I generally agree with John Bartlit. On the issue of compactness of voting districts, I acknowledge that I have also advocated that in the past. However, I now must disagree. (link)
I have realized that compactness can lead to similar results as does gerrymandering. There is unequivocal measure of how democratic a voting system is: It is the agreement between the number of representatives of each party and the relative fraction of votes cast for each party.
For example, if 45 percent of voters in a state have voted for representatives of party A and 55 percent for B, then if there are a total of 40 representatives elected, 18 should be from party A and 22 from party B. Small deviations may be expected, but if 27 are from party A and 13 from party B (as has proportionally occurred in some state legislatures), democracy has been thwarted however the districts were determined. Even compactness can produce 90 percent majorities for party B in some high-density districts and slim majorities for party A, even in geometrically compact districts.
An independent, non-partisan districting commission, on observing such a result, should be able to revise districts as necessary. The goal should be that in the next election, barring mass movements of voters, a more democratic result would be more likely. The ideal of compactness might not be able to achieve that result.