<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p.msonormal0, li.msonormal0, div.msonormal0
{mso-style-name:msonormal;
mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
span.EmailStyle18
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style>
</head>
<body lang="EN-US" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal">Consider a network where the nodes represent individual membership in a district and the edges connect any two individuals that could possibly be considered as being in the same area. An edge has a weight of -1 if the neighbors are in
opposing political parties and 1 if they are the same. A node has the value of 1 if it is in a district and -1 if it is not in that district. Districts are mutually exclusive, so all of the nodes associated with an individual, when considered as binary
values, must sum to one. Specifically suppose there are two districts, and node(A,D) is defined as individual’s A participation in district D. Then (node(A,0)+1)/2+(node(A,1)+1)/2 = 1. Constraints like this can be converted into penalties by moving the
RHS to the LHS, negating the value, and then squaring the LHS. An energy for the whole network can be written as a sum of all of the network’s interactions.
<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"> sum(edge_weight(i,j)*node(i,d)*node(j,d)) where i < j for i,j from the set of nodes and d from the set of districts<o:p></o:p></p>
<p class="MsoNormal"> + K*(all mutual-exclusion penalties as above) where K is a large number<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Now minimize this energy using a system that can find the ground states of a high dimensional Ising model, such as a quantum annealer. This function will be minimal when each district has neighbors that tend to be in different parties.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal"><b><span style="font-size:12.0pt;color:black">From: </span></b><span style="font-size:12.0pt;color:black">Friam <friam-bounces@redfish.com> on behalf of Tom Johnson <tom@jtjohnson.com><br>
<b>Reply-To: </b>The Friday Morning Applied Complexity Coffee Group <friam@redfish.com><br>
<b>Date: </b>Saturday, November 3, 2018 at 4:55 PM<br>
<b>To: </b>"Friam@redfish. com" <friam@redfish.com><br>
<b>Subject: </b>Re: [FRIAM] gerrymandering algorithm question<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">First, we would have to agree on whether there will be objectives related to the demography of any district? I prefer only counting the number of current population 18 and over. Or some would argue for the total population of any age.
But given either choice, there will be serious suggestions that doing so would work hardship on racial, ethnic or other groups. Could be, but it could also mean that anyone running for office would probably have to find a way to appeal to ALL voters.
<o:p></o:p></p>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">Second, let's say we're creating Congressional districts. Overlay a state with a grid of hexagons of X diameter; could be 100 yards or 1000. I don't know, but perhaps something like Netlogo could give us a scalable system to run tests.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">Third, given a known population of potential voters, we know how many Congressional districts a state would have. Randomly distribute that number of hexagons across the state with the objective of maximizing the centroid distances of all
the hexagons.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">Fourth, expand out from each hexagon one additional hexagon at a time in a circular fashion with all expansions starting on the same side of the original hexagon. Total the number of potential voters. If there are no potential voters
in a hexagon, advance one more in the rotation. Then repeat the same expansion, total the voters and do it again until the desired district population is reached.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">There are obvious problems here: e.g. what happens when a district encounters a state boundary or another district's hexagon early on? I don't have a solution (yet). But I think this simulation could be easily tested without a lot of
CPU overhead. And after the districts are created, we could start to look at the demographics of the potential voters.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">TJ<br clear="all">
<o:p></o:p></p>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal"><br>
============================================<br>
Tom Johnson<br>
Institute for Analytic Journalism -- Santa Fe, NM USA<br>
505.577.6482(c) 505.473.9646(h)<br>
<a href="http://nmfog.org" target="_blank"><b><span style="color:#0B5394">NM Foundation for Open Government</span></b></a><br>
<b><span style="color:blue">Check out <a href="https://www.facebook.com/pages/Its-The-Peoples-Data/1599854626919671" target="_blank">
It's The People's Data</a></span></b><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><a href="http://www.jtjohnson.com/" target="_blank">http://www.jtjohnson.com</a>
<a href="mailto:tom@jtjohnson.com" target="_blank">tom@jtjohnson.com</a><br>
============================================<o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<div>
<p class="MsoNormal">On Sat, Nov 3, 2018 at 4:14 PM Nick Thompson <<a href="mailto:nickthompson@earthlink.net">nickthompson@earthlink.net</a>> wrote:<o:p></o:p></p>
</div>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D">Oh, I absolutely agree that we could design districts to maximize any variable we wanted. And with a little luck, we might maximize a couple, or even
three. But inevitably, we will encounter some variable that is negatively correlated with those we already maximize, so even we philosopher kings will be dissatisfied with the result.
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D">So, you philosopher-kings out there: if you were designing districts out there, how would you do it. How about all districts at-large? Ranked choice
voting? How about requiring all districts to match the state-wide political distribution of the whole state and redistricting after every election? Seriously. How would you do it?
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D">Nick
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D"> </span><o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D">Nicholas S. Thompson</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D">Emeritus Professor of Psychology and Biology</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D">Clark University</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D"><a href="http://home.earthlink.net/~nickthompson/naturaldesigns/" target="_blank"><span style="color:#0563C1">http://home.earthlink.net/~nickthompson/naturaldesigns/</span></a></span><o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D"> </span><o:p></o:p></p>
<div>
<div style="border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b>From:</b> Friam [mailto:<a href="mailto:friam-bounces@redfish.com" target="_blank">friam-bounces@redfish.com</a>]
<b>On Behalf Of </b>Marcus Daniels<br>
<b>Sent:</b> Saturday, November 03, 2018 11:24 AM<br>
<b>To:</b> The Friday Morning Applied Complexity Coffee Group <<a href="mailto:friam@redfish.com" target="_blank">friam@redfish.com</a>><br>
<b>Subject:</b> Re: [FRIAM] gerrymandering algorithm question<o:p></o:p></p>
</div>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D">Nick writes:</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D">“I don’t mean to say that “fair districts” aren’t possible. I just mean to say that I, as your philosopher-king, could not design them.”</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Wasn’t there a recent effort by the MIT Sloan school to redesign the school bus routes in Boston? They managed to reduce the cost and time of the routes by a large amount, but
then many complained because it didn’t reflect the underlying class structure of the community and the preferences of the richer communities.<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">One can design an optimization to balance any set of goals. It’s just that some of the goals we don’t talk about. They are wired-in to our reptile brain as baseline expectations
and not reflected in the political conversations of dinner parties. <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Marcus<o:p></o:p></p>
</div>
</div>
<p class="MsoNormal">============================================================<br>
FRIAM Applied Complexity Group listserv<br>
Meets Fridays 9a-11:30 at cafe at St. John's College<br>
to unsubscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">
http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>
FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a> by Dr. Strangelove<o:p></o:p></p>
</blockquote>
</div>
</div>
</body>
</html>