[EM] A friend needed help with the Legislature of Equestrian for a Story. I helped with its design using ElectionMathematics.

Kristofer Munsterhjelm km_elmet at t-online.de
Wed Dec 10 08:58:54 PST 2014

On 12/07/2014 05:38 AM, Kathy Dopp wrote:
> There are a few problems with using split line in terms of the
> practicalities of administering and serving for districts:
> 1. don't take into account geographic obstacles like mountain ranges,
> the grand canyon and similar chasms and rivers that may not have a
> bridge for a hundred miles or more (impractical, time consuming,
> expensive for voters and representatives to meet in such districts)
> 2.  doesn't take into account census tract boundaries or election
> administration boundaries, making it virtually impossible to
> administer and to assign voters to voting districts and to assign
> ballot definitions to voters, etc.
>   Perhaps the split line algorithm has the potential to be further
> adjusted for such  practicalities.

I'd guess that the first point can be dealt with by using splitline on a 
cartogram where the points are distorted so that the straight line 
distance between two points is equal to the travel distance (or some 
other distance[1]) in the real world. Similarly, the second point could 
be handled by using census blocks instead of geographical points as the 
"pixels". But this would make the splitline algorithm less than exact; 
you can't put an exact fair share into each area if you're absolutely 
constrained by administration boundaries.

> I've proposed a new general algorithm for drawing districts that makes
> the number of districts representing certain population densities
> proportional to the number of persons living in those population
> densities, as much as possible. However, really, no redistricting plan
> can assure proportional representation of political parties or views,
> as I'm sure we all understand here.  My paper on redistricting can be
> viewed at ssrn.com just search on my name Kathy Dopp.

Ultimately, though, you're right. It is rarely possible to have both 
local representation and political proportionality at the same time. So 
one or both has to give.

In single-member district systems, political proportionality is what 
gives. Minorities get left out.

In multiwinner systems, local representation is weakened in favor of 
political proportionality. Party list PR takes this further (assuming 
party proportionality is a good proxy for political proportionality in 
general), and this reaches an extreme in party list systems with a 
single district (e.g. Israel).

MMP also weakens local representation, but whereas multiwinner uniformly 
weakens local representation (every candidate is a little less local 
than in a single-winner district), MMP augments locally representative 
but potentially politically disproportional constituency members with 
locally unrepresentative but politically proportional list members.

Fair Majority Voting (and biproportional apportionment in general) 
strengthens national political proportionality by weakening local 
political proportionality.

Although there is a tradeoff between local representation and political 
proportionality, I'm think that the gerrymandered US single-member 
district system is pretty far on the Pareto front. There is probably 
also a pretty steep diminishing returns effect as you go towards the 
extremes of either: to get the increased local representation of SMD 
compared to say, 5-seat districts, you have to give up quite a bit of 
political proportionality.


[1] or, if you don't want roads or other manmade constructions to affect 
the outcome, set the distance between to two points to be the length of 
the shortest curve that follows the surface of the Earth between those 

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