[EM] [CES #17111] Re: Automatic Primary + Pairwise Runoff (APPR), a class of cloneproof top-two-style methods

[Ted Stern]

Toby, you bring up a valid point.  There are indeed pathological cases in
which the Condorcet winner does not have broad support.

My intention in introducing Automatic Primary as an adjunct method was to
address the main problem possessed by top two or top N methods (such as
SRV/STAR or 3-2-1), that the results are distorted by crowding.

For example, in 3-2-1, there might be a strong minority faction united
behind a crowded slate of candidates, while the majority faction has a
contentious chicken dilemma, effectively splitting its first place votes
beyond the top three.  The same could be true in top two methods using
approval, score or majority judgment.

I was hoping that some form of Condorcet compliance would be a side benefit
of my earlier proposed automatic primary technique, but you have pointed
out a situation in which that compliance could actually lead to a result
with lower social utility or higher variance.

So I have thought of a further simplification that focuses solely on the
crowding/splitting problem:

For any top two or top N method, run two different versions:  one with the
original method, and another with automatic primary.  Each method will have
a pairwise winner.  If the original top N method winner differs from the
winner of the automatic primary pairwise runoff, the overall APPR winner is
the pairwise preferred between those two candidates.

Automatic primary means:  for a particular ratings method, find the top
scoring candidate  Then deweight ballots according to the degree that each
ballot supports the ratings winner, and calculate the total rating winner
using the remaining ballots or fraction of a ballot.  If using a top-3
method, apply another round of deweighting on those remaining ballots and
find the next ratings winner.

In top two approval:

   - Use a rating ballot with an approval cutoff, e.g. 5,4,3 = approved;
   2,1,0 = disapproved; infer rankings from ratings.  Equal rating implies no
   pairwise preference vote.
   - Find candidates A0 (highest approved) and A1 (approval runner-up).
   - Drop all ballots that approve of A0
   - Find the candidate with highest approval among ballots that don't
   approve of A0.  Call this candidate B.
   - Do pairwise comparisons A0 vs. A1 (top two) and A0 vs. B (auto
   primary).  If the top two pairwise winner is different from the auto
   primary pairwise winner, the APPR winner is the most preferred the two.

In top two score [Score Runoff Voting (SRV) AKA Score + Automatic Runoff
(STAR)]:

   - Use a ratings ballot, infer rankings from ratings.  Equal rating
   implies no pairwise preference vote.
   - Find candidates A0 (highest total score) and A1 (runner-up total
   score).
   - For each ballot that gives A0 a score less than max-score, give each
   candidate their original score times (max_score - A0_score).  With scaling,
   this is the equivalent of removing the total score fraction for A0 from the
   original ballots.
   - The automatic primary runner-up is the candidate with highest total
   score among these remaining candidates.  Call this candidate B.
   - Proceed as before for APPR-Approval

One can proceed similarly for APPR-Majority Judgment.

It is interesting that the same idea APPR idea could also be applied to
3-2-1:

   - Use a 3-2-1 3-slot ballot:  Good, OK, Reject.
   - Find the total votes for each score level for each candidate.
   - Find the top three candidates by total Good rating, A0, A1, A2.
   - Drop the candidate with the most Reject scores.
   - The 3-2-1 winner is the pairwise preferred between the remaining 2
   candidates.  Call that winner A*.
   - Find the automatic primary runner-up and second runner-up by first
   counting Good ratings on only those ballots that Reject A0.  The Good vote
   winner on those ballots is B1.
   - Then count Good ratings on only those ballots that reject both A0 and
   B1.  The Good vote winner on those ballots is B2.
   - Apply 3-2-1 on A0, B1, and B2.  Call that winner B*.
   - If A* is not the same candidate as B*, the APPR-3-2-1 winner is the
   the pairwise preferred between A* and B*.

As with top-N methods, APPR applies another level of stabilization to the
original ratings method.


On Tue, Oct 10, 2017 at 5:36 AM, 'Toby Pereira' via The Center for Election
Science <electionscience at googlegroups.com> wrote:

> I'm not sure that passing the Condorcet criterion is a primary aim of
> these methods, otherwise we might as well propose using one of the many
> Condorcet methods on offer. I think the main aim of methods like STAR and
> 3-2-1 voting is to maximise utility, without so much concern about strictly
> passing particular criteria in all cases.
>
> In any case, there are situations where I think passing the Condorcet
> criterion is not a good thing. The following example has 3 candidates, 100
> voters and score ballots with a maximum score of 10.
>
> 49 voters: A=10, B=0, C=1
> 49 voters: A=0, B=10, C=1
> 2 voters: A=1, B=0, C=10
>
> C is the Condorcet winner, but a very weak winner. There are two main
> candidates (A and B) that polarise support, and a non-entity (C). C wins
> because the 98 A/B supporters decide to put C (marginally) above the main
> candidate they dislike. They might not even know anything about C.
>
> This is a fairly extreme example, but it shows what can happen when you
> have two main candidates and a non-entity.
>
> I think using score voting and then finding the top two candidates
> proportionally is a good idea. I would do this sequentially though, since
> we are ultimately looking for a single winner, not a two-person committee,
> and it would be strange to eliminate the top scoring candidate, which is
> what could happen with non-sequential election.
>
> This method would still not be cloneproof as it stands, but I would
> solve this not by trying to eliminate the effect of clones, but by
> embracing clones. I would effectively clone each candidate. If the top two
> candidates in the sequential proportional election are a candidate and
> their clone, then that candidate would automatically be elected without the
> need for a top two head-to-head. If a candidate has that much of a lead
> over the others in a score ballot, then I don't think the head-to-head
> would be necessary, or even desirable. It would help eliminate the
> possibility of very weak winners, as could happen in my example above under
> some methods.
>
> Toby
>
>
> On Thursday, 28 September 2017 21:46:12 UTC+1, Dodecatheon Meadia wrote:
>
>> I am interested single-winner methods that find the variance-minimizing
>> candidate, with resistance to strategic voting.
>>
>> Top two approval, STAR (top two score), and 3-2-1 voting, while all very
>> good at resisting strategic voting, all fail clone resistance.
>>
>> When I raised the topic of top two approval on the EM list last November (
>> http://election-methods.electorama.narkive.com/Vlwq75Zy/em-
>> top-two-approval-pairwise-runoff-ttapr), it was suggested that using the
>> ballots to approximate a two seat Proportional Representation style
>> "parliament" would avoid the crowding effect of cloned candidates.
>>
>> There are several problems with this idea ... to start with, in a 3
>> person election, it fails the Condorcet criterion, which would be a minimal
>> threshold for centrist approximating methods.  Another problem is that
>> while picking the top two approved candidates is vulnerable to crowding,
>> replacing the second-place winner with the second-seat parliament member
>> means that there is no incentive for factions to cooperate, because doing
>> so would lead to elimination from the second round.
>>
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