T. Takahashi, T. Cheon / World Journal of Neuroscience 2 (2012) 183-186 185

often appears in quantum decision theory [9,10]. Taken

together, it can be concluded that so-called “quantum de-

cision theory” is a special case of more general nonlinear

population coding theory of neural information (i.e.,

Eq.2-1 and 2-3) in which Stevens’ exponent is fixed at s

= 2. When s is an integer larger than 2, there appears

more interference terms. It should further be noted that

the present theory removes the necessity of quantum

physical effect (and associated complex-numbered vec-

tors in the Hilbert space) in the human brain in explain-

ing the seemingly “quantum-like” phenomena in human

cognition and decision making. Also, psychophysical

experiment demonstrated that subjective intensity of muscle

force follows Stevens’ power law with the exponent

(

1.7s

http://www.cis.rit.edu/people/faculty/montag/vandplite/

pages/chap_6 /ch6p10.ht ml) which is close to 2, support-

ing our present hypothesis on human choice behavior.

3. IMPLICATIONS OF THE PRESENT

THEORY TO NEUROECONOMICS

AND DECISION NEUROSCIENCE

Rapid advances in neuroeconomics suggest the impor-

tance of psychophysical considerations for proper the-

ories in decision neuroscience (we can call it “psycho-

physical neuroeconomics”, [23-26]). For instance, ano-

malies in human decision making (i.e., deviations from

normative decision theory or axioms in microeconomics)

such as preference reversal over time in intertemporal

choice has been explained by nonlinearity of subjective

time in terms of physical time [25-28]. Therefore, future

studies in neuroeconomics and decision neuroscience

should incorporate the nonlinearity arising from popu-

lation vector cording of decision parameters (e.g., utility

function, psychological time, subjective probability, pro-

bability weighting function), by combining neuroeco-

nomic theory and quantum theory of cognition and de-

cision.

4. ACKNOWLEDGEMENTS

The research reported in this paper was supported by a grant from the

Grant-in-Aid for Scientific Research (Innovative Areas, 23118001;

Adolescent Mind & Self-Regulation) from the Ministry of Education,

Culture, Sports, Science and Technology of Japan.

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