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

Lipovetsky, Stan

doi:10.1590/0103-6513.20210007

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Thematic Section - Advances in Analytic Hierarchy Process • Prod. 31 • 2021 • https://doi.org/10.1590/0103-6513.20210007 linkcopy

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

Authorship SCIMAGO INSTITUTIONS RANKINGS

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

ratio K	Shares (5)	Logarithm (8)	log/shares	log-shares	abs(log-shares)
1/9	-0.400	-0.477	1.193	-0.077	0.077
1/8	-0.389	-0.452	1.161	-0.063	0.063
1/7	-0.375	-0.423	1.127	-0.048	0.048
1/6	-0.357	-0.389	1.089	-0.032	0.032
1/5	-0.333	-0.349	1.048	-0.016	0.016
1/4	-0.300	-0.301	1.003	-0.001	0.001
1/3	-0.250	-0.239	0.954	0.011	0.011
1/2	-0.167	-0.151	0.903	0.016	0.016
1	0.000	0.000		0.000	0.000
2	0.167	0.151	0.903	-0.016	0.016
3	0.250	0.239	0.954	-0.011	0.011
4	0.300	0.301	1.003	0.001	0.001
5	0.333	0.349	1.048	0.016	0.016
6	0.357	0.389	1.089	0.032	0.032
7	0.375	0.423	1.127	0.048	0.048
8	0.389	0.452	1.161	0.063	0.063
9	0.400	0.477	1.193	0.077	0.077
mean	0.000	0.000	1.060	0.000	0.031
std	0.330	0.363	0.098	0.042	0.026

	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-0.0077	0.2545	-0.0301	0.9761
A	-0.7938	1.0844	-0.7321	0.4689
H	-1.0094	1.0844	-0.9308	0.3581
gender.1	0.5447	0.4405	1.2366	0.2243
age.1	-0.0019	0.5361	-0.0036	0.9972
Household.1	-0.3090	0.3080	-1.0033	0.3224
Education.1	-0.0844	0.3844	-0.2196	0.8274
Employment.1	0.1885	0.2428	0.7765	0.4425
Income.1	1.3361	0.2410	5.5437	0.0000
gender.3	-0.0576	0.4405	-0.1307	0.8968
age.3	0.2398	0.5361	0.4473	0.6573
Household.3	-0.0125	0.3080	-0.0405	0.9679
Education.3	0.3052	0.3844	0.7939	0.4324
Employment.3	0.3348	0.2428	1.3792	0.1763
Income.3	0.6978	0.2410	2.8954	0.0064
R²	0.7327
F-statistic	7.05
p-value	1.14E-06

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