[EM] Smith IBIFA

[Ted Stern]

I've modified my electowiki page to include a simpler calculation of
Relevant Rating:


   1. Initialize the rating level R to MAXRATING
   2. Initialize candidate totals, *T(X)*, to zero
   3. Initialize *TCA(X,C)* to the highest approval for any candidate on
   ballots that rate X below R
   4. Repeat until a winner is found:
      1. For each candidate X, add ballots rating X at level R to T(X)
      2. Is *T(X) > TCA(X,C)*? If so X is a member of the current
      qualifying set
      3. If the current qualifying set has at least one member Q, the
      candidate with the highest T(Q) is the winner
      4. Otherwise, decrement R by one
      5. For each candidate X, set *TCA(X,C)* to the highest approval for
      any candidate on ballots that rate X below the new R rating level
      6. For each candidate X, is *T(X) > TCA(X,C)* (using new TCA(X,C))?
      If so, then X is a member of a new qualifying set.
      7. If the new qualifying set has at least one member Q', then the
      candidate with the highest T(Q') is the winner.


You could easily augment this algorithm with your Condercet modification.

On Fri, Jun 14, 2019 at 11:12 AM C.Benham <cbenham at adam.com.au> wrote:

> IBIFA very naturally meets Plurality, Minimal Defense and Non-Drastic
> Defense so it occurred to
> me to use it as a "Condorcet-completion" method thus:
>
> *Voters fill out out either unlimited rankings ballots or multi-slot
> ratings ballots.
>
> A  pairwise-beats-all candidate wins. Otherwise carry on the IBIFA process
> until a
> Smith-set member qualifies. If only one does that candidate is elected.
>
> If more than one does in the same round, then simplest and probably good
> enough
> is just to elect the one with highest score in that round.*
>
> (That last provision is Bucklin-like as in original IBIFA. Using the Smith
> set the more
> complex Relevant Ratings and the possibly a bit arbitrary-looking "revised
> IBIFA"
> I think would be very unlikely to give  different winners.)
>
> I think this is my favourite method that meets both Condorcet and Minimal
> Defense.
>
> Also it can be used with an approval cutoff  to meet what Forest was
> asking for on 30 May 2019.
>
> All rankings/ratings would be used to identify the Smith set, but for the
> IBIFA stage ballots would
> be treated as if they truncate all their unapproved candidates. The
> default should be approval of
> all candidates voted above at least one candidate.
>
> Chris Benham
>
>
> *Forest Simmons* fsimmons at pcc.edu
> <election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3CCAP29onet%2BO9hCZJ6hvNnnpUWNyrDkKa9xFXrX5P-RPoF6ndtfw%40mail.gmail.com%3E>
> *Thu May 30 *
>
> In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.
>
> I am interested in simple methods that always ...
>
> (1) elect candidate A given the following profile:
> P: A
> Q: B>>C
> R: C,
>
> and
> (2) elect candidate C given
> P: A
> Q: B>C>>
> R: C,
>
> and
> (3) elect candidate B given
> P: A
> Q: B>>C  (or B>C)
> R: C>>B. (or C>B)
>
>
>
>
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