本文探讨了在面对大量选项时，进行“最佳”评判的困难性。作者指出，由于“优秀”等概念的模糊性，以及选项数量增多导致选项间质量差异减小的趋势，使得进行可靠的比较变得困难。作者以正态分布为例，说明了当选项数量增加时，比较选项的难度也随之增加，找到“最佳”选项的可能性降低。文章强调，在面对大量选项时，与其追求“最佳”，不如寻找“明显优秀”的选项，并通过比较将其筛选到前列。

🤔 **模糊性导致难以进行可靠的比较：** “最佳”等评价标准具有主观性和模糊性，只有当选项之间差异足够大时，才能进行明确的比较。随着选项数量的增加，选项间的质量差异会趋于缩小，使得比较结果变得不稳定和不可靠。

📈 **选项数量与比较难度成正比：** 作者以正态分布为例，说明了当选项数量（n）增加时，比较选项所需的难度也随之增加，因为选项间的差异会逐渐减小，找到“最佳”选项的概率也随之降低。

📊 **“最佳”的确定需要大量比较：** 只有当选项数量较少，或者投入大量精力进行比较时，才能确定一个选项在特定类别中“最佳”。因为“最佳”意味着优于其他所有选项，这需要进行严格的比较和验证。

💡 **从“最佳”到“明显优秀”：** 作者建议，与其追求“最佳”，不如寻找“明显优秀”的选项，即选择一个相较于其他选项都表现出“优于”或“不确定”关系的选项，将其筛选到前列。

🗣️ **案例：食物、邻居、编程语言等：** 作者以食物、邻居、编程语言等领域为例，说明了在面对大量选项时，找到“最佳”选项的困难性，因为这些领域都包含数十种甚至上百种选项，难以在合理的时间内进行全面比较。

Published on December 4, 2024 8:46 PM GMT

If you ask for my "favourite", or whatever is "best", in any broad domain, I will refuse to answer, or else give an answer I know to be probably wrong.

Goodness-judgments are fuzzy, i.e. subjective and intuitive. Fuzzy values only compare one way or the other when values compared are far enough apart. The more items there are to compare in a set, the closer together their respective qualities will be, on average. Hence, as sets get larger, fuzzy comparisons among its members get less reliable.

Something confidently known to be best in its category is (definitionally) known to be strictly better than each other item in its category. So we can only be certain about the best item in a category if the category is small, or if we expend great effort to compare items.

More precisely, suppose you ask about a domain of n objects, with qualities ($x_1$ thru $x_n$) sampled from a normal distribution. In the average scenario, the normal CDF of $x_1$ thru $x_n$ is evenly-spaced by $\frac{1}{n}$. To find the best item, we must (at worst) compare best to second-best. That entails comparing inverse CDF values at $\frac{2n-1}{2n}$ to those at $\frac{2n-3}{2n}$.

Comparing is difficult in inverse proportion to the difference. As n increases, that difference in inverse CDF values approaches $\frac{1}{2}$.

Questions about favourites have included foods, neighbours, and programming languages. In each case, I'm familiar with dozens of options. That large n prohibits finding a confidently, correctly-known best option in any convenient timescale.

"X" isn't [my favourite] word, but it's the first word that comes to mind.

— Chuck Palahniuk, approximately

What I can do instead is alter the question from "which is your favourite?" to "which is distinctly good?", picking an option which compares as either greater-than or ambiguous against each other option, and so is in the top few.

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