[EM] Agenda Based Progression

[Forest Simmons]

Continuing onward... let's talk about agenda setting first.

An agenda is a complete ranking of the candidates ... so a good agenda is a
good complete ranking of the candidates.

But if we already have a good complete ranking of the candidates, then
we're done ... just use that ranking as our finish order ... right?

Well kinda!

In traditional use of SPE in Deliberative Assemblies the agenda order is
set by wrangling,horse trading, and other highly political, exterior, non
Universal Domain methods.

The best of these is in the context of alternatives to a status quo. For
example, the participants are asked which of the alternatives they prefer
to the status quo. The more participants that prefer any particular
alternative, the more favorable position it gets to occupy on the agenda.

In other words, the agenda is set by an Approval vote. Or if each
participant rates the alternatives on a scale of one to ten, then those
scores determine the agenda order.

So ideally, SPE ballots should allow complete preference information along
with additional information like grades, scores, or approval cutoffs: so
the preference information can be used in the elimination final stage ...
after the agenda has been established by use of the approval, score, or
judgment information.

But our challenge is to stay strictly within the "Universal Domain" meaning
ordinal input only ... that is, pure unadorned RCV style ballots.

So somehow we have to get a decent nominal order from the ordinal ballots
without any input exterior to the Universal Domain.

Why not just use first place votes?

The problem is vote splitting ... the same spoiler problem that is the
raison de etre of voting reform in the first place ... the reason approval
voting is used in traditional agenda setting ... the reason that
brainstorming sessions suspend judgment until a later stage ... first the
bulking before the cutting ... the processing stage is a refinement of the
first approximation ballpark stage that is based on the more reliable
direct majorrity comparison information.governing each elimination.

Why not use Borda Counts?

The vote splitting would away, but at the expense of a more subtle
distortion ... an unfair advantage to the candidate with the most clones
... just as votes splitting methods like Plurality disadvantage candidates
with too many clones ... Borda is hard on candidates that have too few
clones to prop up their Borda count.

So these considerations suggest something between Borda and Plurality ...
something called Implicit Approval.

A candidate's implicit approval is the number of ballots on which the
candidate is ranked above bottom (i.e. ranked ahead of at least one
candidate), which is a kind of minimal standard of approval ... nut plenty
good for agenda setting which is not supposed to be the final order ... but
just a nominal "seed" order to keep the agenda deterministic and correlated
with the questions of favorabie vs unfavorable, promising or not, strong or
weak, etc.

As we pointed out before, the agenda order makes no difference in the usual
case ... whenever there is one candidate that is preferred in every
head-head contest ... that candidate will never be eliminated, because
agenda based eliminations are always done by majority vote of the
participating voters ... unlike in the case of IRV, for example.

Still, it is important in public elections that the agendas be non random,
decisive, etc and have as high a degree of correlation with the public will
as possible without amounting to a full blown elaborate stand alone
election method in its own right ... otherwise we could just use Ranked
Pairs as an agenda setter.

We need something simple like Approval ... and the closest thing to
Approval in the Universal Domain is Implicit Approval.

The first place votes idea that we rejected for setting the agenda is
perfectly adequate for breaking ties when two candidates have the same
implicit Approval, especially if equal first rankings are allowed.

There is a mild tension against both equal Top and equal Bottom usage in
the UD domain because it creates a tradeoff between the need for unequal
preference expression for use in the agenda processing (on the one hand)
and the need to use equal whole Top/ Bottom approval/ disapproval counts
for clone free agenda setting (on the other hand).

That tension is much weaker ... practically non existant really, at the
Bottom ... which is why we reserve the equal Top count for tipping the
balance in the relatively rare cases where candidates' Bottom counts might
be identical (resulting in implicit approval ties).

The only other UD agenda setting method that we have found to be both
simple and adequate is through the Max Pairwise Support scores.

The support score for one candidate relative to another is information
that is essential anyway for the majority eliminations that are central to
the agenda processing ... so why not take advantage of that information in
the agenda setting stage?

