2 to 7, and the complexity results (theorems 8 to 10). The rest not read.\n\n**For us.** \"Grounds for agreement\" is the formal version of a bridge. It names the claims on which two lenses can agree although they differ elsewhere. The hardness results only bite with many values, so keep the value set small, or sample rankings. The third feature is a warning for any design where a reader enters global weights once. Better that a priority appears as a claim made in a context, with reasons (see 1.5).\n\n### 1.3 Perelman and Olbrechts-Tyteca: particular and universal audience [3, 4, 5, 6]\n\n**Says.** Every argument is addressed to an audience. A particular audience shares specific values. The universal audience is all reasonable people. The speaker projects it, so it is a regulative ideal and not a fixed group. The authors call an argument persuasive when it claims validity for a particular audience, and convincing when it claims to win every rational person. In their account, something counts as a fact only if universal agreement can be assumed. Scholars dispute whether the universal audience is coherent. One proposal splits it into a practical role (widening agreement) and an epistemic role (defining facts). Another reading says it handles facts and truths, while particular audiences handle values. Bench-Capon's empty preference relation is the formal stand-in for it.\n\n**Read.** Excerpts of secondary sources: an encyclopedia entry [3] that quotes the Treatise, a journal article [4], a catalogue abstract [5] and an abstract [6]. The Treatise itself not read.\n\n**For us.** The universal audience is always projected by whoever builds it. So \"holds under every lens\" depends on which lenses were entered. Say \"holds under all N lenses entered\", not \"holds universally\".\n\n### 1.4 Preference-based argumentation: Amgoud and Cayrol 2002; Amgoud and Vesic 2009 [7, 8]\n\n**Says.** Amgoud and Cayrol add a preference order on arguments. An attack counts as a defeat unless the attacked argument is strictly stronger. Amgoud and Vesic show a flaw shared by this, by Bench-Capon's values and by Modgil's extended frameworks. In their violin example, an expert's argument is stronger than a child's argument that contradicts it. The attack is dropped because the attacker is weaker. Then both arguments land in the same accepted set, although they contradict each other. They ask that accepted sets contain no internal attack, and they propose a repair that compares conflict-free sets.\n\n**Read.** Amgoud and Vesic: part, the first 22,000 characters (abstract, introduction, sections 2 and 3, start of section 4). Amgoud and Cayrol: excerpts (abstract, introduction, conclusion).\n\n**For us.** Deliberus uses a gradual semantics in which no attack \"fails\", so this exact flaw does not arise today. It would arise if a lens were added as a switch that cancels links. Check any such design for it.\n\n### 1.5 Modgil 2009: extended argumentation frameworks; Modgil and Prakken [9, 10]\n\n**Says.** A preference between two arguments can itself be an argument. That argument attacks the attack between the two. So a preference can be argued for and can be attacked, and Dung's ordinary semantics still apply. Modgil and Prakken build a general framework on ASPIC+. They separate attacks that depend on preferences from attacks that do not. They define \"conflict-free\" by attacks, not defeats, and they reply to critiques of preference-based frameworks.\n\n**Read.** Modgil 2009: not read. The page I reached showed only metadata and references. My description comes from Amgoud and Vesic [8] and from search summaries. Modgil and Prakken: part, the abstract and the first 9,000 characters.\n\n**For us.** This is the formal home for \"a holder's priority is the holder's own claim\". A lens could be the set of preference claims that holder has asserted or endorsed. I did not look for a gradual-semantics version, and the sources above use yes-or-no semantics. How a claim \"A outweighs B for this holder\" should change strengths in a graded semantics is not answered here. I did not verify that Amgoud and Vesic 2009 is among the critiques Modgil and Prakken answer.\n\n### 1.6 Kaci and van der Torre 2008: arguments supporting several values [11]\n\n**Says.** It extends Bench-Capon so that one argument can promote several values. Preferences may be given over values or over arguments. It derives the most likely preference order from default knowledge about preferences.\n\n**Read.** Abstract.\n\n**For us.** Needed, because a real claim often bears on more than one value.\n\n---\n\n## 2. Reasons as defaults\n\n### 2.1 Horty, Reasons as Defaults (2012); Nair and Horty (2018) [12, 13, 14]\n\n**Says.** A reason is the premise of a default: \"if A, normally B\". A default theory has facts, defaults and a priority order on the defaults. A default is triggered when its premise holds. Two defaults conflict when their conclusions clash. A stronger default defeats a weaker one. If two conflicting defaults have no priority between them, the theory has several extensions, each a consistent set of conclusions (the Nixon diamond). Oughts can be read two ways. On the credulous reading, P ought to hold if some extension supports P. Conflicting oughts are then allowed. On the skeptical reading, P ought to hold only if every extension supports it. Priorities can come from specificity, reliability, authority or one's own reasoning, and they can themselves be derived by defaults. Undercutters and exclusionary reasons use one device: a default whose conclusion says another default is out. Horty argues that exclusion is not just very low weight. In some cases a weak default can exclude a strong one, for example a promise to weigh only one person's interests. In other cases it cannot, for example a lower officer cannot cancel a higher officer's order. He calls the right choice open. Floating conclusions are conclusions that hold in every extension through different premises. His slides call it an open question when to accept them.