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Linkage Scores: Does This Argument Actually Connect?

How It Works: Debates Inside Debates

On the Idea Stock Exchange, every belief has a page. That page shows two columns: Reasons to Agree and Reasons to Disagree. But here is what makes this different from any other debate platform: each of those reasons displays its own Linkage Score — a number that measures not whether the argument is true, but whether it actually connects to the conclusion.

And then it goes one level deeper. You can click on any Linkage Score and debate it.

That click opens a new page dedicated entirely to the question: "Does Argument X actually support Conclusion Y?" On that page, you will see:

• Reasons to agree that the linkage is strong
• Reasons to disagree that the linkage is strong
• Each of those reasons has its own Linkage Score, which can itself be clicked and debated

This creates an infinitely navigable tree of logic — from the top-level belief all the way down to foundational assumptions. Every connection between ideas is itself a claim that can be tested. The platform tracks two distinct types of links to maintain precision:

• ECLS (Evidence-to-Conclusion Linkage Score): How directly does raw data or a source support a claim? Example: A peer-reviewed atmospheric study → 95% linkage to "CO₂ traps heat."
• ACLS (Argument-to-Conclusion Linkage Score): How strongly does one argument or belief support another? Example: "Solar prices dropped 80%" → 75% linkage to "We should expand renewable subsidies."

The Problem This Solves: True but Irrelevant

Traditional debate has a fatal flaw: it treats all true statements as equally valid support for a conclusion. They are not. "The sky is blue" is 100% true. It is also completely irrelevant to whether we should implement a carbon tax. In a traditional debate, someone can state it anyway, and it sounds like evidence.

Linkage Scores separate two questions that debate almost always conflates:

1. Is this argument true? (Measured by the Truth Score)
2. Does this argument connect to the conclusion? (Measured by the Linkage Score)

A perfect truth score with zero linkage contributes nothing. That is not a bug — it is the platform's primary noise filter.

The Scale: -1.0 to +1.0

Linkage Scores act as a multiplier on every argument's contribution to its parent conclusion:

• 1.0 — Proof: Deductive logic. If the premise is true, the conclusion must follow. (Rare outside mathematics.)
• 0.7 to 0.9 — Strong Support: Direct, causal relevance. The conclusion heavily rests on this argument.
• 0.4 to 0.6 — Context: Helpful background, but the conclusion could stand without it.
• 0.1 to 0.3 — Weak: Tangential. Technically related, but the logical gap is large.
• 0.0 — Irrelevant: True, but does not move the needle at all.
• Negative — Contradicts: If true, this argument actively undermines the conclusion.

How the Community Calculates the Score

The Linkage Score is derived from the community's own nested debate about the connection, using this formula:

Where A = the total adjusted weight of arguments supporting the linkage, and D = the total adjusted weight of arguments opposing it.

For example: if a connection has strong arguments scoring A = 3 on the supporting side and D = 1 on the opposing side, the Linkage Score is (3 − 1) / (3 + 1) = 0.50. The argument passes 50% of its potential weight up to the conclusion. If support and opposition are equal, the score is 0.0 — the argument contributes nothing until the debate is resolved.

The Master Formula

In the ReasonRank Algorithm, the contribution of any argument to its parent conclusion is:

Each factor is necessary. A perfectly true argument with zero linkage contributes nothing. A highly relevant argument built on weak evidence gets discounted. And the whole system is recursive — sub-arguments feed into arguments, which feed into conclusions, with scores propagating up the entire tree automatically whenever anything below them changes.

Proportional Belief Updating: Why This Changes Everything

Linkage Scores enable mathematically precise, automated belief updates across the entire platform. When new evidence strengthens one node, every conclusion that depends on it updates automatically — in exact proportion to its reliance on that node.

Example: A landmark new study strengthens the argument "CO₂ traps heat," raising its Truth Score by 10 points.

• "Climate change is real" (linked at 90%) → automatically gains 9 points
• "We should ban gas cars" (linked at 40%) → automatically gains 4 points

This is how a rational mind should work. When a foundational premise changes, every downstream conclusion updates in proportion to how much it depends on that premise. The platform makes that process visible, systematic, and immune to motivated reasoning.

What Low Linkage Scores Reveal

Non Sequiturs

A non sequitur is an argument where the conclusion simply doesn't follow from the premise. "Candidate X is a nice person" may score 90% on Truth but 10% on Linkage to "Candidate X will be an effective executive." Niceness is real; its predictive power for executive competence is not. Linkage Scores make that gap visible immediately.

The Gish Gallop, Neutralized

One of the oldest tricks in debate is the Gish Gallop: bury your opponent in a blizzard of loosely related, technically-true facts. Without Linkage Scores, volume wins. With them, 100 weak connections (linkage: 0.1) are mathematically outweighed by a single strong one (linkage: 0.9). The algorithm does not get tired or impressed by quantity.

Hidden Assumptions

Often a low Linkage Score is not a logical failure — it is a sign that an unstated assumption is doing heavy lifting in the background. "We have global warming" only weakly links to "We need a carbon tax" (linkage: ~40%) because several steps sit between them: that carbon taxes reduce emissions, that they outperform alternatives, that the economic trade-offs are acceptable. When the system detects a moderate linkage, it prompts: "Is there a missing assumption required to connect these ideas?" Users can then add an Assumption node to bridge the gap, making the hidden reasoning explicit and testable.

How the Platform Elicits Linkage Scores

Rather than letting users freely assign a number (which invites gaming), the platform derives scores from answers to specific diagnostic questions:

• Direction: Does this argument support or oppose the conclusion?
• Relevance: If this argument were proven 100% true, would it force an update to the conclusion?
• Necessity: If this argument were proven false, would the conclusion suffer significantly?
• Sufficiency: Does this argument alone justify the conclusion, or does it require additional support?

The platform also runs two automated checks. When an argument scores high on Truth but low on Linkage, the interface flags it as "True but Irrelevant." When community scoring settles on a moderate Linkage (40–60%), the system prompts users to identify the missing assumption and add it as its own debatable node.

System Logic Requirements for Developers

The following describes the logical architecture the Linkage engine requires, without prescribing implementation patterns.

The Linkage Score is a property of the edge (the connection between two beliefs), not either belief itself. A single argument can have a 90% linkage to one conclusion and a 15% linkage to a completely different conclusion — these are independent relationships stored separately. Community votes on linkage are weighted by each voter's established reputation in logical reasoning, not general popularity. When a Linkage Score changes significantly, the system propagates the effect up the tree, recalculating every ancestor node that depends on it. This recursive propagation is the same mechanism that makes the entire ReasonRank system self-correcting.

See Also:

• Truth Scores — Measuring factual accuracy, independent of relevance.
• ReasonRank — The master scoring algorithm.
• Assumptions — Bridging the gap in low-linkage arguments.
• Importance Score — The third factor in the contribution formula.

Contact me to help refine Linkage scoring definitions.