Standard Simplex Conjecture for ranked choice voting

Let $\rho\in(0,1)$ and $n\geq k!+k-1$. Consider partitions $\Omega_1,\ldots,\Omega_k$ of $\mathbb{R}^n$ with Gaussian measure $\gamma_n(\Omega_i)=1/k$ that maximize the ranked-choice noise-stability problem associated with the Borda count and the Condorcet Loser Criterion. The candidate regions are the regions determined by the corresponding regular-simplex comparison inequalities. Standard Simplex Conjecture for ranked choice voting. The maximizing sets are precisely those defined in the source's equation $(\mathrm{ome1})$. This is presented as the continuous version of the Borda Count is Stablest Conjecture; its resolution is not given in the supplied text.