Journal on Policy and Complex Systems sion choices .
It can be contended , however , that description and prescription are two facets of the same decision process ( Norton , 2005 ) and that ( 1 ) each descriptive decision algorithm , in order to formally and precisely describe the decision behavior , and ( 2 ) each “ normative ” decision algorithm — in order to arrive at a final “ correct ” recommendation — makes a priori methodological assumptions for deciding about a host of meta-decision choices .
Formally , let A ≠ ∅ be defined as a nonempty set or vector of alternatives ( also called policies , actions , strategies , or feasible solutions ) of a decision problem . 2 Further , in a most generalized sense , let a multi-criteria outcome function f be defined as follows :
( 1 ) _____________ f : A → R x Each function f k
: A → R with f k
( a ) = z k ( k ∈ { 1 ,…, x }, a ∈ A ) and f ( a ) =
( z 1 ,…, z x
) is defined as a multiple value function . In the most general sense , ϕ = ( A , f ) is defined as a multiple criteria decision-making ( MCDM ) problem , wherein ϕ is a matrix showing a generalized decision problem involving a set or vector of Alternatives A faced by n decision makers and containing f outcomes . The decision makers measure the outcomes by z x values . More specific formulation of decision problems is undertaken by adding future events ( e . g . decisions under uncertainty ) and / or replacing multi-criteria values with a utility function . Some examples of specific formulation of decision problems can be seen in the literature cited in Table 1 .
For defining and solving the decision problems in public decision-making contexts , next , the formal version of four meta-decision problems — choosing the alternative set , criteria set , weighting methodology , and method set — are presented in the decision problem formulation context of equation 1 . Other meta-decision choices mentioned in Table 1 are not explicitly addressed to delimit the scope of this paper . A brief review of the meta-MCDM problem is then undertaken to demonstrate that algorithmic solutions to model and understand meta-MCDM problems face severe constraints in the case of designing environmental policies .
2.1 . Choice of Space – Time Boundaries
The first meta-decision problem concerns whether the set of alternative paths A is a finite set ( as defined by many Expected Utility and Multiple Attribute Decision-Making ( MADM ) theorists ) or is it infinite ( as defined by Multiple Objective Decision-Making ( MODM ) theorists ) or is it fuzzy ( as defined by Fuzzy set theorists ). Further , what meta-criteria , such as space – time boundaries of a decision problem , should be used to include or exclude an alternative path from A ? What is the logic of establishing space – time boundaries by which an alternative is included in the set of policy and planning alternatives ? These questions can be referred to as the meta-decision problem of the
2 The set of alternatives is always nonempty because the alternative of “ no action ” is always an alternative in any decision problem .
10