A cure for Gerrymandering

I read this thread today and I think it makes a lot of sense, but I thought I'd write down my ideas on how to fix gerrymandering.  Here are some legitimate concerns I think we should consider when drawing districts.

Rule 1. All districts should have roughly the same population. To not do so is unconstitutional. 

Rule 2. Maps have to be in compliance with the VRA

Rule 3. There should be some consideration for preserving incumbents do to the value of seniority (even as this has become less valuable)

Rule 4. There should be some consideration for boundaries/compactness.

That being said, my idea is to use computers, randomization and a round-robin veto to end up on something that everyone likes and dislikes pretty evenly. Here's the basic idea:

A. Start with the existing map. The system could just choose starting precincts at random, but starting with the existing map is meant to address Rule 3. 

B. If a district has to be added choose a random precinct* to start with and make that the new district for use below. If one has to be eliminated, eliminate one chosen at random by the computer.

C. Remove "purge" selected edge precincts from the most populous district and add them to neighboring ones until it is no longer the most populous. Then switch to the new largest district and repeat until all the district are in compliance with Rule 1.

D. Analyze the map to see if it is in compliance with Rule 2. If not, throw it out and start over at Step A. If it is, keep it as an option. 

E. If you have X options go on to Step F and if not go back to Sep A to start on another option. X would be equal to the number of state legislators plus 2. 

F. With X options in hand, start with the least senior member of the legislature and let them veto one. Then on to the next least senior, etc... until every one has vetoed a map and only two remain. The Governor then chooses from among the two last options. 

To address rule 3, the computer should give more weight in the random selection of precincts to purge to those that are least connected to the the others. So if the existing District includes one entire county and 300 precincts in another, those 300 precincts would be made more likely to be purged. Same with precincts that are far from the geographic center of the District. 

Starting with the old maps means that past gerrymandering would - to some extent -carry over to the next one but with each decade this would become less and less true until one day it no longer is. 

Letting legislators and governor veto maps means that the most partisan-unfair ones are removed - because Democrats will remove the maps that most benefit Republicans and Republicans would remove the ones that most help Democrats. And the use of randomness brings with it fairness.