Projective Market Model Approach to AHP Decision-Making

TL;DR

This paper extends the Analytic Hierarchy Process (AHP) to projective geometry, enabling intransitive decision-making and linking it with portfolio theory for broader applications.

Contribution

It introduces a novel projective geometry framework for AHP, generalizing it to intransitive cases and providing financial interpretations.

Findings

Extended AHP model to intransitive preferences

Unified AHP with portfolio theory concepts

Proposed simplified version of the generalized model

Abstract

In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the Analytic Hierarchy Process (AHP). We use these observations to extend the AHP model to projective geometry formalism and generalise it to intransitive case. We give financial interpretations of such generalised model and propose its simplification. The unification of the AHP model and projective aspect of portfolio theory suggests a wide spectrum of new applications such extended model.