Monotonicity conjecture for balanced Radon partitions of Gaussian points

Let $N,dfin\mathbb{N}$ satisfy $N\geq d+2$. For a partition $[N]=A\cup B$, let $\mathbb{P}_d(A,B)$ denote the probability that $(A,B)$ is a Radon partition among $N$ independent random Gaussian points in $\mathbb{R}^d$. Consider two partitions $[N]=A\cup B=A'\cup B'$ with $|A|<|A'|\leq|B'|<|B|$. Balanced-partition conjecture. Then

$$\mathbb{P}_d(A,B)<\mathbb{P}_d(A',B').$$

The conjecture asserts that, in the random Gaussian setting, more balanced partitions are more likely to be Radon partitions. Balanced partitions are unavoidable for sufficiently large point configurations, whereas highly unbalanced partitions can be avoided; the general comparison remains open.