[EM] Invitation to a new discussion

[Simmons, Forest]

Jobst asked for comments about methods zero through seven (below) for deciding among alternatives, especially in the case of small groups.
 
These methods should be considered for completing single winner Asset Voting elections, in the case of large electorates.  
 
In each proposer round the candidates would have probabilities of being chosen as proposer in proportion to their voting assets.
 
Candidates' voting assets (i.e. proxy weights) are determined by counting the voters' approval style ballots "cumulatively," i.e. normalized so that each of the k candidates approved on the ballot gets an asset increment of 1/k from that ballot.   
 
The methods that require an approval poll round would also make use of the usual approval tallies of the ballots, for the first such round.
 
All of the other rounds (whether approval, veto, etc.) would be proxy votes of the asset holders (i.e. the candidates).
 
Forest 


(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).


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