# [EM] Smith IBIFA

Ted Stern dodecatheon at gmail.com
Mon Jun 17 10:28:03 PDT 2019

```Chris and Steve, you might find it interesting to compare my restatement of
Relevant Ratings with a similar formulation for Majority Judgment:

1. Initialize the rating level R to MAXRATING
2. Initialize candidate totals, *T(X)*, to zero  *[T(X) is a shorthand
for the total number of ballots voting for X at ratings >= R]*
3. Assume *TR(X,R)* *[the total number of ballots rating candidate X at
rating R]* has been tabulated while counting ballots
4. Repeat until a winner is found and R is greater than zero.
1. For each candidate X, add *TR(X,R)*, the number of ballots rating
X at level R, to T(X)
2. Is *T(X) > 50%*? 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, is *T(X) > (50% - (TR(X,R)/2))* (using new
R)? If so, then X is a member of a new qualifying set.
6. If the new qualifying set has at least one member Q', then the
candidate with the highest T(Q') is the winner.
5. If no winner has been found, the candidate with highest T(X) is the
winner.

In Majority Judgment, each candidate has a majority grade 3-tuple,
consisting of their median rating, followed by the rating that occurs after
removing median ballots, followed by the number of ballots that break the
secondary tie.  The median rating is found by following the above process
for each candidate separately.

If X satisfies the comparison in step 4.2, X's majority grade is *(R, R-1,
TR(X,R)).*

If X satisfies the comparison in step 4.5, X's majority grade (using the
initial R before decrementing) is *(R-1, R, TR(X,R))*

If X falls through to step 5, X's majority grade is *(0,0,T(X)).*

Hopefully it should be clear how this is the same as relevant rating when
every ballot is relevant -- the maximum approved candidate on ballots that
rate X below rating R will simply be the total number of ballots (100%)
minus the ballots rating X at and above R.  So for T(X) > TCA(X,R) is
equivalent to T(X) > 100% - T(X), == 2*T(X) > 100%, == T(X) > 50%.
Similarly for the other comparison.

On Fri, Jun 14, 2019 at 1:48 PM Ted Stern <dodecatheon at gmail.com> wrote:

> 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
>> *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)
>>
>>
>>
>>
>> www.avg.com