\n\n**Read.** The review [13]: full. Horty's lecture slides [12]: full. Nair and Horty [14]: search summary only. The book: not read.\n\n**For us.** My reading: a lens is a priority order over the same reasons. Keep two cases apart in anything the trial shows. In the first, one lens leaves a conflict open because it ranks neither rule over the other. In the second, two lenses settle the same conflict in opposite ways. A gradual semantics always returns a number, so the first case then looks like a mild lean instead of an open conflict. On undercutters: the design (an exception attacks the relevance claim) matches Horty's device. But lowering a link's strength numerically is the \"very low weight\" view he argues against in some cases. A weak exception that is valid may need to cut a link completely. \"Same result, different reasons\" deserves its own state in the view, not a plain \"agree\".\n\n---\n\n## 3. Supposition, belief change and intervention\n\n### 3.1 The Ramsey test and the suppositional theory of conditionals [15]\n\n**Says.** To judge \"if A, then C\", you add A hypothetically to what you believe and see how far C follows (Ramsey, 1929). For degrees of belief this is conditional probability (Adams). Lewis proved in 1976 that no proposition has, in every probability distribution, a probability equal to the conditional probability. So conditionals are not ordinary statements of fact. Jackson's objection: some conditionals you accept would not survive learning that the antecedent is true. The standard example is a speaker who says that if a certain president had worked for the KGB, the speaker would never find out. Learning that he did would make the speaker drop that very statement.\n\n**Read.** Part. About 80,000 characters retrieved. I read the suppositional theory and conditional probability sections and the passages on Lewis's and Jackson's results. I skimmed the rest.\n\n**For us.** A what-if view is a supposition in Ramsey's sense, with one difference. Ramsey's supposing moves belief both ways: supposing a conclusion also raises belief in its reasons. The system's strength calculation flows one way, from reasons to conclusion. The view is therefore narrower than a true supposition, and it should say so. The KGB example is the case where granting a premise makes a holder reject the link and not accept the conclusion. The relevance claim can be the casualty. The view should let a reader mark a link as no longer accepted under the grant.\n\n### 3.2 AGM belief revision and the Ramsey test [16]\n\n**Says.** In the AGM model, beliefs form a logically closed set. Revising by p adds p and restores consistency by giving up conflicting beliefs. What goes first is guided by entrenchment: give up what has least explanatory and informational value, so single facts go before natural laws. The Ramsey test says a conditional \"p ⇒ q\" is believed exactly when q is believed after revising by p. Gärdenfors proved that this test cannot be combined with a set of plausible revision postulates. Responses: reject the test (Rott), or keep it as a validity test but do not store such conditionals as beliefs (Levi).\n\n**Read.** Part. About 71,000 characters retrieved. I read the history, the revision and entrenchment parts and the Ramsey test and impossibility section.\n\n**For us.** Entrenchment is the same idea as a lens priority: what a holder gives up first. A clamp is not AGM revision. AGM would remove what conflicts with the granted claim. The clamp keeps everything and overrides one value. Do not describe the view as \"if you believed X you would believe Y\". The Gärdenfors result is the formal reason that phrasing cannot be made exact alongside standard revision rules. \"If X were settled\" is safer.\n\n### 3.3 Revision and enforcement in argumentation frameworks [17]\n\n**Says.** A survey of changes to yes-or-no argumentation frameworks. Changes include adding arguments or attacks, enforcing that a set be accepted (strictly or only included in an extension), and revising the framework with AGM-style postulates adapted from Katsuno and Mendelzon. Quality of change is measured by minimal change, for example the fewest attacks added or removed. The survey notes that changes in acceptance are usually a side effect and not a first-class goal. Change of semantics is the least studied.\n\n**Read.** Part. Abstract, and excerpts of sections 3.2 and 5.3.\n\n**For us.** \"Make this set accepted by changing the structure\" is a different operation from \"take this as given\". The first asks what I would have to add. The second asks what follows. All of this work uses yes-or-no semantics, not graded ones.\n\n### 3.4 Pearl's do-operator and structural counterfactuals [18, 19]\n\n**Says.