[EM] 3-slot, burial resistant Approval mod: Condorcet // Top-rated

[Ted Stern]

I favor Approval, but am mindful of objections to its lack of preference.

It seems to me that the simplest extension of Approval is to add a second
level of approval as in 3 slot methods.  The ratings could be called Good,
Ok, Reject as in 3-2-1 voting, but for now the rating names are not
important.

I would also like the option of a 2nd round of voting if there isn't a
clear majority.

With that in mind, I was wondering if this variant has every been
considered:

   - 3 slot method
   - Rating above Reject counts as Approval
   - If there is a beats-all (Condorcet) winner, that's the first round
   winner
   - If not, the candidate with the most top-ratings is the first round
   winner
   - If the first round winner has majority approval, the method is
   completed with no second round.
   - Otherwise, there is a second round, between the round-1 winner (R1W);
   the candidate who has highest total approval on ballots that don't approve
   of the first round winner (complementary approval winner = CAW); all
   candidates in the Smith Set; and the total approval winner.
   - In case of ties for beats-all or top-rated, all those tied candidates
   would be included in the second round.
   - In the second round, the method terminates with that round's R1W
   before the second-round step.

The intent here is to avoid strategic bullet voting, chicken dilemma or
burial, while creating an incentive to add second choice approval for
compromise candidates.  Participation and FBC failures, if any, also appear
to be minimal.

Is there an incentive for plurality top-rated candidate supporters to
create a cycle to fall back to top-rated votes?  Possibly, but I don't see
any way that could happen without a second round and the additional risks
that entails.

The reason I consider this as an Approval mod is that the optimal strategy
is to vote all approved candidates as top-rated.  But if you are concerned
about a bullet-voting or chicken dilemma attack, there ought to be nothing
lost by putting compromise candidates in second place.
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