|Man Without Qualities|
Monday, April 01, 2002
As everyone should know but almost nobody does, Lewis Carroll (Charles L. Dodgson), the author of the Alice books and other fanciful works, made foundational contributions to the mathematics of voting that are perhaps as profound as those made by anyone, ever. Completed at a time when such matters were of urgent public interest and of paramount importance to the then rapidly evolving British political system – in the throes of a radical expansion of its voting franchise and rethinking the very basis of its democracy – Carroll’s work was, of course, entirely ignored except in the few instances in which it was dismissed with utter contempt. It goes without saying that those involved in political matters in Carroll’s day did not understand the significance of even the most basic mathematical structures applicable to their field. On the other hand, the Alice books did pretty well.
As recounted in a marvelous book, Carroll’s profound work was rediscovered many years later by the brilliant Scottish economist Duncan Black, who explained and extended them with a commensurate profundity. Completed at a time when such matters were of urgent public interest and paramount importance to the then rapidly evolving American political system as well as to the political systems of newly emerging nations throughout the world, Black’s work was, of course, all but ignored and often dismissed with contempt. It goes without saying that those involved in political matters in Black’s day did not understand the significance of even the most basic mathematical structures applicable to their field. In such nuances the course of progress may be discerned.
The waters of representation and voting theory have remained treacherous. Lani Guinier became perhaps their most spectacular recent victim when her nomination to high office was unceremoniously withdrawn by then President Bill Clinton, who explained that he had simply not read the works of a woman who had been his “good friend” for 20 years, without explaining on what basis he had nominated her in the first place.
Carroll asked as what he called a “preliminary question” to his investigation, “are we to count population, or Electors [that is, voters] only?” He suggested that if general population and voter population are always nearly proportional to each other, then it doesn’t matter. Implicitly, he observed that if general population and voter population are not nearly proportional to each other, then it does matter which we choose to count.
Are general population and voter population nearly proportional to each other? Many people are not eligible to vote by law. The ineligible include children, non-citizens and (in many states) those convicted of a felony. For the sake of an example, consider two hypothetical Congressional districts, the first populated entirely by Hispanic and African American people in equal numbers. The number of children in such a district might be higher than average – suppose two-thirds of the district’s population are children under the age of 18. Suppose further that one-half of the Hispanic adults in the district are not citizens, and therefore are not eligible to vote and that the district lies in one of the states that prohibit all felons from voting-whether in prison, on probation, on parole, or having fully served their sentences (including Alabama, Nevada, New Mexico, Virginia, and Wyoming). In such states, one-quarter to one-third of all adult African-American men are excluded from the franchise. Combined, the eligibility requirements reduce the fraction of people in the district who are qualified to vote to something like 5/24, or about twenty per cent of the total populace of this district.
Suppose the second district consists entirely of retired, white citizens. Combined, the eligibility requirements leave the fraction of people in this district who are qualified to vote at one hundred per cent of the populace of this district.
The two districts have the same population, yet the number of voters in one is roughly one-fifth the number of voters in the other. This means that in electing a member of the House of Representatives, the vote of each voter in the first district has roughly five times the weight of the vote of each voter in the second district. This result – set by the Constitution for Congressional districts - is mandated throughout the legislatures of each State and elsewhere as the direct and necessary consequence of the Supreme Court’s so-called “one person-one vote” line of cases.
Two Congressional districts approximately fitting the above suppositions may or may not exist. But it is quite clear that the use of general population to define political districts must combine with the irregular distribution of ineligible voters to give some voters vastly more power to elect members in the House of Representatives (or to the State legislatures) than voters in other districts. The ratio in the Congressional case may not reach five-to-one, but it is hard to believe the ratio does not exceed two-to-one. This is unavoidable under the Constitution with respect to the House of Representatives, but the Supreme Court had to demolish many decades of its own Constitutional precedent to impose this result on the State legislatures. Imposing its so-called “one person-one vote” rules on the nation the Supreme Court famously said:
"Legislators represent people, not trees or acres. Legislators are elected by voters, not farms or cities or economic interests. … And, if a State should provide that the votes of citizens in one part of the State should be given two times, or five times, or 10 times the weight of votes of citizens in another part of the State, it could hardly be contended that the right to vote of those residing in the disfavored areas had not been effectively diluted. It would appear extraordinary to suggest that a State could be constitutionally permitted to enact a law providing that certain of the State's voters could vote two, five, or 10 times for their legislative representatives, while voters living elsewhere could vote only once. And it is inconceivable that a state law to the effect that, in counting votes for legislators, the votes of citizens in one part of the State would be multiplied by two, five, or 10, while the votes of persons in another area would be counted only at face value, could be constitutionally sustainable. … The resulting discrimination against those individual voters living in disfavored areas is easily demonstrable mathematically. Their right to vote is simply not the same right to vote as that of those living in a favored part of the State. Two, five, or 10 of them must vote before the effect of their voting is equivalent to that of their favored neighbor. Weighting the votes of citizens differently, by any method or means, merely because of where they happen to reside, hardly seems justifiable. One must be ever aware that the Constitution forbids "sophisticated as well as simple-minded modes of discrimination."
Can the Supreme Court’s “one person-one vote” rule, which leads to voters in one district having their votes multiplied in power in comparison to other districts, as the example above illustrates, really be justified by the Court's observation that “it is inconceivable that a state law to the effect that, in counting votes for legislators, the votes of citizens in one part of the State would be multiplied by two, five, or 10, while the votes of persons in another area would be counted only at face value, could be constitutionally sustainable.”
The Supreme Court’s reasoning appears to emerge from the other side of Mr. Carroll’s famous Looking Glass. Perhaps the good Justices should spend more time reading his mathematical texts – and less time patterning their writing after the Alice books.
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