Charles R. Johnson
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View article: Completions of pairwise comparison data that minimize the triad measure of inconsistency
Completions of pairwise comparison data that minimize the triad measure of inconsistency Open
We consider incomplete pairwise comparison matrices and determine exactly when they have a consistent completion and, if not, when they have a nearly consistent completion. We use the maximum 3-cycle product as a measure of inconsistency a…
View article: Exact bounds for efficient consistent matrices obtained from a reciprocal matrix
Exact bounds for efficient consistent matrices obtained from a reciprocal matrix Open
For a given reciprocal matrix A, we give a union of matrix intervals in which any consistent matrix obtained from an efficient vector for A lies, and, conversely, any consistent matrix in this union comes from an efficient vector for A. Th…
View article: AI Behavioral Science
AI Behavioral Science Open
We discuss the three main areas comprising the new and emerging field of "AI Behavioral Science". This includes not only how AI can enhance research in the behavioral sciences, but also how the behavioral sciences can be used to study and …
View article: Distributional Approach to Risk Preferences
Distributional Approach to Risk Preferences Open
We propose a distributional framework for eliciting risk preferences that treats an individual’s attitude toward risk as a full probability distribution rather than a point estimate. By parameterising preferences with the flexible beta fam…
View article: Fundamental graphs for the maximum multiplicity of an eigenvalue among Hermitian matrices with a given graph
Fundamental graphs for the maximum multiplicity of an eigenvalue among Hermitian matrices with a given graph Open
Our purpose is to identify the graphs that are “fundamental” for the maximum multiplicity problem for Hermitian matrices with a given undirected simple graph. Like paths for trees, these are the special graphs to which the maximum multipli…
View article: Perron similarities and the nonnegative inverse eigenvalue problem
Perron similarities and the nonnegative inverse eigenvalue problem Open
The longstanding nonnegative inverse eigenvalue problem (NIEP) is to determine which multisets of complex numbers occur as the spectrum of an entry-wise nonnegative matrix. Although there are some well-known necessary conditions, a solutio…
View article: Pairwise comparison matrices with uniformly ordered efficient vectors
Pairwise comparison matrices with uniformly ordered efficient vectors Open
Our primary interest is understanding reciprocal matrices all of whose efficient vectors are ordinally the same, i.e., there is only one efficient order (we call these matrices uniformly ordered, UO). These are reciprocal matrices for whic…
View article: Cycle products and efficient vectors in reciprocal matrices
Cycle products and efficient vectors in reciprocal matrices Open
We focus on the relationship between Hamiltonian cycle products and efficient vectors for a reciprocal matrix $A$, to more deeply understand the latter. This facilitates a new description of the set of efficient vectors (as a union of conv…
View article: Efficiency of the convex hull of the columns of certain triple perturbed consistent matrices
Efficiency of the convex hull of the columns of certain triple perturbed consistent matrices Open
In decision making a weight vector is often obtained from a reciprocal matrix A that gives pairwise comparisons among n alternatives. The weight vector should be chosen from among efficient vectors for A. Since the reciprocal matrix is usu…
View article: Efficiency analysis for the Perron vector of a reciprocal matrix
Efficiency analysis for the Perron vector of a reciprocal matrix Open
In prioritization schemes, based on pairwise comparisons, such as the Analytical Hierarchy Process, it is necessary to extract a cardinal ranking vector from a reciprocal matrix that is unlikely to be consistent. It is natural to choose su…
View article: Large Language Models for Behavioral Economics: Internal Validity and Elicitation of Mental Models
Large Language Models for Behavioral Economics: Internal Validity and Elicitation of Mental Models Open
In this article, we explore the transformative potential of integrating generative AI, particularly Large Language Models (LLMs), into behavioral and experimental economics to enhance internal validity. By leveraging AI tools, researchers …
View article: Sufficient conditions for total positivity, compounds, and Dodgson condensation
Sufficient conditions for total positivity, compounds, and Dodgson condensation Open
A $n$-by-$n$ matrix is called totally positive ($TP$) if all its minors are positive and $TP_k$ if all of its $k$-by-$k$ submatrices are $TP$. For an arbitrary totally positive matrix or $TP_k$ matrix, we investigate if the $r$th compound …
View article: Efficiency analysis for the Perron vector of a reciprocal matrix
Efficiency analysis for the Perron vector of a reciprocal matrix Open
In prioritization schemes, based on pairwise comparisons, such as the Analytical Hierarchy Process, it is necessary to extract a cardinal ranking vector from a reciprocal matrix that is unlikely to be consistent. It is natural to choose su…
View article: Efficient vectors in priority setting methodology
Efficient vectors in priority setting methodology Open
The Analytic Hierarchy Process (AHP) is a much discussed method in ranking business alternatives based on empirical and judgemental information. We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of …
View article: Cycle products and efficient vectors in reciprocal matrices
Cycle products and efficient vectors in reciprocal matrices Open
We focus upon the relationship between Hamiltonian cycle products and efficient vectors for a reciprocal matrix $A$, to more deeply understand the latter. This facilitates a new description of the set of efficient vectors (as a union of co…
View article: Square matrices with the inverse diagonal property
Square matrices with the inverse diagonal property Open
Producción Científica
View article: Generation Next: Experimentation with AI
Generation Next: Experimentation with AI Open
We investigate the potential for Large Language Models (LLMs) to enhance scientific practice within experimentation by identifying key areas, directions, and implications.First, we discuss how these models can improve experimental design, …
View article: L’économie de l’incertitude morale : essais en économie comportementale et expérimental
L’économie de l’incertitude morale : essais en économie comportementale et expérimental Open
This thesis, rooted in experimental economics, political behavioral economics, and macroeconomic behavioral economics, tackles diverse topics concerning the decision-making processes of economic agents. In the first chapter, we conduct an …
View article: Efficient vectors for block perturbed consistent matrices
Efficient vectors for block perturbed consistent matrices Open
In prioritization schemes, based on pairwise comparisons, such as the Analytical Hierarchy Process, it is important to extract a cardinal ranking vector from a reciprocal matrix that is unlikely to be consistent. It is natural to choose su…
View article: The complete set of efficient vectors for a reciprocal matrix
The complete set of efficient vectors for a reciprocal matrix Open
Efficient vectors are the natural set from which to choose a cardinal ranking vector for a pairwise comparison matrix. Such vectors are the key to certain business project selection models. Many ways to construct specific efficient vectors…
View article: Efficient vectors in priority setting methodology
Efficient vectors in priority setting methodology Open
The Analytic Hierarchy Process (AHP) is a much discussed method in ranking business alternatives based on empirical and judgemental information. We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of …