Scoring Beliefs and Conclusions: An Algorithmic Approach for an Online Forum

This online forum employs a relational database to catalog reasons supporting or opposing various conclusions. It allows users to submit a belief as evidence to back another belief (Refer to Figure #1). According to Equation #1, a conclusion receives a score derived from the scores of its underpinning assumptions. Similarly, assumption scores are calculated based on their corresponding assumptions, until we reach verifiable data.

Basic Algorithm:

Conclusion Score (CS) is a weighted sum of different types of scores, each calculated as the difference between supporting and opposing elements for the given conclusion. It is represented as:

Conclusion Score (CS) = ∑ [(LS * RS_agree - LS * RS_disagree) * RIW]
+ ∑ [(LS * ES_agree - LS * ES_disagree) * EIW]
+ ∑ [(LS * IS_agree - LS * IS_disagree) * IIW]
+ ∑ [(LS * BS_agree - LS * BS_disagree) * BIW]
+ ∑ [(LS * IMS_agree - LS * IMS_disagree) * IMIW]
+ ∑ [(LS * MS_agree - LS * MS_disagree) * MIW]

Where:

• CS: Conclusion Score
• LS is the Linkage Score, representing the strength of the connection between an argument and the conclusion it supports.
• n represents the number of steps an argument is removed from an idea. For instance, a direct reason to agree or disagree is one step removed, whereas a reason to agree with a reason to agree is two steps removed.
• RS, ES, IS, BS, IMS, and MS are scores associated with reasons, evidence, investments, books, images, and movies respectively that support or counter the belief. Each score is associated with a weighting factor (RIW, EIW, IIW, BIW, IMIW, and MIW) to signify its importance.

In this equation, each element (reason, evidence, investment, etc.) is first multiplied by its respective Linkage Score (LS) to represent the strength of the association with the conclusion, and then it contributes to the overall conclusion score (CS) in proportion to its importance weight (RIW, EIW, IIW, etc.). The score for each type is calculated as the difference between the scores for supporting and opposing elements.

Assistance Needed!
I'm seeking feedback on the clarity and feasibility of this concept. If there are any areas of confusion, or if the mathematical notation could be improved, I'd greatly appreciate suggestions.

Assumptions:
For instance, consider the belief that the leaders of Nazi Germany were evil. This belief is bolstered by many arguments, yet it can also serve as an argument itself, supporting other conclusions such as the idea that it was justifiable for the US to join WWII.

· Numerator: The numerator is obtained by subtracting the count of unique reasons to disagree from the count of unique reasons to agree. Consequently, if the "valid" reasons to agree are fewer, the numerator will be negative.

· Denominator: The denominator comprises the total count of reasons, both for and against. This computation normalizes the equation, rendering the conclusion score (CS) as the overall percentage of agreeable reasons. Therefore, the conclusion score will fluctuate between -100% and 100% (or -1 and +1).

· Definitions:
- A: Represents unique arguments that agree with a conclusion.
- D: Represents unique arguments that disagree with a conclusion.
- L: Stands for Linkage Score, a number between zero and 1. This metric quantifies the strength with which an argument is purported to support a conclusion.

· Unique Arguments: Every belief would have a template that enables the proposal of a statement that articulates the same idea more effectively. This statement would become a new argument with its unique conclusion score. For instance, if the rephrased belief gets a similarity rating of 98%, then it would contribute just 2% of its score to the new conclusion.

· For n = 1: Arguments like A(1,1) and A(1,2) are the first and second reasons to agree, respectively. Each contributes one point to the conclusion score, with the contribution moderated by the L (linkage score) multiplier.

· For n = 2: Arguments such as A(2,1) and A(2,2) are the first and second reasons to agree, where n equals 2. These could either be reasons agreeing with a reason to agree or reasons disagreeing with a reason to disagree. Each of these contributes half a point to the conclusion score due to the equation's design. Modifying the equation could change these contributions to a quarter point each to the conclusion score. This contribution is crucial since weakening an assumption logically weakens all conclusions built upon it. This value of n could be iteratively updated for reasonable results or uniquely determined by each platform. Note that D(n,j) represents reasons to disagree, and they function similarly. Here, j instead of i is used to indicate their independence. As such, second-order reasons to disagree could include reasons disagreeing with reasons to agree or reasons agreeing with reasons to disagree.

· L = Linkage Score: Let's consider the conclusion, "It was good for us to join WWII." An argument submitted could be, "Nazis were doing bad things," to support the conclusion. If this belief already has a high score of, say, 99%, it could be granted a linkage score of 90% towards supporting the conclusion. As a result, it would contribute 0.495 points (0.99 X 0.5) to the conclusion score for the belief, "It was good for us to join WWII". Another belief submitted could be, "Nazis were committing wide-scale systematic genocide," supporting the conclusion. Given that not all countries that "do bad things" justify a war, this linkage score could potentially be higher, perhaps 98%.

Investment-Based Scoring:

M = Money invested in a belief
TM = Total Money invested in the forum
#B = Number of beliefs

The average amount of money invested in an idea is computed as TM / #B. The aim of this metric is to assign 1 point for an idea with an average investment, and 2 points for a belief with double the average investment.

This concept is predicated on the idea of users being able to purchase “stock” in a belief based on its idea score, with the expectation that the idea score would rise. Transaction fees would be set high enough to prevent financial losses and ensure that only those with sound judgment profit from this mechanism. Additionally, stocks would only be sold for ideas that are relatively stable.

Certified Logic Instructors

• NP: Represents the number of times a certified** logic instructor has validated or invalidated the logic of a reason to disagree. By summing "ns", we can account for instances where a logic professor disagrees with a specific belief.

In our context, a "certified" logic instructor is defined as someone possessing a ".edu" email address associated with the philosophy department of an accredited university. This stipulation helps ensure that the individuals evaluating the logic of arguments have a credible academic background in the field of philosophy.

Book References

• B: Denotes books that support or oppose the given conclusion.
• BS: Book Score - takes into account factors like the number of books sold, as well as reviews and ratings of the books.
• BLS: Book Link Score - It's possible to have a well-regarded book that doesn't necessarily support the proposed belief. Each argument suggesting that a book supports a belief becomes its own claim with its own book "linkage score" that is calculated according to the above formula.

Voting System

• UV/DV: Upvotes or Downvotes.
• #U: Number of Users.
  We'll use an overall upvote or downvote system, in addition to votes on specific attributes like logic, clarity, originality, verifiability, and accuracy, among others.

Additional Evidence Sources

Movies, songs, expert opinions, and other sources of evidence can also support or oppose different conclusions, similarly to books. For example, movies - often documentaries - could be evaluated based on scores from sites like Rotten Tomatoes. This data could be imported, along with formal logical arguments that a movie attempts to support or oppose a belief.

**Certification for logic instructors is assumed to be from a reputable institution or organization. The exact criteria for certification can be defined based on the requirements of the forum.

Link Score (L)

When users submit beliefs as reasons to support other beliefs, they may occasionally attempt to forge a link where one doesn't truly exist. For instance, someone might submit the belief "The grass is green" as a reason to support the conclusion "The NY Giants will win the Super Bowl". Although the belief that "the grass is green" might receive a high score for its general acceptance, the "Link Score" in this context would be near zero due to its irrelevance to the conclusion.

• As we refine this system, we might have to apply multiplication factors to some elements to ensure that they do not carry too much or too little weight in the overall scoring.