[EM] Optional Later-no-harm AER

[Chris Benham]

  An  idea for improving  Approval  Elimination Runoff   (an 
 Approval-STV hybrid) :

1: Voters rank the candidates and also place an Approval cutoff. 
 Truncation allowed, and if equal preferences are allowed
then the votes are split. Default placement of  the cutoff  can be 
either below  first preference or below lowest  ranked
not-in-last-place candidate.
2:  A candidate with a majority of first preferences is elected.  If  no 
candidate has a majority, then eliminate the candidate
with the fewest  approvals and  transfer preferences  IRV-style. 
Whenever  a candidate is the highest ranked of  those
remaining candidates on a majority of  the ballots that distinguish 
between them; then that candidate is elected.
3: If, after one or more eliminations, there are ballots that no longer 
make any approval distinction between the remaining
candidates, then those ballots that approve none of the remaining 
candidates shall be counted as approving the highest-ranked
of  them  and those ballots that approve all of  them will be counted as 
approving all  but the lowest-ranked.

This last feature is my new idea. Ranking but not approving  a candidate 
 can never harm an approved candidate, so voters
can have as much  Later-no-harm as they want.
Without this feature, AER  and other methods that use an  approval 
cutoff  give too big an advantage to well-informed
strategic voters. My idea is that as and when a  voter's approval cutoff 
 in it's original position becomes redundant/useless
(because it no longer distinguishes between the remaining candidates), 
it is moved the minimum distance neccessary for
this to be not the case.
Some people who are not  Condorcet fans have been down on the idea of  a 
 "low utility" CW with very few first preferences
winning. They can be reassured that with this method such a candidate 
cannot win unless they are explicitly  "approved" by
a significant  proportion  of  the voters.
This method  can easily be adapted  to elect more than one winner by  PR.
It  doesn't meet the Condorcet Criterion, but that is incompatible with 
Later-no-harm.
A while ago (Sat.Apr.13,2002) Adam Tarr  posted something on 
"Approval-Completed Condorcet".
In his example, these were the sincere preferences:

49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
100 voters. Gore is the sincere CW.

With approval cutoffs, this was his problematic scenario:

49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush

"Now, Bush wins the approval runoff 55-51-33.  This is where ACC's favorite 
betrayal scenario comes in.  Since Bush wins the approval vote, the only 
way the majority can guarantee a Gore win is to make Gore the initial 
Condorcet winner, which requires that the Nader camp vote Gore in first place:"

My point is that this is no problem for AER. Nader is easily eliminated and then Gore
(the sincere CW) wins.

Chris Benham



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