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Related Concept Videos

Measures of Intelligence01:29

Measures of Intelligence

Psychologists measure intelligence by using standardized tests that produce a score known as the intelligence quotient or IQ. To understand IQ tests, it's important to recognize the key principles behind their construction: validity, reliability, and standardization.
Validity refers to how well a test measures what it claims to measure. An intelligence test should accurately assess intelligence rather than another characteristic, like anxiety. Criterion validity is one way to evaluate this; it...
Ratio Level of Measurement00:54

Ratio Level of Measurement

The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. For analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
A set of data measured using the ratio scale takes care of the ratio problem and provides complete information. Ratio scale data are like interval scale data, except they have a zero point and ratios can be calculated. For...
Nominal Level of Measurement00:56

Nominal Level of Measurement

The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. Not every statistical operation can be used with every set of data. For analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
The data that cannot be measured but can be grouped into categories fall under the nominal level of measurement. Data that is measured using a nominal scale is...
Law of Rational Indices01:29

Law of Rational Indices

The Law of rational indices is a fundamental principle in the field of crystallography. According to this law, the intercepts of a crystal face along the crystallographic axes (the three-dimensional axes along which a crystal is measured) can be expressed as either equivalent to the unit intercepts (a, b, c) or simple whole number multiples of them. These multiples are typically denoted as na, n'b, and n''c, where n, n', and n'' are simple whole numbers.To illustrate, consider a crystal with...
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
Rationalizing Substitutions01:29

Rationalizing Substitutions

Integrals involving non-rational functions are often difficult to evaluate using standard techniques, especially when radicals appear in the integrand. Rationalizing substitution provides a systematic method for simplifying such integrals by converting them into rational forms that are easier to handle.Consider a rod whose linear mass density depends on a constant linear density, a characteristic length, and the distance from the left end of the rod. Determining the total mass requires...

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Related Experiment Video

Updated: Jul 12, 2026

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
03:14

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness

Published on: December 6, 2024

Benchmarking Large Language Model Rationality Using Measurement Axioms.

Kiwon Song, James Jennings, Clintin Davis-Stober

    Research Square
    |July 10, 2026
    PubMed
    Summary

    Large language models (LLMs) often show irrational decision-making, violating preference transitivity. This new framework evaluates AI coherence beyond simple accuracy, revealing systematic issues in many models.

    Area of Science:

    • Artificial Intelligence
    • Decision Theory
    • Cognitive Science

    Background:

    • Current AI evaluations prioritize benchmark accuracy over decision coherence.
    • Interpretability and alignment with human values are hindered by opaque AI decision-making.
    • Utility theory provides axioms for rational choice, including transitivity of preference.

    Purpose of the Study:

    • To introduce a measurement-theoretic framework for evaluating AI decision-making coherence.
    • To assess Large Language Models (LLMs) for transitivity violations in preferences.
    • To provide a principled method for evaluating AI rationality beyond accuracy.

    Main Methods:

    • Applied formal axioms from utility theory, focusing on transitivity of preference.
    • Utilized classic choice paradigms known to induce intransitive preferences in humans.

    Related Experiment Videos

    Last Updated: Jul 12, 2026

    Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
    03:14

    Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness

    Published on: December 6, 2024

  • Tested 20 distinct LLMs, varying question format, generation temperature, and contextual memory.
  • Main Results:

    • Found substantial and systematic transitivity violations in many LLMs.
    • Observed patterns in violations that partially mirrored human decision behavior.
    • Demonstrated that LLM decision-making can be systematically irrational.

    Conclusions:

    • A measurement-theoretic framework offers a principled approach to evaluating AI decision coherence.
    • Transitivity violations undermine LLM interpretability and complicate alignment with human values.
    • This framework complements benchmark accuracy for a more holistic AI evaluation.