The dimension-dependent importance of SC performance conjecture for polar codes

Consider polar codes decoded by list decoding with a fixed list size $L$, and let $k$ denote the code dimension. Dimension-dependent SC-performance conjecture. The SC-performance of polar codes becomes more important as the code dimension $k$ increases; conversely, SC-performance becomes less important as $k$ decreases. This is a qualitative design rule for comparing polar codes under fixed-list-size decoding, and the supplied text gives no proof or resolution.