Bell Curve The Law Talking Guy Raised by Republicans U.S. West
Well, he's kind of had it in for me ever since I accidentally ran over his dog. Actually, replace "accidentally" with "repeatedly," and replace "dog" with "son."

Monday, August 31, 2009

Redistricting Redux

I found an intriguing paper on redistricting by Zeph Landau, a mathematician at UC Berkeley. In it he proposes a novel method of redistricting (for two major parties only) which I think The Citizens might appreciate. I do my best to summarize it here.

The essence of the method is to divide the state in two and let the Republicans draw all the boundaries for one part while the Democrats draw all the boundaries for the other. The paper largely deals with the critical issue of how to divide the state initially. It would be elegant if we could do it in the classic way in which two children can divide a slice cake--one cuts and the other chooses--but unfortunately party preferences are not that simple and it is possible for one party to partition the state such that it will be to their advantage no matter which region they end up with.

Fortunately, there is a more robust variant of this method. Start with the most unequal partition possible (the smaller portion containing only enough people to elect a single representative) and then grow the smaller region in mincing steps until the inequality has been completely reversed. At each step along the way, ask the parties to indicate which region they would prefer to redistrict. If at any time the parties prefer opposite regions, then agreement has been reached--but otherwise just wait for that critical juncture when both parties "jump" from preferring region A to preferring the region B--then choose randomly between the proposed partitions from the steps immediately before and after the jump. One can make the method even more robust by running through the entire exercise several times and choosing the final outcome deemed least objectionable by both parties.

This proposed redistricting process has several nice features. First, it avoids the whole "non-partisan" issue. Second, the paper demonstrates that this method can be relied upon to produce an outcome that neither party will find particularly disadvantageous, even when their preferences are based on completely different principles. (For example, one may seek to maximize the size of its delegation while the other seeks to protect its incumbents.) Finally, despite the lengthy description here, this method is actually more practical than most such programs because only a single "cut" needs to be decided upon: after that the individual parties do all the rest of the work.

Anyway, I thought it was pretty interesting. It just goes to show that we can harness the adversarial process in more clever ways than we usually do.

(One technical note: Since party preferences are not necessarily linear, there may be several "jumps" from which one would have to randomly draw.)


Raised By Republicans said...

Sounds neat. One problem. The Democrats currently expect a HUGE advantage if they control the legislature at the time of the next redistricting (a likely event). So switching to this plan would represent a significant loss of advantage for them. What incentive would they have to agree to the switch?

That this plan only works for two parties, isn't a particularly nasty problem for me. You don't tend to see multi party systems unless you have a proportional electoral system of some kind and district size and shape has different effects in those kinds of systems. When you have single member districts (like we have in the US and UK and Canada), you CAN see more than one party in the system as a whole but in any one district you will only see two competitive parties (for the most part).

Dr. Strangelove said...

I agree: There is no incentive for the Democrats in California to change at this point.

The Law Talking Guy said...

We enacted Proposition 11 in 2008 that provides for a "citizens" redistricting commission for all state senate and assembly districts. It does not apply to Congressional districts. So we can see, perhaps, with two overlapping systems at once, how legislative and "nonpartisan" redistricting look. Note that there are 80 assembly seats, 53 US Congressional seats (not subject to the rule) and 40 state senate seats. The rough equivalence means we can examine how gerrymandered one set is over the other.

The Law Talking Guy said...

I think the Dems should agree to such a redistricting plan as part of a "precondition" (to use an awful word) of a constitutional convention.

Dr. Strangelove said...

What was your opinion of this method?

Raised By Republicans said...

At the risk of going off topic, why would we expect a constitutional convention to be more likely after redistricting reform?

Dr. Strangelove said...

I think LTG was suggesting that the Democrats really want a California state constitutional convention, and they should be willing to accede to a Republican demand for this kind of redistricting in order to get it. Because, as you indicate, at the moment it would help Republicans.

Raised By Republicans said...

Got it. Of course, that deal won't happen if the Democrats think they can get over the 2/3 threshold through redistricting.

The Law Talking Guy said...

RBR - as I mentioned, the redistricting for state offices is no longer in the legislature's sole hands in California after Prop 11 in 2008. So the Dems can't bet on a successful gerrymander for 2010. So that's why - as I mentioned before - Democrats could offer a redistricting tradeoff or a "condition" of the desired constitutional convention

The Law Talking Guy said...

Your summary is interesting, Dr.S., but the paper itself is fairly opaque to a non-mathematician. There, I said it. I need a little bit of plain English to go along with my math. One of the inherent difficulties in academic settings is the tendency of academics to express themselves only in the jargon of their field.

