AHP in nonlinear scaling: from two-envelope problem to modeling by predictors

Abstract

Paper aims

Extending the AHP abilities to new areas from explaining the famous Two-Envelope paradox to finding priorities as functions of auxiliary variables is suggested.

Originality

The proposed innovative and advantageous approach permits to find the non-constant priorities via regression modeling for the exponential or Cobb-Douglas production functions.

Research method

Transforming the ratio scale into the additive or logarithmic scales, which correspond to the multiplicative utility function, opens new possibilities in the multiple-criteria decision making.

Main findings

Two-Envelop problem is resolved, priority vectors are presented as functions by auxiliary variables, preferences are predicted and profiled by predictors.

Implications for theory and practice

The suggested techniques open novel possibilities of multiple-criteria decisions helping to researchers and managers to discover useful features of priority behavior due to the demographic, socio-economic, or technical properties of the compared alternatives, and to find optimal solutions for individual customers.

Keywords
AHP; Two-envelope paradox; Nonlinear scaling; Multiplicative utility; Priority as function; Exponential function; Cobb-Douglas production function