S. S. Stevens proposed in 1957 that the relationship between physical stimulus intensity and perceived magnitude follows a power function rather than Fechner's logarithmic function. Through magnitude estimation experiments — where observers assign numbers proportional to perceived intensity — Stevens found that the exponent n varies systematically across modalities.
ψ = perceived magnitude
I = physical intensity
k = scale constant
n = exponent (modality-specific)
Exponents Across Modalities
The exponent determines whether the psychophysical function is expansive (n > 1), compressive (n < 1), or linear (n = 1). Electric shock has n ≈ 3.5 (strongly expansive — small increases in current produce large increases in pain), while brightness has n ≈ 0.33 (strongly compressive). Length estimation yields n ≈ 1.0, and loudness gives n ≈ 0.67. These exponents have proven remarkably stable across laboratories, cultures, and decades.
Theoretical Implications
Stevens argued that his Power Law was more fundamental than Fechner's Log Law because it was based on direct measurement of sensation rather than indirect inference from JNDs. In log-log coordinates, a power function becomes linear, and the slope gives the exponent directly. The debate between Stevens and Fechner continues, with Bayesian and information-theoretic analyses suggesting that both laws capture different aspects of the same underlying neural coding principles.