[EM] "Top 2+1 Approval" primaries

[Kristofer Munsterhjelm]

On 07/24/2013 08:54 PM, Jameson Quinn wrote:

> Certainly you could propose complex systems that could be better than
> this proposal in some ways. For instance, you could use a proportional
> representation system such as Bucklin Transferrable Voting (BTV) for the
> first round. But this proposal is a simple balance of the requirements:
> nonpartisan voting, a balance of candidates and parties in the general
> election, yet focused attention on a few strong candidates.

What do you think of a sequential PAV style primary? It seems to be 
simple enough:

1. Pick the winner.
2. Deweight all votes who approved of this winner by 1/3.
3. Pick the highest scoring candidate that's not the winner.

Would this be better than just picking the two Approval winners? It's 
not setwise PR, but setwise PR can, as you say, get very complex very fast.

The three-seats completion would either be:

1, 2, 3. As above.
4. Based on the original ballots, deweight those that approved of one of 
the winners by 1/3; of two of the winners by 1/5.
5. Pick the highest scoring candidate not already picked, based on the 
deweighted ballots,

or

1, 2, 3. As above
4. Start from the original ballots.
5. If the two picked candidates are from the same party, remove all 
candidates of this party from the ballots.
6. Pick the highest scoring candidate that has not already been picked.