I puzzled over this description for quite a while, "Let us suppose that we would like to produce a division of a state into n
districts with d people in each district. Before describing the protocol, we
need to define the notion of a k split. Consider splitting the state into two
contiguous pieces, call them X and Y, such that the size of the population
in the piece X is kd; we will call the pair (X,Y) a k split of the state."

If k can be any number, then can't X be any number, and Y is just what is left over from the population? Am I to understand that "k" means an integer of some kind or a number greater than one? The phrase "k split" then appears only once more in the document. What follows is a discussion of an "i split" which must be related to a "k split." Perhaps an "i split" is a particular kind of "k split," but it's not defined as such.

Yes, I am not familiar with how these mathematical papers are written. Yes, this makes me a buffoon, whatever.

I don't like being made to feel stupid when I'm perfectly sure of two things (1) that I can understand whatever the author means and (2) that it would have to be translated into my language, legalese, in order to become law anyway.

Inasmuch as Dr.S has described it, my reaction is that it violates certain philosophical ideas that resonate with voters. I know this is hard to explain, but let me try. Imagine I agree to vote for your candidate and you agree to vote for mine. We watch each other vote. A person might object that my act of voting for a person I did not choose - literally, my act of checking off someone else's choice on the page -undermines the idea of democracy. It cheapens the act of voting. You can argue about how true this is, but certainly some people will feel that way. Imagine if it is 1932 Germany and you agree to vote for a Nazi if a Nazi supporter agrees to vote for the SDP. I mean, do you really want to tick that box? Especially with hindsight? Are we so easily resolved of the responsibilities of our own actions?

By comparison also, a problem with the "national popular vote" scheme is that it requires states to be prepared to cast their electoral votes for a person that their state did not favor because of the compact. Thus, Californians could have to "vote" for McCain and Alaskans for Obama. Some just find this offensive.

Similarly, some lawyers are okay with representing horrible guilty defendants because they know that "the system" depends on it. And indeed it does. But to actually defend a person you believe in your heart is guilty of a horrible crime? To work to get that person out of jail and on the street so that he can commit another crime against another innocent person? Some cannot handle the task.

The problem with this proposal for redistricting is that it permits some pretty unsavory acts in the name of a larger balance and fairness. It permits, in other words, the corrupt acts of gerrymandering to continue, just containing the evil effects. Worse, it actually may require the corrupt acts, since the fairness of the whole seems to be predictated on an equal willingness to engage in the crassest, most partisan gerrymandering.

The Law Talking Guy said...

I meant absolved, sorry. Itchy fingers.

The Law Talking Guy said...

A focus on whether acts are just and pure, rather than results, is, of course, philosophically contested. It's more than just "do ends justify the means."

Dr. Strangelove said...

It is not you, LTG! Sadly, I actually feel this paper was one of the more transparent mathematical papers you will find out there. As one famous physicist once said, "There are only two kinds of mathematical articles: those you cannot read beyond the first page, and those you cannot read beyond the first sentence." (No doubt mathematicians feel similarly about physics papers!)

To clarify the particular paragraph you called out... the variables X and Y represent regions or areas of the state. And as you observed, the letters "i" and "k" are used to mean the same thing. So what the authors name a "i split" (or "k split") is simply a partition of the state in which region X contains enough people to elect i representatives (or k representatives). Region Y would naturally contain the remainder of the state.

The problem you are running across--and it is something we all struggle with--is that there are a lot of unwritten conventions concerning which symbol is used to mean which quantity. So those steeped in mathematical lore would immediately recognize that the capital letters X and Y are meant to represent sets or regions, while lowercase i and k are merely interchangeable indices. (Actually, the index k is more often used to indicate an index in isolation, while the index i refers to an index that belongs to a series. That is why they used different letters in different parts of the paper--but in this case it just made the paper more opaque.)

I must confess that, however bad mathematicians may be, physicists are worse. For example, E is an electric field, but E means energy; meanwhile e is an arbitrary unit vector, while e is either Euler's constant or the fundamental electric charge, depending on the context. And if you do not already know that H and B refer to magnetic fields, a great many papers on plasma physics will make no sense.

Raised By Republicans said...

LTG, yeah, as soon as I hit return on that one, I realized I misspoke. Sorry about that. What I meant to say was that if the Democrats think they can get over the 2/3 threshold for what ever reason (I think you mentioned they are hopeful of doing that soon), then they may not feel compelled to give anything to the Republicans.

The Law Talking Guy said...

If you want to see a masterful example of legal obfustication, check out Section 394 of the California Code of Civil Procedure. Basic translation: if you are sued by another county, you can ask to move that suit to a neutral county.