From memories of a quantum mechanics class and [Wikipedia](http://en.wikipedia.org/wiki/Uncertainty_principle):



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> In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously. For instance, the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.
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In practical terms the product of the uncertainty in the position and the uncertainty in the momentum is at least of the order of magnitude of the [Planck constant](http://en.wikipedia.org/wiki/Planck_constant).


A reason why an analogous of this principle could be found in social sciences is that (in my understanding) its origins are purely mathematical. It is a [Cauchy-Schwarz](http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality)-like inequality applied to the scalar product [Bra-ket](http://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation) under the dynamic of a [particular pde](http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation). However, the nanoscopic nature of quantic measurements and the ~10^-34 Planck constant are so small that the uncertainty principle is irrelevant in physics of larger particles, not to mention the other sciences.


A common operation in decision sciences is < belief || outcome > (or < price vector || vector of goods > at a larger scale) and the solution concepts in game theory, for example, allow tremblings as small as possible (epsilon > 0) with fixed outcomes! Therefore,
Is there (yet) an equivalent of Heisenberg's uncertainty principle in the game theory, decision theory etc. ?



Is there an equivalent of Heisenberg's uncertainty principle in the decision sciences ?
Let me answer in terms of operator theory. The uncertainty principle can be interpreted as some particular inequality (as you say) such as
$$
\frac{\hbar}{2}\Vert{u}\Vert^2\le \Vert{D\_xu}\Vert\Vert{xu}\Vert,
$$
inequality due to the identity
$
2\Re\langle\hbar\frac{1}{i}\partial\_x u, ixu\rangle=\hbar\Vert{u}\Vert^2,
$
and in fact to the non-commutation of the unbounded operators $D\_x=\frac{\hbar}{i}\partial\_x$ with $x$ (multiplication by $x$). Incidentally you can note that the non-commutation of bounded operators $A,B$
(say finite matrices) could never lead to 
$$
[A,B]=I\tag{NC}
$$
as it is the case for $A=\frac{1}{i}\partial\_x$, $B=ix$. In fact (NC) is not possible for matrices since the trace of a commutator is 0. This is one reason for which the quantization requires (necessarily infinite dimensional) unbounded operators.


Now this non-commutation property is at the source of quantum mechanics and produces the uncertainty principle inequalities. Each time you will have to deal with a non-commutative algebra of operators, you will have some type of uncertainty principle. In particular if your unknown quantities do not belong to a commutative algebra, you will have an uncertainty principle: the paradigmatic example remains the transfer from classical mechanics where the unknown quantities belong to a commutative algebra (functions on the phase space, such as position $x$ or momentum $\xi$), transfer to quantum mechanics where the unknown quantities are quantization of the previous quantities and are operators, such as $D\_x,x$.


The uncertainty principle is simply the signature of non-commutativity and is not limited to quantum mechanics.


