Epistemologium
Methods, assumptions & limits
How to reproduce and interpret Epistemologium's constructed mathematical investigations.
A claim should have visible workings
We distinguish observed evidence, constructed models and interpretation. The opening investigations use constructed models. No numbers on these pages are presented as measurements of an organization or its workers.
The coalition model
There are three contributors, A, B and C, and eight possible coalitions including the empty set. The empty set has value zero. Inputs are nonnegative whole numbers up to 1,000 in illustrative units.
For each of the six permutations, a person's marginal contribution is the coalition's value after their arrival minus its value before their arrival. Their allocation is the arithmetic mean of those six contributions.
Here the sum runs over all six orders, and Pᵢ is the set of contributors preceding i in that order. Telescoping differences make every row sum to v(ABC). Averaging preserves that total.
Assumptions & limits
- Coalition values are supplied, not inferred by the calculator.
- All orders have equal weight.
- The output measure is the same for all coalitions.
- Values need not be monotone: adding someone can reduce output, producing a negative marginal contribution.
- An allocation under these assumptions is not a judgment of someone's worth or a complete theory of fairness.
Reproduce a result
Copy this state preserves the model version, seven editable values, selected order and contributor in the URL. Download workings exports the input values, all six rows and exact fractional allocations as JSON. Invalid or unsupported states restore the original example with a visible notice.
Provenance and shared origins
Provenance records where something came from and how it was derived. In this simplified citation model, a report points to what it cites; an observation ends a known path.
Six reports can reach O1 through several intermediate reports. That is six reports and one reached observation. A report with both a known origin and a missing branch belongs in both the known and unresolved counts.
Distinct origins do not establish independence, reliability or truth. An untraced report is missing lineage, not an extra observation.
provenance-v1 · bounded constructed inputs, exact workings, versioned links and fixed records. Saved comparisons require compatible definitions; unsupported model versions remain read-only.
Definitions and primary sources → · Open the instrument →Aggregation and Simpson’s paradox
An aggregate rate combines group rates using population weights. Simpson’s paradox describes a reversal between an aggregate comparison and the comparisons within its groups.
Period A: 80/100 in the higher-rate group and 20/100 in the lower-rate group, totaling 100/200. Period B: 18/20 and 54/180, totaling 72/200. Both group rates rise ten percentage points; the observed overall rate falls fourteen. Equal 50/50 weights give B 60%.
A reversal in aggregate rates does not establish a causal effect or improvement for every individual. Equal weights describe a chosen comparison, not the observed population.
aggregation-v1 · bounded constructed inputs, exact workings, versioned links and fixed records. Saved comparisons require compatible definitions; unsupported model versions remain read-only.
Definitions and primary sources → · Open the instrument →Classification thresholds
A classification threshold maps a score to a decision. Here a message is flagged when its score is greater than or equal to the cutoff. Comparing that decision with a supplied label produces one of four outcomes.
At cutoff60, seven spam messages and two legitimate messages are flagged; one spam message is missed and ten legitimate messages pass. At80, the counts are three, one, five and eleven. Precision is TP/(TP+FP); recall is TP/(TP+FN). If nothing is flagged, precision has no denominator and remains undefined.
These scores are not calibrated probabilities, and twenty supplied messages do not estimate real-world performance. Assigned costs are fictional points, not objective harm.
thresholds-v1 · bounded constructed inputs, exact workings, versioned links and fixed records. Saved comparisons require compatible definitions; unsupported model versions remain read-only.
Definitions and primary sources → · Open the instrument →Proxies and incentives
A proxy is a measure used to stand in for an intended outcome. Incentives attach a reward to a measure; the rewarded action can depend on what that measure counts.
With twenty effort units, twenty administrative closures yield twenty closed cases and zero resolutions. Ten resolutions use the same effort and yield ten closed cases with ten resolutions. At the default midpoint, five resolutions and ten administrative closures yield fifteen closed cases. The two counts overlap; they are not additive categories.
This model supplies the action costs and assumes perfect confirmation of resolutions. It does not predict how real people behave or prove that every target fails.
incentives-v1 · bounded constructed inputs, exact workings, versioned links and fixed records. Saved comparisons require compatible definitions; unsupported model versions remain read-only.
Definitions and primary sources → · Open the instrument →Network sampling
A sampling procedure determines how often each member can enter a sample. In a simple undirected network, a person’s degree is their number of connections. Uniform edge-end sampling reaches a person in proportion to that degree.
