Multi-objective decision making by reference point theory for a wellbeing economy

Abstract

Traditionally, perhaps unconsciously, all multi-objective decision methods, reference point theory included, are situated in the production sphere. In production economics, it is quite common that measurement is done in a linear way. The consumption sphere asks for another approach. In the wellbeing economy consumer sovereignty is put central. Indifference Curves visualize the economic Law of Marginal Decreasing Utility on its turn the translation of consumer sovereignty. With reference point theory the danger exists that the Reference Point is situated above the highest possible indifference curve. In addition, a reference point will have a tendency to pull the discrete points of the alternatives into the forbidden zone, the target being to minimize the corresponding distances. The Minkowski Metric shows different forms of reference point theory, which are very unsatisfactory such as the Rectangular Distance Metric and the Euclidean Distance Metric. In this way, one can criticize all other values given to the Minkowsky metric too, with exception of infinity (the Min-Max Metric). Tests show that Min-Max normalized with ratio analysis is the most in concordance with indifference curves analysis.

Appendix

Table 2 Min-Max with Square Root Ratios: ${\text{Min}}.\,M_{j} = {\mathop {{\text{Min}}}\limits_{{\left( j \right)}} }{\left\{ {{\mathop {\max }\limits_{{\left( i \right)}} }{\left( {r_{i} - {}_{{\text{N}}}x_{{ij}} } \right)}} \right\}}$ with ${}_{{\text{N}}}x_{{ij}} = \frac{{x_{{ij}} }} {{{\sqrt {{\sum\nolimits_{j = 1}^m {x^{2}_{{ij}} } }} }}}$

Table 3 Min-Max with Total Ratios: ${\text{Min}}.\,M_{j} {\text{ }} = {\text{ }}{\mathop {{\text{Min}}}\limits_{{\left( j \right)}} }{\left\{ {{\mathop {\max }\limits_{{\left( i \right)}} }{\left( {r_{i} - {}_{{\text{N}}}x_{{ij}} } \right)}} \right\}}$ with ${}_{{\text{N}}}x_{{ij}} = \frac{{x_{{ij}} }} {{{\sqrt {{\sum\nolimits_{j = 1}^m {x_{{ij}} } }} }}}$

Table 4 A rectangular Metric: ${\text{Min}}.\,M_{j} = {\sum\nolimits_{i = 1}^{i = n} {{\left( {r_{l} - {_{\text{N}} x_{{ij}}} } \right)}} }$ where j = 1, 2,……,m; m: the number of alternatives

Table 5 Rectangular Metric with weight 2 for leisure: ${\text{Min}}.\,M_{j} = {\sum\nolimits_{i = 1}^{i = 2} {{\left( {r_{i} - \omega _{i} x_{{ij}} } \right)}} }$ with ω₁ = 2 ω ₂ = 1

Table 6 Rectangular Metric with weight 2 for salary: $Min.\,M_{j} = {\sum\nolimits_{i = 1}^{i = 2} {{\left( {r_{i} - \omega _{i} x_{{ij}} } \right)}} }$with ω₁ = 1 ω₂ = 2

Table 7 Euclidean Metric ${\text{Min}}.\,M_{j} = {\left\{ {{\sum\nolimits_{i = 1}^{i = n} {{\left( {r_{i} - {_{{\text{N}}} x_{{ij}}} } \right)}^{2} } }} \right\}}^{{1/2}}$ where j = 1, 2,……,m; m: the number of alternatives