** A structural model gives each variable its own equation from its causes. An intervention replaces one variable's equation with a constant and leaves the others unchanged. Graphically it cuts the arrows into that variable. Effects then spread only forward, to its descendants. Conditioning on an observed value is different. It keeps the variable's equation and lets information flow back to its causes. The equations must be autonomous, meaning each stays valid when others change. Counterfactuals evaluated by intervention do not backtrack: they do not reason from the supposition back to its causes. The antecedent is realised by intervention even if it already holds.\n\n**Read.** Pearl [18]: part, the first 59,000 characters (structural equations, invariance, do(x)). The encyclopedia entry [19]: part, about 60,000 characters (interventions, structural counterfactuals).\n\n**For us.** My reading, with a code check. In `hinge.py` the clamp overrides a claim's strength regardless of what feeds it. The graph version passes the override into the same recursive calculation the badge uses (`compute_badge_recursive` in `badge_inputs.py`). There a clamped claim returns at once with the set strength, so its own supporters and attackers are never read. That is an intervention: replace one node's rule and leave the rest. Two consequences:\n\n- The graph's edges are reasons, not causes. The analogy is about the operation (override one node, keep the rest), not about causal meaning. Read \"intervene\" as \"set the reader's stance\", not \"make it true\".\n- Setting a base score to 1.0 would be a different operation. Under the quadratic energy model a claim with base score 1.0 still falls if its attackers outweigh its supporters [21]. So a partial grant (\"I lean towards this\") is a base-score change and should be labelled as one.\n\nBecause the clamp cuts incoming links, any attacks on the granted claim are silenced. That is exactly where the other side will object. The view should list the attackers and supporters set aside.\n\n### 3.5 Assumptions and accepted statements in argumentation systems [20, 44]\n\n**Says.** In assumption-based argumentation, an assumption is a sentence taken to hold without proof. Attacks aim only at assumptions, through their contraries. An argument with no assumptions cannot be attacked. In Carneades each statement has a status: undisputed, at issue, accepted or rejected. An accepted or rejected statement holds no matter what arguments exist. The authors point out that this stays transparent: anyone can check whether the decisions fit the arguments. A presumption holds until someone questions it.\n\n**Read.** Toni [20]: excerpts (abstract, sections 3 and 4). Carneades 2006 paper [44]: part, about 40,000 characters, nearly all of it.\n\n**For us.** The system's \"supposed\" claims (asserted by nobody, no strength) are close to assumptions, but not the same. An assumption is a sentence that others may attack through its contrary. The Carneades \"accepted\" status is the clamp, with one useful design choice: the decision is shown as the reader's act, separate from the computed strength. Do the same for a grant.\n\n---\n\n## 4. Sensitivity and attribution in graded argumentation\n\n### 4.1 Potyka's quadratic energy model and its properties [21]\n\n**Says.** A weighted bipolar graph has claims with initial weights, attacks and supports. Strength settles where three forces balance: a pull towards the initial weight, an upward push from supporters and a downward push from attackers. The energy at a claim is the sum of its supporters' strengths minus the sum of its attackers' strengths. A bounded function turns energy into a change in strength. On acyclic graphs the model always converges and can be computed in one pass in topological order. Convergence on graphs with cycles is open in general. The model satisfies directionality: influence runs only along the edges. The author contrasts this with probabilistic approaches, where influence also flows backwards. Strength does not saturate at the first strong supporter, and claims with initial weight 0 or 1 can still be moved.\n\n**Read.** Part, the first 40,000 characters (most of the tutorial). The original papers not read.\n\n**For us.** This matches \"independent arguments add\". Directionality is the reason the what-if view cannot reason backwards, which is the point of 3.1 and 3.4. Cyclic graphs are the open case.\n\n### 4.2 Yin, Potyka and Toni 2023: argument attribution explanations [22]\n\n**Says.** It borrows feature attribution from machine learning. The attribution of claim B to a topic claim A is the slope of A's final strength with respect to a small change in B's initial weight. It is worked out for one specific graded semantics on acyclic graphs. Influence is positive, negative or neutral. Along a single path the slope is a product along the path, like the chain rule. Properties include missingness, completeness, counterfactuality (removing a helpful claim lowers the topic) and monotonicity. Completeness and monotonicity can fail when B reaches A by several routes. Two case studies: rumour detection and movie recommendation.\n\n**Read.** Part. The arXiv technical report, about 59,000 characters. I read the abstract, the definition, the property statements and the conclusion. I skimmed the case studies and proofs.\n\n**For us.** A slope answers \"how sensitive is the result now\". The hinge swing answers \"how much could this claim move it at most\". They differ. Premises shared by several lines of argument, which is the normal case in a claim graph, are where slope-based scores lose their guarantees. Clamp-and-recompute is safe there, because it recomputes the whole graph.