It is often said that inverse problems, say the generation of an image from some remote sensing method, benefit from overdetermination by multiple measurements. It matches intuition, but other than a simple "corner case" such as reduction of white noise by signal averaging, I never see a mathematical explanation of this.
I assume this can be framed in terms of the condition number
$$ \kappa(A) = \frac{\sigma_{max}(A)}{\sigma_{min}(A)} $$
where A is the matrix of observations and $\sigma$ max and min are the highest and lowest singular values, and overdetermination is likely to lower this ratio.
The only explanation I can see, is that when the eigenvalues of $A$ are calculated, for a tall $M \times N$ matrix where $M > N$, each entry of $A^{T}A$ will sum $M$ multiplications rather than $N$ which is in fact similar to noise power reduction by signal averaging.
A good discussion of condition number takes place in [1]: it describes a poor condition number as evidence of collinearity. So perhaps the use of overdetermination is better described as strongly reducing the possibility of collinearity?
[1] Belsley, David A., Edwin Kuh, and Roy E. Welsch. Regression diagnostics: Identifying influential data and sources of collinearity. Vol. 571. John Wiley & Sons, 2005.