FLOOD09697

• County: Statewide
• Community: Nationwide
• Basin: Statewide
• Title: Mathematical Modeling of a Sociological and Hydrologic Decision System
• Date: 6/1/1978
• Prepared By: Institute for Social Science Research on Natural Resources, Utah State Univ.
• Floodplain - Doc Type: Educational/Technical/Reference Information

three from the values of perceived low cost, but in-
stead have exclusively positive numbers.

If the value of the perceived cost of a proposal
is placed directly into the acceptance function, IF
function Cs would have to have a maximum rather
than a minimum for acceptability. The companion
variable would have 10 be changed in that case also,
either by reversing PA YL so that it became unwilling-
ness to payor by use of another variable such as im-
portance oflost cost in a flood control proposal. If
this model is followed, it would be unnecessary 10
worry about the sign of the lerm as regression analysis
would set the sign according to the relationship of the
term with public evaluation. The sign would probably
be negative when perceived cost figures are directly
inserted into an evaluation equation. As evidenced
above, it is necessary to be concerned about zero points
of variables in interaction terms. In future research,
it is recommended that both in the public and agency
evaluation equations, the perceived cosl of a proposal
be entered. into the equation without transformation
and IF statement Cs be modified accordingly. This
would have been done with this model except Ihe equa-
tions and systems had been calibrated and some sensi.
tivity analyses performed before the problem was
found, and it was not feasible to change the equations
at thai point. The model can still be assessed with
this problem present if interpretations are adjusted
appropriately.

In the model, C IF statements are do or die
mechanisms. They all must be mel or the flood con-
trol proposal fails and the process begins anew with
another proposal. An alternate approach would be to
have a deficient level of a function trigger a second
evaluation equation. This evaluation equation would
be for a special interest group whose concern is the
same as that of the IF statemen t that triggered the use
of the equation. The factor under consideration would
then be expanded greatly for that group in the general
population. The degree of opposition by the group
could then be calculated. Rejection of a plan could
hinge on a combination of the different special inter-
est groups and/or mean public evaluations reaching
a cerlain negative level. This scheme would include
more of the dynamics and also allow for the cumula-
tive effects of different evaluations within the public.

The possibility described above is another illus-
tration of how the model can be extended 10 cover
different and more complex situations. The discussion

of this mathematical model has been thorough and
candid, and the errors and consequent problems have
been presenled. This frankness should not be held
against either the equations or the system as a whole.
The model did well, usually simulating reactions in a
reallstic way and providing insighl inlo the reverbera-
tions which a change in one or two variables can make.
Interrelationships among parts of the model, transla.
tion of the social system model into a compuler model,
and the resulls of sensitivity and simulation analyses
are discussed in the next chapters.

Summary of the General Equations
of the Model

Table 5.9 summarizes the general equations in
unstandardized form derived from application of the
theory and methodology of this study. The model is
designed to permil use of several values for the vari.
abies in order to identify possible reactions to flood
control proposals. This chapter explains development
of the equations used in the mathematical model for
the various stages of the process.

Table 5.9 brings together the various mathemati-
cal relationships proposed for representing institution-
al and public response to flood control plans by quanti-
fying the social variables and functions of a complex
system. The deductive conceptual model of Figure
4.1 was mathematized by the inductive process of the
discovery and identification of significant dependent
and independent variables. After these variables were
specified, their numerical values were determined, and
relationships among them were specified. This required
specifying different lypes of variables and factors in.
fluencing those variables. Once these elements were
developed into a mathematical model, it was possible
to simulate the decision process.

The model is not expected to provide precise
predictions of human behavior, but it is capable of
providing important insights to planners and those
making decisions in communities. Because it indicates
sensitivities, the model enhances an understanding of
the relationships between the needs, interests, inten-
sities of feelings, and possible reactions to various con-
ditions and proposed changes. In particular, the model
illuminates the interaclions between factors and rela-
tionships in the system. With further development,
this tool should help reduce poor choices and the time
for making decisions and thus reduce the social and
economic costs of flood conlrol planning.

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