\n\n### 4.3 Kampik, Potyka, Yin, Čyras and Toni 2024: contribution functions [23]\n\n**Says.** It compares four ways to say how much one claim contributes to another's final strength: removal (strength with and without it), removal after cutting the claim's own incoming links, Shapley (an average over all subsets of the other claims), and gradient. It states principles: directionality; contribution existence (if the strength differs from the starting weight, some claim has a non-zero contribution); local faithfulness; counterfactuality. No function meets all of them. Shapley meets the strongest version of existence, because its contributions add up to the total change. It costs more to compute. In one example a topic claim has n identical independent supporters. Removal and gradient scores fall towards zero as n grows and are near zero by about n = 10. The Shapley score is still visibly non-zero. The authors call the removal and gradient scores misleading there. For the quadratic energy model, removal and gradient do meet the plain version of existence.\n\n**Read.** Part. About 79,000 characters. I read the introduction, the four definitions, the many-supporters example and the principle summaries. I skipped proofs.\n\n**For us.** Two points. First, the warning: a claim backed by many parallel independent supporters will show a low hinge for each of them, even if together they carry the conclusion. A group clamp, or a sampled Shapley score, would show the cluster. Exact Shapley over a region of 200 claims is not feasible, so it would have to be sampled (my reading). Second, where the hinge sits. In the plain energy sum, setting a supporter's or attacker's strength to 0 gives it zero energy, which is the same as removing it. So the 0.0 half of the hinge is close to a removal score. (The system's rule for jointly required parts goes further than removal: denying a required part drags the whole conclusion down.) The 1.0 half, full grant, has no counterpart in their list. It answers a different question: what if this were completely settled.\n\n### 4.4 Amgoud, Ben-Naim and Vesic 2017: Shapley value for attacks [24]\n\n**Says.** It proposes to measure how much each attack, not each claim, contributes to the loss in an argument's strength. It sets axioms and proves that the Shapley value is the only measure meeting them, for the semantics studied. A later paper's snippet adds that Shapley-style scores are harder to compute than removal or gradient scores.\n\n**Read.** Abstract and a search snippet.\n\n**For us.** Links carry weight too. Each link has its own relevance claim in the system. Attribution to links, not only claims, may be worth having.\n\n### 4.5 Counterfactual explanations: CE-QArg; change explanations; Sakama [25, 26]\n\n**Says.** Attribution says who matters. It does not say how to change a result. CE-QArg takes a topic claim and a target strength. It looks for a change to the initial weights that reaches the target at low cost. It defines three problem versions: exact, approximate within a tolerance, and weak. If the semantics returns a claim's own weight when nothing feeds it, a trivial solution always exists: set the topic weight to the target and everything else to zero. So a cost measure is needed. The algorithm chooses direction and size of each change. Tests are on random graphs. Kampik, Čyras and Ruiz Alarcón explain why the order between two topic claims changed after a graph update. They name sufficient, necessary and counterfactual sets of changed claims. Sakama (2014), named in the CE-QArg paper, asked what happens in yes-or-no frameworks if an accepted argument were rejected.\n\n**Read.** CE-QArg: part, the first 15,000 characters (abstract through the problem definitions). Kampik et al.: excerpts (abstract, introduction). Sakama: not read.\n\n**For us.** The most useful question for a reader of a disputed conclusion is \"what would have to be different for this to flip\". CE-QArg answers it with base-score changes, not clamps. It needs a cost model, for example a claim the holder asserted should cost more to change than one they only voted on. My reading: the change-explanation work could be used to compare two lenses. Treat lens A and lens B as two versions of the graph and ask which differing claims explain the different verdicts. It is defined for the order between two topic claims, so the topic pair would need choosing.\n\n### 4.6 Oren and Yun 2025: eliciting initial weights [27]\n\n**Says.** People often cannot give a precise initial weight. They confuse the initial weight with the final standing once other arguments are present. The authors ask for an interval of final acceptability for each argument instead. They check whether the intervals can be reached under a chosen semantics. They shrink intervals that can be, repair those that cannot, and recover the possible initial weights. They cite an earlier experiment finding that people rate reinstated arguments lower, and a study finding that people reason better from a graph than from text.\n\n**Read.** Excerpts of the arXiv version and of the 2026 IJCAI version: abstract, introduction, section 3, conclusion. The two cited experiments not read.\n\n**For us.