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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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A rational function is defined as the quotient of two polynomials:  where Q(x)≠0, These functions often exhibit asymptotes, which are the lines that the graph approaches but never touches. These asymptotes are classified based on how the function behaves near specific values of the input.Vertical asymptotes occur where the denominator is zero, and the numerator is not, causing the function to be undefined. These are found by solving Q(x)=0. For example:  has a vertical...
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Collective decision making by rational individuals.

Richard P Mann1

  • 1Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom r.p.mann@leeds.ac.uk.

Proceedings of the National Academy of Sciences of the United States of America
|October 17, 2018
PubMed
Summary
This summary is machine-generated.

This study presents a rational model for collective decision-making, explaining apparent behavioral variability through information asymmetries. It demonstrates how rational agents can produce diverse social decision rules, aligning with empirical observations in humans and animals.

Keywords:
agent-based modelcollective behaviorrational choicesocial informationutility

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Area of Science:

  • Behavioral Ecology
  • Decision Theory
  • Social Psychology

Background:

  • Collective decision-making in humans and animals is widely studied, with a focus on social feedback rules.
  • Existing models often deviate from rational choice theory to explain behavioral variability and stochasticity.
  • Understanding social information use is key to predicting group behavior.

Purpose of the Study:

  • To develop a model of social information use and collective decision-making based on fully rational agents.
  • To demonstrate how information asymmetries can explain seemingly stochastic social decision rules.
  • To reconcile rational decision-making theory with empirical observations of collective behavior.

Main Methods:

  • Developed a theoretical model of social information use.
  • Incorporated fundamental information asymmetries between agents and observers.
  • Analyzed emergent decision rules from a rational agent perspective.

Main Results:

  • The model shows that rational agents can produce a wide range of social decision rules.
  • Apparent stochasticity and variability in behavior emerge from information asymmetries.
  • Rational decision-making is consistent with observed collective behaviors.

Conclusions:

  • Rational agents can explain complex social decision-making patterns without ad hoc departures from theory.
  • Information asymmetries are a key factor in understanding variability in collective behavior.
  • The model offers testable predictions for human and animal group decision-making.