论文标题
标准化人口座位指数的平等表示
Standardizing Representation for Equality with a Population Seat Index
论文作者
论文摘要
长期以来，比例代表（PR）一直认为是个人在将立法机关的席位分配给子小组中的理想体系。我们观察到PR隐含地假设（标准）代表数与人口成正比，这种情况不再自1820年代以来观察到。为了解决这个问题，我们建议通过明确指定标准功能$ f $来在更广泛的上下文中提出分配问题，以使$ f（p）$是标准的，可能是人口$ p $的代表，其中PR假设$ f（p）\ propto p $ p $。对于这个普遍的分配问题，我们给出了人口座位索引（PSI）$ \ frac {f^{ - 1}（s）} {p} $，以量化个人在为人口$ p $分配$ s $ seacts的贡献中，其中$ f^{ - 1} $是$ f $ $ f $。使用PSI，我们以绝对和相对个人平等的形式得出分配方案。特别是，对于$ s $座位，人口$ p_1，\ ldots，p_k $和标准函数$ f（p）= a + b p^γ$带常数$ a，b，b，γ\ ge 0 $，理想的，可能是子组$ i $ $ a + a + a + a + \ frac \ frac {（s-s-ka）p _ sum {s s-s-ka）p_i^raus的理想，可能是分数的座位。 p_j^γ} $，不是$ \ frac {sp_i} {\ sum p_j} $由pr计算的，该$仅适用于$ a = 0 $，$γ= 1 $。最后，由于现实世界的观察结果表明标准函数$ f \ propto p^γ$，$γ<1 $ $，我们得出结论，PR代表人口较少的亚组中的个体小于人口较多的亚组中的个人。
Proportional representation (PR) has long been believed the ideal system for the equality of individuals in apportioning the seats of a legislature body to subgroups. We observe that PR implicitly assumes the (standard) number of representatives is proportional to the population, a situation no longer observed since 1820s. To address this issue, we suggest to formulate the apportionment problem in a broader context by explicitly specifying a standard function $f$ such that $f(p)$ is the standard, possibly fractional number of representatives for population $p$, where PR assumes $f(p)\propto p$. For this generalized apportionment problem, we give a population seat index (PSI) $\frac{f^{-1}(s)}{p}$ for quantifying the contribution of an individual in assigning $s$ seats to a population $p$, where $f^{-1}$ is the inverse of $f$. With the PSI, we derive apportioning schemes with absolute and relative individual equality. Particularly, for $s$ seats, populations $p_1, \ldots, p_k$, and a standard function $f(p) = a + b p^γ$ with constants $a, b, γ\ge 0$, the ideal, possibly fractional number of seats for subgroup $i$ is $a + \frac{(S-ka)p_i^γ}{\sum p_j^γ}$, not $\frac{Sp_i}{\sum p_j}$ calculated by PR which works only for $a=0$, $γ=1$. Finally, since real-world observations indicate a standard function $f \propto p^γ$ with $γ< 1$, we conclude that PR represents individuals in less populous subgroups less than individuals in more populous subgroups.