** Building a lens from slider settings has this trap. A reader who moves a slider is probably reporting a final standing, not a starting weight. Either ask for final standing and back out the starting weight, or show both side by side. Ranges are more honest than points.\n\n### 4.7 Čyras et al. 2021: argumentative explainable AI, a survey [28]\n\n**Says.** It surveys explanation methods built on argumentation: intrinsic and after-the-fact, different frameworks, different forms of delivery, with a roadmap. Yin et al. credit a 2022 workshop paper on dispute trees (Čyras, Kampik and Weng) as a source of the removal-based idea.\n\n**Read.** Excerpts: abstract, introduction, conclusion. The dispute-trees paper: not read.\n\n**For us.** Orientation only.\n\n---\n\n## 5. Systems that show perspectives or bridge disagreement\n\nCoverage note. I searched for tools that let a reader set or accept premises and see the conclusion change. Beyond the ones below I found only research or hobby tools that I did not assess: TOAST (an online ASPIC+ evaluator that takes preferences), ConArg (extension solver), and small unreviewed argument mappers.\n\n### 5.1 Kialo: Perspectives and impact votes [29, 30, 31, 32]\n\n**Says.** Kialo is a debate-tree site. Each user rates a claim's impact on the claim above it, from 0 to 4. The help text says impact combines how true the claim is and how relevant it is to its parent. By default the bars show the average of all votes. Perspectives lets a reader switch to the votes of one user, of a group, or of a custom perspective. A custom perspective is a profile a user votes under to show a point of view, for example \"the view you think a particular expert would take\" (the help page's wording). The education blog suggests giving students stakeholder roles and comparing the vote patterns. Vote visibility can be hidden to stop people following the crowd. Votes do not record reasons. None of the pages I read describes any calculation from child claims to a parent. The bars are vote averages.\n\n**Read.** Perspectives help page [29]: full (short page). Voting help [30]: excerpts. Blog [31]: excerpts. Wikipedia [32]: part, about 20,000 characters. These are the Kialo Edu help pages. I did not read the main site's help.\n\n**For us.** It is a precedent for a per-person and per-group view of one tree. Three differences. Nothing is derived. A custom perspective is a person voting as someone else, which the lens rule excludes. And one number mixes truth and relevance. The system's separate relevance claim lets a reader reject the link and keep the premise.\n\n### 5.2 Polis [33, 34]\n\n**Says.** Participants post short statements and vote agree, disagree or pass on others' statements. The votes form a matrix of participants by statements. Missing votes are filled with the statement's average. Participants with fewer than seven votes are dropped. The matrix is reduced to two dimensions by principal components. A clustering step (k from 2 to 5, chosen by silhouette) makes opinion groups. Each group gets representative statements. A group-aware consensus score is the product, over groups, of the smoothed chance that a group member agrees. It is high only when every group agrees. The algorithm uses no language and assumes no relation between statements beyond that they can be compared. The authors list limits. It needs dozens of people and statements. It suits open prompts, not narrow yes-or-no questions or ranking options. Arrival order biases what gets seen. Moderation can bias. The handling of missing data is ad hoc. A 2023 paper tests language models on Polis summaries.\n\n**Read.** Polis paper [33]: full, about 45,000 characters (through the conclusion, before the bibliography), via a hosted copy. The 2023 paper [34]: abstract.\n\n**For us.** Polis maps where groups sit. It derives nothing. It conflicts with the lens rule in two ways: groups are inferred from votes, and missing votes are imputed. A lens must not impute. Where a holder has no stance, show \"no stance\". The group-aware product could cheaply rank claims for attention, but a product is zero when any one group disagrees, which makes it a brittle summary.\n\n### 5.3 The Community Notes (Birdwatch) ranking [35]\n\n**Says.** Raters mark notes helpful or not. The model predicts a rating as a global term, plus a rater term, plus a note term, plus a dot product of a rater vector and a note vector. The plain terms are strongly shrunk. A note earns a high note term only if raters across the vector dimension rate it helpful beyond what that dimension predicts. In the paper the vectors have one dimension, because a second added little on the small data set. A note counts as helpful when its note term reaches 0.40. In a survey experiment, notes picked this way were rated helpful across political groups more than baselines. On the live platform, people who saw them were less likely to reshare the post.\n\n**Read.** Part. About 50,000 characters. I read the abstract and the method. I did not read the experiments in detail.\n\n**For us.** Bridging here means \"liked beyond what the viewpoint axis predicts\". The axis is learned, not declared, and it has one dimension. The lens rule says positions are declared by the holder.\n\n### 5.4 Community Notes in practice [36, 37, 38, 39]\n\n**Says.