[EM] Thought on Redistricting Algorithms

[Abd ul-Rahman Lomax]

At 03:46 AM 6/23/2005, Alex Small wrote:

>Anyway, those are my thoughts.  I wonder if concepts of physics and phase 
>transitions might yield insight on surprising properties of seemingly 
>neutral redistricting algorithms.

I don't think the results of Mr. Small's preliminary analysis are at all 
surprising.

A useful technique in analysis is to consider the extremes, and the 
extremes in this case would be

(assuming that people vote straight party ticket)

(1) a uniform population as to voting pattern.
In this extreme district size is irrelevant: the majority party will win in 
all districts with standard plurality voting. Even if its vote margin is 
only one vote in all districts. Gerrymandering is irrelevant. Only some 
form of proportional representation will solve the problem of lack of 
representation of the minority party (or my own obvious favorite, doing 
away with elections for representatives entirely and replacing it with a 
proxy system and proportional *voting* in the representative body, which 
makes district assignments irrelevant; this *totally* solves the lack of 
representation problem which is inherent in elections).

(2) a population distributed 100% into pockets of uniform affiliation.
This situation is maximally affected by gerrymandering. District size is 
important. Again, in the extreme, if the district is the entire state, the 
minority party ends up unrepresented. And in the other extreme, tiny 
district size results in effective proportional representation.

I think it is easy to assume that the fairness function (Fairness being 
apparently inversely proportional to uniformity of affiliation and also to 
size of district) is continuous in the middle. And we can get a rough 
approximation of fairness by assuming that the relationship is 
approximately linear.

Random assignment of districts will solve the problem of deliberate 
manipulation of districts to skew representation, but if the population is 
uniform enough or the districts are large enough, it will not solve the 
completeness of representation problem, which is inherent in elections, not 
merely in how districts are drawn. Elections inherently disenfranchise 
minorities within a district. No election method (if we except disregard 
methods combined with proxy voting within the elected body, i.e., members 
have voting power proportional to vote enjoyed, which is a major structural 
change, not merely an election method change) can solve this problem. 
Gerrymandering, done neutrally with the designed goal of widening 
representation so that the legislative body reflects the affiliations of 
the population, is the only solution I can see within a district-election 
system. To even be possible, the district size would generally have to be 
small.

PR might be simpler, but I think that an algorithm for converting fair 
affiliation maps into gerrymandered maps could be designed. Input desired 
body size and a fine-grained map of population affiliation, and the degree 
of fairness desired, and district maps meeting the fairness criterion would 
be output. Note maps.

It might be possible to approximate maximum fairness, but a strict solution 
is probably intractable. *Highly* intractable. Like the travelling salesman 
problem, however, approximate solutions are possible. If the algorithm is 
fixed, that is, if it produces a single outcome, and this outcome can be 
shown to be reasonably fair, it would be enough.

Note that such a system still leaves third parties out in the cold, unless 
there are pockets with majority affiliation for that party.

Now, it is conceivable that the districts could be virtual districts. That 
is, the districts would not be set in advance of the election. (There are 
certain problems with this, I'll note, but those problems, I think, could 
be solved to reasonable satisfaction.) Then parties would be allotted a 
number of representatives according to the statewide vote, and these 
representatives would be distributed to districts according to the vote in 
those districts. In this system the electoral precincts become the unit 
from which districts are derived, so there would still be gerrymandering of 
precincts, there would still be a need to do that fairly. But it would no 
longer become fatal to third party representation; if the assembly has 100 
members to be elected, a party which can gain 1% of the vote statewide 
would have one representative. In this method, "districts" would merely be 
an assignment of elected representatives to geographic districts, and the 
party districts would not be the same from party to party, a party district 
could be as large as the whole state (in the 1% third party example).

Thus, for each party with a sufficient proportion of the vote, each voter 
affiliated with that party would have a representative, and that 
representative would approximately represent the same number of voters in 
the assembly, which seems eminently fair within the confines of the 
election problem. However, the geographic closeness of that reps office 
would vary. If you are affiliated with the majority party, you'd, on the 
average, live the closest to your party representative. And, again, this 
seems fair.

But proxy voting accomplishes the same goal to perfection. If we were 
starting out ab initio, I think that proxy voting would be the method of 
choice, from the start. Corporations start ab initio all the time; 
corporations could have created election methods instead of allowing 
proxies, but they didn't and don't, and I think the reasons are obvious. 
The corporate proxy system still has problems, but those problems are 
eminently solvable by delegable proxy, and, it is important to realize, *it 
is not necessary to change the corporate structure or laws in order to 
implement, effectively, delegable proxy.* All that is needed is for the 
shareholders to independently organize in a Free Association with Delegable 
Proxy (FA/DP), and then to name legal proxies according to the free choice 
of each member of the FA/DP shareholder organization, but, this time, being 
informed about the identities of these proxies instead of depending on such 
information coming from the fox.

(Foxes actually do consider the welfare of the hens. They want the hens to 
be healthy, if they are smart. But I don't think that smart hens would 
choose a fox as proxy. As they say, the good is the enemy of the best.)