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

Andy Jennings elections at jenningsstory.com
Thu Jul 19 07:09:57 PDT 2018

```On Wed, Jul 18, 2018 at 4:37 PM, Kristofer Munsterhjelm <
km_elmet at t-online.de> wrote:

> On 2018-07-19 00:26, Rob Lanphier wrote:
>
>> There are many ways of dealing with this:
>>
>> 1.  Only allow 2 candidates to advance, keeping with the spirit of
>> "top two", and use simple plurality in the general election.
>> 2.  Have higher limit (e.g. 5 candidates) and only allow the top 5
>> approval getters to advance.  Tally the general election using
>> approval voting > 3.  Choose the 5 candidates for whom at least one is
>> approved.
>> Calculating this seems complicated, but the goal would be the 5
>> finalists would be A1-left, A2-left, A3-left, B-center and C-right.
>> Once again, tally the general election using approval voting.
>>
>
> If I recall correctly, choosing the candidates to maximize the number of
> voters who approve of at least one of them is NP-hard for general n. See
> https://en.wikipedia.org/wiki/Maximum_coverage_problem.
>
> The best you can do without P = NP is a very obvious greedy algorithm
> (successively pick the candidate that maximizes the number of additional
> voters covered by the set of candidates so far). The greedy algorithm makes
> it relatively easy to start with one or more candidates picked by other
> means (e.g. the Approval winner) and then filling in the rest.

I believe runtime is exponential in the number of winners, so "2 advance"
and "3 advance" are quite tractable, and "5 advance" should be possible in
most cases.
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