** Four recent studies, read at abstract level. A large-scale analysis of about 1.8 million notes finds that 11.5 percent reach agreement on publication, and that 69 percent of noted posts get conflicting classifications [36]. Another finds that about 12 percent of notes calling a post misleading become visible, and 85 percent lack enough ratings from diverse raters. It adds that the share of polarizing content left unresolved is a design choice set by the diversity threshold and the shrinkage [37]. A simulation study finds that more than 40 percent of helpful notes go unpublished, and that 5 to 20 percent bad raters can suppress targeted notes [38]. A fourth finds most notes never reach a rated status, and that the 0.40 threshold makes a cliff [39].\n\n**Read.** Excerpts only: abstracts and passages in search results. Treat them as pointers. The simulation is not field evidence.\n\n**For us.** On contested topics, \"no consensus\" is the common result. Those are the cases where a what-if view is wanted. It should not wait for consensus.\n\n### 5.5 Ovadya and Thorburn 2023: bridging systems [40]\n\n**Says.** A bridging system raises mutual understanding and trust across divides and makes room for productive conflict. It does not aim to make everyone agree. The paper treats ranking, collective response systems such as Polis, and facilitated deliberation as ways of allocating attention. It lists signals such as agreement across groups and low bimodality in ratings. Limits: formal metrics capture a small part of the intuition. Showing content from across a divide can raise division. Bridges can form around harmful ideas. Some divides should not be bridged. Conflict can drive change. The authors want a set of measures, not one.\n\n**Read.** Part. The first 70,000 characters, from the abstract through the start of the limits section.\n\n**For us.** Do not let a bridging score stand for the goal. A view that keeps disagreements visible is more in line with this paper than a \"common ground\" score.\n\n### 5.6 The Habermas Machine: Tessler et al., Science 2024 [41]\n\n**Says.** A language model writes candidate group statements from participants' written opinions and critiques. It refines them over rounds. A reward model trained on human ratings predicts group approval. In UK experiments (5,734 participants, plus a demographically representative virtual assembly), participants preferred the model's statements to those of human mediators and rated them clearer and more informative. Disagreement fell after mediated deliberation but not after plain exchange. Minority critiques were taken into the revised statements. The authors say representativeness and good faith matter. Two unreviewed reader comments on the page make further points. Trust may rise because people see an algorithm as objective. The choice of aggregation rule can change which statement wins. And fairness should weight by how much each person has at stake.\n\n**Read.** Part. The journal page: editor's summary, structured abstract, abstract, reference list and the reader comments. The full text and supplement not read.\n\n**For us.** It shows a model can write bridging text that people endorse. Ownership rests on approval, not on authorship. Under the rule that no language model plays a person, the safe form is: the model drafts, the holder edits or endorses, and the text is shown as endorsed by the holder, never as spoken by them. The output is a statement of common ground, not a derivation. It can paper over a crux.\n\n### 5.7 Consider.it: Kriplean et al. 2012 [42]\n\n**Says.** Each user builds a personal pro and con list of points. A user can adopt points others wrote. The authors treat adoption as a way of listening. A stance slider records overall position. The results page ranks points by three terms: how persuasive a point is (inclusions divided by views), how evenly it appeals across stance groups (an entropy score), and raw inclusions. A reader can click a stance group to see the points that group favours. It was used by thousands of people in a state election. The authors note that schema-heavy argument tools were hard for ordinary users to learn.\n\n**Read.** Part. The first 30,000 characters, to the start of the ranking description.\n\n**For us.** Adoption is a plain way to make a lens out of a holder's own chosen contributions. The per-stance drill-down is a ready precedent. It has no derivation.\n\n### 5.8 The Deliberatorium: Klein 2012 [43]\n\n**Says.** Large argument maps need attention metrics that show where contributions are most useful, which results are mature, and where intervention is needed. The system has been used in several organisations.\n\n**Read.** Abstract.\n\n**For us.** The hinge score is an attention metric of the same kind. No what-if.\n\n### 5.9 Carneades: Gordon, Walton, Prakken [44, 45, 46, 47]\n\n**Says.** It models argument graphs with pro and con arguments, three premise types (ordinary, presumption, exception), statement statuses, and proof standards (scintilla, preponderance, dialectical validity, beyond reasonable doubt). In the 2006 version, an argument's weight is the weight of its weakest premise, on an ordinal scale of 0 to 10. The authors chose ordinal on purpose, doubting that users can estimate finer values. In the 2008 version, an audience is a set of assumptions plus a weight for each argument. Acceptability is computed for that audience. The weights are real numbers from 0 to 1 in the later version and the manual. Preponderance compares the best applicable pro argument with the best applicable con argument. The manual says audience weights may be gathered by polls. It tells users they may disagree with a result because arguments are missing, weights differ, or the model is wrong.