In the eight-person star, the degrees sum to14, so the uniform-person mean is14/8=1.75. Squared degrees sum to56, so the uniform-edge-end mean is56/14=4. The center has weight1/8 as a person and7/14 as an endpoint. With no edges, endpoint sampling is undefined. Choosing a person first and then their neighbor is a different procedure.
These are two exact sampling procedures on a supplied graph. They do not show that every person has fewer connections than their contacts, or measure friendship quality.
networks-v1 · bounded constructed inputs, exact workings, versioned links and fixed records. Saved comparisons require compatible definitions; unsupported model versions remain read-only.
Definitions and primary sources → · Open the instrument →Constraints and objectives
A constraint determines which assignments are allowed. An objective ranks the allowed assignments using a stated measure. Multiple objectives can prefer different assignments, and a high total can hide a poor outcome for one person.
Every guest occupies one of 24 seats, with six seats at each of four tables. Alex and Morgan need designated accessible positions. Blair and Harper, and Noor and Taylor, must sit at different tables. Within those constraints, familiarity ranks known pairs together; introductions ranks cross-circle pairs. Both break a tie by minimizing guests with no known contact. Inclusion first minimizes guests with no known table contact, then maximizes the minimum contact count, then known pairs. Any remaining ties keep the supplied candidate order. Changing the priority changes the ranking, not the seats. Applying a plan is a separate action.
These are fictional relationships and three supplied arrangements, not a wedding-planning recommendation or a global optimum. A known contact is not a measure of comfort. Cross-circle pairs need not be new acquaintances.
seating-v1 · bounded constructed inputs, exact workings, versioned links and fixed records. Saved comparisons require compatible definitions; unsupported model versions remain read-only.
Definitions and primary sources → · Open the instrument →The selection model
Selection-v1 accepts four whole project counts totaling at most 200. Each project has a supplied strategy and known six-month outcome. Visibility changes which projects enter the view; it does not change the population. A strategy share among successes and its success rate use different denominators. Zero denominators remain undefined. These rates do not estimate a causal strategy effect.
Selection and source scope → · Try the selection explorer →
The voting model
Voting-v1 accepts counts for all six complete rankings of A, B and C, totaling at most 200 voters. Plurality counts first choices. Borda adds 2/1/0 points. Instant runoff elects a strict majority or eliminates the unique lowest candidate and transfers ballots to the next remaining choice. Every round retains all ballots. A tied-lowest elimination is unresolved; a tied final remains tied. No alphabetical tiebreaker is used.
Zero voters means no result. Saved records preserve the complete profile, rule definitions, round counts and all three outcomes. Comparisons distinguish rule changes from profile changes and never subtract points from votes or compute a winner delta.
Rule definitions and primary source → · Try the voting explorer →
The subscription cost model
The cost-v1 model calculates constant monthly price × billed seats × months. Prices are represented as whole USD cents. Both scenarios share one duration and currency; zero is a valid input. Bounds are USD 0–1,000,000 per seat per month, 0–100,000 seats and 0–120 months.
These are constructed scenarios, not observed invoices. Tax, discounts, price changes, usage charges, implementation, training and switching costs are excluded. Saved records preserve both scenarios, exact results, duration and model version. Numerical notebook comparisons require the same duration as well as the same model and currency.
Inspect the units → · Open the commitment calculator →
The denominator model
The denominator-v1 model takes three nested whole counts: completed ≤ started ≤ invited. Each must be between zero and 1,000,000. Completion among starters is completed ÷ started × 100; completion among invitees is completed ÷ invited × 100. A zero denominator has no defined rate.
The story, instrument, exported workings and saved records use the same calculation. Dots represent individuals only for cohorts up to 200; larger cohorts use group bars with exact counts. Displayed percentages are rounded to one decimal, while comparisons use the unrounded values.
Saved experiments are explicit, fixed records in this browser. Reopening creates a working copy. A model-version change never silently recalculates an old record. Unknown versions remain readable where the recorded format is supported. Private reflections stay out of shared links.
Definition, source and limits →
Primary reference
Shapley, L. S. (1952). A Value for N-Person Games (RAND P-295). doi:10.7249/P0295. This link identifies the working paper edition.
Corrections
A correction should identify the affected claim, the prior value or wording, the revised result and the reason. Changes to a model require a new version so saved states cannot silently change their meaning. This is the first review edition; no correction history has been published.