# [EM] A simpler approval based way of replacing the CA jungle primary

Kristofer Munsterhjelm km_elmet at t-online.de
Sat Aug 11 13:50:10 PDT 2018

```On 2018-07-24 00:03, Rob Lanphier wrote:
> Andy and Kristofer, thanks both of you for weighing in on this.
> Kristofer: thanks for teaching me about the "maximum coverage
> problem".  It's been a lonnnng time since I've been in a C.S./math
> class to study that sort of thing.  But since I'm an unrepentant
> packrat, I was able to find my textbook from when I was in C.S.
> learning about similar problems (e.g. the four color theorem).  The
> Wikipedia article was way more helpful  :-D  Andy, I suspect your
> hunch is correct; if "2 advance" is all we compute, that doesn't seem
> too difficult to achieve via brute force algorithm.

It might make the behavior seem too opaque to the voters if it just says
"try every possible alternate choice". On the other hand, voters'
intuition of how methods behave may not correspond to how they behave to
begin with; consider e.g. the chaotic nature of IRV.

I also happened across the following draft paper by James Green-Armytage
on the question of how to select candidates for a top-two runoff:
http://jamesgreenarmytage.com/runoff.pdf

It seems the best approaches he found use proportional representation
methods. For {L,R} in the LCR scenario, just running a 2-seat
proportional representation method; and for {L, C}, choosing an initial
winner by a majoritarian method, then use a 2-winner proportional
representation method to find the most representative set of two winners
subject to that one of them must be what the majoritarian method chose.

So the "deluxe" option might be: use a majoritarian method to find a
winner. Then use a proportional representation method to find a 2-seat
winning set. If the majoritarian winner is on that winning set, you're
done; use the set. Otherwise use the 2-seat set plus the majoritarian
winner (the classical three-way race you mentioned).

Picking the best PR 3-seat set subject to that one of the candidates in
it must be the majoritarian winner might be better, but on the other
hand, it might encourage tactical nomination. I'm unsure. Under honesty,
it would be somewhat better (e.g. if the majoritarian winner is slightly
to the left, it would deweight left-wing candidates more), but it might
not be worth the complexity.

There might even be a way to accommodate rules for when there's no need
to run a second round, if the PR method can quantify how well the
electorate is represented by the set. The idea would be that if the best
1-seat set (the Approval winner) already represents the electorate very
well, then there's no need for a runoff.
```