\n\n**Read.** 2006 paper [44]: part, nearly all. 2008 paper [45]: excerpts (the audience definition). Manual [46]: excerpts. 2007 journal paper [47]: abstract.\n\n**For us.** This is the nearest working design to a what-if with audiences. Matches: weakest premise governs inside an argument (in the 2006 version), exceptions as a premise type, accepted statements that hold regardless. Differences: the proof standards compare the best argument on each side. They do not add independent arguments, as the quadratic energy model does.\n\n### 5.10 Parmenides: Atkinson, Bench-Capon and McBurney [48]\n\n**Says.** A consultation system built on value-based argumentation. A summary page describes it as structured and survey-based. A related 2006 paper links a discussion forum to agents that reason with social values.\n\n**Read.** Search summary only. I could not retrieve the papers. Detail beyond this is unverified.\n\n**For us.** A pointer to the nearest precedent for per-participant answers on the premises of a proposed action. Check before relying on it.\n\n### 5.11 Judgement aggregation in argumentation: Caminada and Pigozzi 2011 [49]\n\n**Says.** When individuals each give consistent judgements on linked propositions (reasons and a conclusion), voting on each proposition separately can give a group outcome where the reasons do not support the conclusion. This is the discursive dilemma. The authors study how to combine individuals' evaluations of an argumentation framework. They define three operators (skeptical, credulous, super-credulous). They require that the group outcome be compatible with each member's view, in the sense that each member can defend it.\n\n**Read.** Abstract and introduction (excerpts).\n\n**For us.** Any combined view across lenses faces this. The compatibility test is usable as an acceptance test for a common-ground display: could each holder defend what is shown?\n\n### 5.12 Crux: a single web tool [50]\n\n**Says.** A weighted decision matrix. Each person gets a column of weights over a fixed set of concerns. Options are scored once. The tool shows which concern's weight carries the difference, and how far someone's weights would have to move to change the best option. Columns that are guesses are marked as guesses until the person supplies their own. A language model can propose options, scores and guessed weights.\n\n**Read.** Home page text only. No paper, evaluation or verifiable authorship.\n\n**For us.** A lightweight example of per-person weight columns plus a \"how fragile is the lead\" readout. That is the lens idea at decision-matrix level. Marking guessed columns is the minimum. The lens rule goes further and allows no guessed columns.\n\n---\n\n## 6. Policy what-if\n\n### 6.1 OpenFisca and LexImpact [51, 52]\n\n**Says.** OpenFisca is an open-source engine where tax and benefit law is written as executable formulas and parameters. You supply a situation and get computed results, for one household or for a population with survey data. LexImpact is a French National Assembly service, running since 2020, that lets members of parliament estimate the effect of an amendment on example households and the budget. The OpenFisca documentation says plainly what it is not. It is a static model. It gives results for the situation as it is now, with no reaction by people. Human decisions are inputs, not modelled. It does not parse legal text by itself.\n\n**Read.** Excerpts of the documentation and the LexImpact about page.\n\n**For us.** The pattern is reusable: rules as data, run on cases, compare reform against baseline. The static limit is the point where a consequence trial must name which behavioural rules it holds fixed. This is the Lucas critique in practice. OpenFisca states the limit and offers nothing for it.\n\n### 6.2 Catala [53]\n\n**Says.** A language that turns statute into executable code. Its core logic is prioritized default logic: a general case, then exceptions, with a partial order among the defaults. In its small core calculus a default has a justification, a consequence and a list of exceptions. If exactly one exception applies, its value wins. If none applies and the justification holds, the consequence is the result. If two or more exceptions apply and no priority separates them, the run stops with a conflict error. If no rule gives a value, the result is empty. The authors tested it on a section of the US tax code and on French family benefits. They found a bug in the official French implementation. Lawyers and programmers worked from the same code.\n\n**Read.** Full. About 90,000 characters. I read the introduction, the default-logic section, the semantics rules for conflict and empty results, and the evaluation. I skimmed the compilation proofs.\n\n**For us.** This is the nearest executable form of the normative trial. The two outcomes the trial wants to report, \"rules conflict with no priority\" and \"no rule decides\", are Catala's two error values. Catala treats both as faults in the coding. For rules under dispute they are results to show. Catala's authors also say the hard part is classifying messy real situations into the law's categories. In the trial, case facts are where interpretation enters.\n\n### 6.3 RAND robust decision making and scenario discovery [54, 55]\n\n**Says.