Category ►►► Mathemagics

June 15, 2010

Math-terful Solution

Elections , Mathemagics
Hatched by Dafydd

I must admit, this creative solution to an electoral dilemma in Port Chester, NY, strikes me as quite intriguing. Ordinarily, I don't like voting gimmicks; they're generally just special pleading accompanied by "affirmative action" under another name. But this system appears to be designed specifically to avoid racial preferences.

First, the problem:

Although the village of about 30,000 residents is nearly half Hispanic, no Latino had ever been elected to any of the six trustee seats, which until now were chosen in a conventional at-large election. Most voters were white, and white candidates always won.

Federal Judge Stephen Robinson, nominated by George W. Bush and confirmed in 2003, found the current situation to be in violation of the Voting Rights Act; something had to be done.

Of course, the best solution to this problem is to encourage Hispanics to turn out in greater numbers; and let's take it as given that various groups, both within and without the Hispanic community, tried to do so -- yet failed to budge the meter. Now, the normal tack taken in this liberal age would be to change the voting to district by district, then gerrymander one or two of them so that a Hispanic trustee was guaranteed. Indeed, Robinson considered that suggestion and rejected it.

But here is what he did decide instead:

[Judge Robinson] approved a remedy suggested by village officials: a system called cumulative voting, in which residents get six votes each to apportion as they wish among the candidates. He rejected a government proposal to break the village into six districts, including one that took in heavily Hispanic areas.

Let me explain, since it seems a bit confusing at first. Under the old rules, there were six seats and some number of candidates, larger than six. Each voter could cast one vote for up to six different people, and the top six vote-getters were elected.

For sake of clarity, let's change the situation from one of race, which carries too much emotional baggage, to one of party affiliation. Let's assume a hypothetical in which the voting pool comprises 10,000 people, 5,500 of them Democrats and 4,500 Republicans. And let's further assume that for each of the six seats, one Democrat and one Republican runs. Finally, we assume that 90% of Democrats will vote for the Democrat in any contest, while 90% of the Republicans will vote for the Republican.

In each of the six races, the Democrat will get 5,400 votes, while the Republican gets 4,600. That is, despite a 55-45 split among voters -- which, if carried onto the Board of Trustees, would yield 4 Democrats and 2 Republicans -- the actual result is 6 Democrats and 0 Republicans; the Democrats overpower the Republicans on each and every seat.

But under a cumulative-voting system, each voter gets six votes, which he can cast any way he wants -- including all six for the same candidate. Note that every voter, without exception, gets six votes to cast any way he or she desires... not just the minority.

(Giving extra votes just to the minority is the sort of system championed by Lani Guinier, Bill Clinton's nominee to be Assistant Attorney General for the Civil Rights Division; which is why she was forced to withdraw a month after being nominated.)

Under the system Judge Robinson ordered, in our hypothetical example, the Republicans can focus like a laser beam on, say, only two of the six GOP candidates, Ron Nahasapeemapetilon and Nancy Ginsburg: Each Republican voter casts three votes to Nahasapeemapetilon and the other three to Ginsburg.

Assuming the Democrats don't try to vote defensively but instead vote as normal, then Nahasapeemapetilon and Ginsburg will each be elected with more than 12,000 votes; and the Board of Trustees will have four Democrats and two Republicans... which is certainly more representative than six and zip.

The scheme relies upon the strong probability that getting at least a couple minority candidates elected will be more important to minority voters than blocking them would be to the majority; minority voters are more likely to concentrate their votes than majority voters.

Thus even in the real world, where an election will always see both minority defections and some members who cannot bring themselves to throw four of their six candidates under the wolves, the odds are still pretty good that both Nahasapeemapetilon and Ginsburg will be elected.

Or in the case at hand, that a couple of Hispanics will, in fact, be elected to the BoT. Yet no racial or ideological group is being singled out for special preferences; in theory, the majority could focus their own votes to keep both of the two (or three) "focus" minorities off the board; it's just very unlikely to happen for the reason above.

I haven't studied this fully, and I'd like to see some real-world examples; but it is at the least an interesting example of sideways thinking, which I always admire even on those occasions where I oppose the sideways thought itself.

Hatched by Dafydd on this day, June 15, 2010, at the time of 4:53 PM | Comments (5) | TrackBack

October 14, 2005

New Reason to Support Harriet Miers

Injudicious Judiciary , Mathemagics
Hatched by Dafydd

I have been pretty much supportive all along, based solely on the grounds that I think it would be bad for the party if she were slammed out of bounds before she even got a hearing. Then I became more strongly attracted to the notion that we really ought always to have at least one justice who isn't a former judge and isn't an "expert" on the Constitution: "convictions make convicts," as Timothy Leary used to say (I mean when he was alive), and experts who spend all their lives studying the writings of other experts in their subject tend to have a very subjective view indeed.

Bush believes Miers is Reaganesque in the sense of having an innate grasp of right and wrong in many circumstances, and I've seen nothing so far from her opponents that persuades me to the contrary. Examples of trivial mistakes or instances of stepping carefully through a landmine are no more persuasive than are the few mistakes Reagan himself made -- such as yanking our "peacekeeping" troops out of Lebanon directly after the Beirut massacre.

But I have just come across evidence that I haven't seen anywhere else... and this now puts me unabashedly in her corner. I now truly hope she will be confirmed.

Major Disclaimer!

I neither confirm nor deny that Patterico at Patterico's Pontifications may or may not have ever blogged on this subject, nor in the case that he has, do I either agree or disagree or even know what he may have said, in the event that he may have said anything about this at all. I am only an egg. I am Sgt. Schultz.

With that out of the way, we may proceed.

I was just reading the Wikipedia biography of Miss Miers, and I came across the following datum that absolutely clinched the decision for me:

Miers graduated from Southern Methodist University with a bachelor's degree in mathematics (1967) and from its law school with a Juris Doctor degree (1970) .

I suspect we have never had a Supreme Court Justice who actually passed classes in differential equations, possibly even partial differential equations -- and five of you reading this know how amazing that would be! -- group theory, Galois Theory, functional analysis, dynamical systems, and probably even mathematical logic. Imagine a justice who understood how to tell a convergent from a divergent infinite series, how to do a LaPlace Transform, and what Fourier Analysis is for! Or even just a justice who is comfortable thinking in N-space.

Harriet Miers has my full and unstinting support (I was about to say unqualified support, but that is too ambiguous).

Yay, team!

Hatched by Dafydd on this day, October 14, 2005, at the time of 5:41 PM | Comments (26) | TrackBack

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