[EM] Condorcet Enhancement

Abd ul-Rahman Lomax abd at lomaxdesign.com
Mon May 20 10:42:02 PDT 2019

Condorcet compliance is valuable if it is based on *persistent 
preference.* I.e,. if a Condorcet winner as expressed on the ballots 
survives to the next phase, then the method can be Condorcet compliant, 
even if later voter decisions choose someone else. Problem is when we 
have a large candidate set, that "Condorcet winner" may be approved for 
election by only a minority, and it could even be a small minority. Most 
voting systems analysis completely neglects ballot placement, and, as 
well, the problem that Dodgson identified, most voters not having enough 
information to rank many candidates.

Majority approval of an election is a basic democratic requirement, 
necessary in NGOs, generally, but badly neglected in public elections. 
IRV produces a fake majority by ballot exclusion, too often. I've 
suggested using a Score ballot, defining a scoring level as "approved 
for election in place of an additional poll" -- probably midrange -- and 
then considering these rules:

1. The primary cannot complete with an election unless the winner is 
approved by a majority.

2. If a Condorcet winner exists, this candidate must not be eliminated 
from the next round (and write-in votes should always be allowed; doing 
otherwise creates fake majorities).

3. Likewise a Range winner cannot be eliminated.

Whether or not a Condorect winner loses if there is a different Approval 
winner is an issue of balance. Yes, the voters will have approved a 
different winner -- and the voters should have the power to disregard 
their own preference in order to complete an election. But it is 
possible that this is based on misinformation about the true possible 
voting. So maybe a conflict here would require a second election. I have 
no strong position on this. This issue is resolved by Asset.

4.  It is possible that Asset could always find a winner even with only 
one round general election. In this case, the preferences to be 
considered are the preferences of the chosen electors. They may use 
many, many rounds, in their process, and single-winner, a majority of 
electoral votes would be required. I prefer, instead, though, electing 
an Assembly and the Assembly elects officers (i.e., what single-winner 
elections are used for) or makes other Yes/No decisions, which may be 
amended and iterated many, many times, by being a deliberative body with 
immediate voting.

Without Asset, my sense is that using an advanced voting system, such as 
the hybrids proposed, unless candidacies multiply because of improved 
systems, will produce a majority-approved result usually in the first 
round, and failure in a second round would be very rare, and the failure 
might be by such a narrow social utility margin that little harm is done 
by electing the "wrong" candidate. We only toss a coin with exact vote 
equality, but from a social utility point of view, not a great deal of 
harm is done by electing a candidate with 49.9% of the vote. Or a third 
round could be required, how important is it?

Problematic systems will elect a minority-approved candidate under much 
more harmful conditions than that!

However, this is also what I expect. An advanced system will show the 
true support for minority candidates, and this will encourage the 
multiplication of candidacies, which then runs into the problem that 
Asset was designed to address. All roads lead to Asset, and what amazes 
me is that Asset is simply very basic democracy, simply representative 
instead of direct.

What we have called "representative" democracy does not represent the 
voters, but districts, leading to a horrible mess that nobody thinks can 
be fixed.

On 5/19/2019 7:10 PM, Forest Simmons wrote:
> There are various ways to enhance a given method to make it Condorcet 
> compliant:
> 1.  One can elect the ballot CW if there is one, and otherwise fall 
> back on the given method.
> 2. One can apply the given method to the Smith set.
> 3. One can use the given method winner as the starting point in a 
> seamless process that leads to a member of the Smith Set (or better).
> Here is such a process:
> First, create a directed graph whose vertices are the candidate names 
> as follows:
> For each covered candidate X, draw an arrow to that candidate Y (among 
> those that cover X) which is ranked or rated strictly below X on the 
> fewest number of ballots.
> To enhance the winner A of any method, start at candidate A and follow 
> the arrows as far as possible in the directed graph.  The enhanced 
> winner W' is the one at the end of the directed path.
> This W' covers W, but is itself uncovered (a member of the Landau 
> Set), and so also a member of Smith.
> If the original method elects monotonically, then so does the enhanced 
> method.
> If the original method satisfies the FBC or in any case lacks 
> vulnerability to compromise, then the enhanced method gives little 
> incentive for burying Favorite because when there is an arrow from 
> Favorite to Y, candidate Y is already the natural compromise candidate 
> for the supporters of Favorite, the one that is rated strictly below 
> Favorite on the fewest ballots among those that cover Favorite.
> Suggestions:
> A.  Enhanced Approval.
> B.  Enhanced Majority Judgment
> C.  Enhanced Random Ballot
> D.  Enhanced Asset Voting (different possible versions)
> E.   Enhanced Chiastic Approval
> Other versions?
> If method M is Chicken Resistant, does it follow that the Enhanced 
> version of Method M also Chicken Resistant?
> Other thoughts?
> ----
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