The pairwise support score of candidate X relative to candidate Y is the
number of ballots on which candidate X is ranked ahead of candidate Y. So
X's agenda score is the highest of these scores against any opponent Y.
X's position on the agenda is determined by her best support relative to
or  in comparison with the candidate that "let her win" the most votes, so
to speak.

You could say that the candidate whose Max Pairwise Support is minimal is
kind of similar to the candidate with the smallest Implicit Approval ...
and it turns out that they are indeed the same candidate in our crucial
examples ... where they are the first candidate to be eliminated.

Example 1

48 C
28 A>B
24 B (sincere is B>A)

The Implicit Approvals of A, B, and C are respectively 28, 52, and 48 ...
so A has the smallest IA.

The respective MaxPS values are also 28, 52, and 48.

So the elimination agenda order (from least to most favorable) is A C B.

All of our agenda processing methods eliminate A first because C is
preferred over A on 48 ballots while A is preferred over C on only 28
ballots.

Our (new) methods stop there because (in the advanced versions) no
candidate is preferred over both A and C ... and (in the simplest version)
only the candidate with the strongest victory over the first eliminated
candidate is kept.

The old SPE method goes on to eliminate C leaving B as winner ... which is
unfortunate, because in this example, this rewards B for an insincere
truncation ... having thrown the sincere CW (namely A) under the bus.

It's not just old SPE that fails here ... all of the classical Condorcet
methods like Ranked Pairs, CSSD. MjnMax, etc fail ..
 because they have no way of knowing when to stop going around the
artificial cycle created by the insincere truncation of A by the B faction!

That's enough for today ...

To be continued ...





On Fri, Mar 24, 2023, 10:38 AM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

>
>
> On Thu, Mar 23, 2023, 10:07 PM Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
>
>> Calisthenics tutorials make extensive use of "progressions", so that
>> almost anybody with enough patience can progress by degrees over time from
>> a leg assisted partial range "Australian Pullup" to a full range of motion
>> standard form pullup.
>>
>> That's what we are trying to do with our "Pathways to Success" thread ...
>> to make a gradual progression from relatively primitive to more solidly
>> advanced methods.
>>
>> This progression is a progression of agenda based methods ... with
>> Sequential Pairwise Elimination SPE right in the middle of it.
>>
>> Of all the single winner methods that have been used for centuries, SPE
>> is the most solid, respectable, versatile, and unknown to the public at
>> large ... though well known to organizations that convene Deliberative
>> Assemblies goverened by Robert's Rules of Order.
>>
>> We have two things to consider... 1. How to set a good agenda ... and 2.
>> How to process the agenda to extract a winner from it.
>>
>> The agenda plays the same role that seeding does in a tournament. It
>> gives a nominal order that serves more as a tie breaking order than
>> anything else. In the usual case (when rock paper Scissors ties are non
>> existent), the agenda order has no effect on the outcome. The most
>> important thing about the agenda is that it be based on some deterministic
>> statistic correlated with democratic support and not easily distorted by
>> proliferation of clones among the candidates.
>>
>> The agenda processing must be based on the majority rule principle, and
>> must have built in safeguards against strategical manipulation by
>> unscrupulous influencers ... the kinds of manipulations that create the
>> rare, but not rare enough, cycles that can make the outcome depend on the
>> agenda order.
>>
>> We will touch on these aspects in our examples.
>>
>> These concerns are not limited to agenda based methods ... but good
>> agenda based methods (like the ones in our progression) deal with them more
>> transparently and effectively than any other deterministic, single winner
>>
>
> I should have included Universal Domain  in this qualification ...
> comparing non UD methods like Majority Judgment or Approval Sorted Margins
> with the methods in our progression is like comparing Steriod Jacked Body
> Builders with Natties.
>
> methods that we know of ... and we have carefully compared the methods in
>> our progression with the realistic extant alternatives ... as well as many
>> others.
>>
>> To be continued ...
>>
>>
>>
>>
>>
>>
>>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20230324/8313069c/attachment.htm>