eliciting m.f. from Payoff function.

Wen-Feng Hsiao (d8442803@student.nsysu.edu.tw)
Tue, 26 Oct 1999 20:14:32 +0200 (MET DST)

Dear experts,

Recently I have surveyed several membership function elicitation
methods. But I cannot understand the detailed procedure of the 'payoff'
method.

Giles (1979, 1982) defines the degree of membership for the proposition
"x is S" is the amount of money one would be willing to wager in a "fair
bet" against an opponent who has agreed to pay \$1 if x is not S.

From the above description, I can define a "fair bet" as:

p -> -\$m
1-p -> \$1

, where p is the 'chance' that "x is S" and m is the amount that one
wagers. Since it is a "fair bet", the Expected Value should be 0. Thus,
m*p = 1*(1-p). => m = (1-p)/p. Then, it meets difficulties when p
approaches to 0. Further, m will reach 1 when p = 0.5. Do I figure it
wrong? Please give me some help. Thanks!

Wen-Feng Hsiao

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