[EM] Invitation to a new discussion

[Jobst Heitzig]

Dear folks!

Since not much is discussed on the list at the moment, 
I would like to try to start a new discussion:

In the past, we have studied in detail a large number of quite elaborated
Condorcet methods which however some people found altogether too 
complicated to be applicable by ordinary people.

Most of these methods were designed to pick an option (a candidate) 
which could be considered "best" in some sense or other. In particular,
most of those methods consider all kinds of majorities or defeats to be
quite significant. As a consequence, such methods are more "pleocratic"
than "democratic", giving majorities extensive power to oppress minorities.
(see also Ralph's latest comment)

Now I would like to bring into focus some methods which are primarily 
designed to be both extemely simple (in terms of procedural complexity), 
and extremely "fair".

In contrast to the most fair but potentially dangerous method Random Ballot 
(in which a randomly chosen voter decides), these methods are 
nevertheless still "majoritarian" in the sense that an absolute majority 
can still ensure their will. In particular, minorities cannot harm the group
since the majority can take appropriate countermeasures.
But they can do so only by voting strategically, while the "default" behaviour 
gives minorities a "fair" share of the power. 
In this way, it is much easier to vote "socially" than in Condorcet methods.

Here come the methods, all variations of the same idea with only slight differences, 
arranged in an enumerated sequence between Approval Voting and what I called 
DFC in the past. They are formulated for a group which on a regular basis needs 
to decide between several options (e.g. candidates) during their group meetings.
Please tell me what you think about this:


(1. Approval Voting)

2. Approval With Fairness (AWF):
a) Perform an approval poll (=ask who approves of which options).
b) If no option was approved by an absolute majority (=more than 50% of all voters), 
the most approved option is elected.
c) Otherwise, pick a voter at random (e.g. draw a name tag from an urn).
d) Let her choose from those options which were majority-approved.

3. Majority-Approved Fairness (MAF): 
a) Perform an approval poll.
b) If no option was approved by an absolute majority, go back to step a).
c) Otherwise, pick a voter at random.
d) Let her choose from those options which were majority-approved.

4. Majority-Confirmed Fairness (MCF): 
a) Pick a voter at random and let her propose an option.
b) Ask the voters to confirm the choice by showing hands.
c) If the proposed option is not confirmed by an absolute majority, go back to step a) 
(excluding neither the picked voter nor the proposed option from further consideration!).

5. Majority-Vetoable Fairness (MVF):
a) Pick a voter at random and let her propose an option.
b) Ask the voters who wants to veto the proposed option.
c) If it is vetoed by an absolute majority, go back to step a).

6. Majority-Restricted Fairness (MRF):
a) Perform an approval poll.
b) Pick a voter at random and let her propose an option.
c) If she proposes the approval winner, that option is elected.
d) Otherwise, ask the voters who wants to veto the proposed option.
e) If it is vetoed by an absolute majority, go back to step b).

7. Majority-Paired Fairness (MPF), aka DFC: 
a) Perform an approval poll.
b) Pick a voter at random and let her propose an option.
c) If she proposes the approval winner, that option is elected.
d) Otherwise, check by show of hands whether at least one of 
those options who were more approved than the proposed option 
is preferred to the proposed option by an absolute majority.
e) If so, go back to step b).


Hoping for interesting comments,
Jobst


PS:
The complexity of these methods could be measured by the number 
of necessary yes-no-questions to be answered by all voters, 
given the number N of options. This is as follows:
Methods 1,2 need N yes-no-questions.
Method 3 needs R*N yes-no-questions, 
where R is the (usually small) number of poll rounds needed.
Methods 4,5 need P yes-no-questions, where P is the number of proposals needed,
which is usually considerably smaller than N.
Method 6 needs N+P yes-no-questions, and finally 
method 7 needs in the worst case at most N*(N+1)/2 yes-no-questions but will 
probably need only about N to 3N on average.

For comparison, most Condorcet methods discussed in the past need at least N*N, 
often even N*N*N or more yes-no-questions.


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