** For deep uncertainty, where parties cannot agree on the model, the probabilities or how to value outcomes, do not predict. Build large ensembles of scenarios, from hundreds to millions. Each is one guess about how the world works, paired with a strategy. Look for strategies that do reasonably well across them, \"robust\" rather than optimal. Prefer adaptive strategies. Design the analysis for interactive exploration, with the computer searching for counterexamples to cherished hypotheses. Evaluate strategies under the several value systems different parties hold. Scenario discovery runs a model over many input combinations, marks the cases where a policy misses its goal, and uses data mining to find simple regions of inputs that predict those cases. Those regions are the scenarios worth discussing.\n\n**Read.** Excerpts: the report summary [54], the abstract and introduction of [55], and an algorithm page.\n\n**For us.** This is the lens-plus-hinge logic extended. Sweep weights and assumptions, and report the regions where the verdict flips, not just one verdict. The report's definition of deep uncertainty fits the disagreement the platform deals with.\n\n### 6.4 Assumption-based planning: Dewar et al. 1993; Dewar 2002 [56, 57]\n\n**Says.** Five steps. List the assumptions a plan rests on. Find those that are load-bearing and vulnerable within the planning horizon. Define signposts, which are indicators that an assumption is weakening. Define shaping actions, which keep an assumption true or make it fail. Define hedging actions, which prepare for it failing.\n\n**Read.** The 1993 report: abstract and a library record that lists the five steps. The 2002 book: chapter titles and one chapter summary. Not the full text.\n\n**For us.** \"Load-bearing\" is the hinge idea applied to assumptions. The consequence trial's list of behavioural rules assumed to hold is step one. Signposts would be observations that one of those rules is breaking.\n\n### 6.5 Bankes 1993: exploratory modelling [58]\n\n**Says.** Using computational experiments to reason about systems under significant uncertainty is a different use of models from consolidating knowledge to predict. It needs a different method.\n\n**Read.** Abstract.\n\n**For us.** Support for not showing one predicted outcome in the consequence trial.\n\n### 6.6 HYPO, CATO and legal hypotheticals [59, 60, 61, 62]\n\n**Says.** HYPO models how lawyers argue with real and invented cases. Cases are described along dimensions that favour one side or the other. For a new case, HYPO finds the most on-point precedents and builds three-step arguments: a point, a response, a rebuttal. It uses near-miss dimensions to pose hypotheticals, such as asking what would change had an extra fact been present. CATO is a teaching version built on factors. A paper comparing it with jurisprudence says it handles weights in a non-numeric, context-sensitive way. A later project paper describes hypotheticals in Supreme Court oral argument as probes. Justices test a proposed rule by inventing cases at its edge, and the advocate revises the rule. The authors say factors and dimensions are not enough to model this and a deeper representation of concepts is needed.\n\n**Read.** Excerpts only: a publisher page, a summary page, an excerpt of the project paper and an abstract. The books and original articles not read.\n\n**For us.** A hypothetical here is a case built to test a rule. It is not a prediction. The trial's \"cases no rule decides\" are what a near-miss search would produce. Mark invented cases as invented. The non-numeric treatment of weights in legal practice is a caution for numeric lenses.\n\n---\n\n## 7. What the reading leaves open\n\n- I did not look for a graded-semantics version of \"a claim about priority changes strengths\". The preference-argument work I read uses yes-or-no semantics.\n- I did not search for user studies of what-if views on argument graphs. The only user-side evidence I met is Oren and Yun's point on weights, as cited there.\n- A lens could be built on a few named values (value-based argumentation) or on holders' weights for each claim and link (what the attribution and counterfactual papers vary). The sources do not decide between them. Few values keep things legible and tractable. Per-claim weights are closer to what holders actually say.\n- Whether a grant view should show set-aside attackers by default is my suggestion from Pearl and Carneades, not a finding.\n\n## Sources\n\nDepth tags: full / part / abstract / excerpts / not read.\n\n1. Bench-Capon, T. (2003). Persuasion in practical argument using value-based argumentation frameworks. Journal of Logic and Computation 13(3):429-448. https://cgi.csc.liv.ac.uk/~tbc/publications/jcl03.pdf (full)\n2. 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(1991). Modeling legal arguments: reasoning with cases and hypotheticals. MIT Press. https://mitpress.mit.edu/9780262011143/modeling-legal-arguments/ (publisher page only)\n60. Summary of Ashley and Rissland, \"Compare and contrast, a test of expertise\". https://lacuna.tiptreesystems.com/work/compare-and-contrast-a-test-of-expertise (excerpts of a third-party summary)\n61. Teaching creative legal reasoning with examples from Supreme Court oral arguments (project paper). https://www.cs.cmu.edu/~hypoform/Paper1.pdf (excerpts)\n62. An AI model of case-based legal argument from a jurisprudential viewpoint. Artificial Intelligence and Law (journal record). https://link.springer.com/article/10.1023/A:1019513821567 (abstract)\n"}