<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html;charset=ISO-8859-1">
<title></title>
</head>
<body>
<meta http-equiv="Content-Type" content="text/html;charset=ISO-8859-1">
<title></title>
<title></title>
An idea for improving Approval Elimination Runoff (an Approval-STV
hybrid) :<br>
<br>
1: Voters rank the candidates and also place an Approval cutoff. Truncation
allowed, and if equal preferences are allowed<br>
then the votes are split. Default placement of the cutoff can be either
below first preference or below lowest ranked<br>
not-in-last-place candidate.<br>
2: A candidate with a majority of first preferences is elected. If no
candidate has a majority, then eliminate the candidate<br>
with the fewest approvals and transfer preferences IRV-style. Whenever
a candidate is the highest ranked of those <br>
remaining candidates on a majority of the ballots that distinguish between
them; then that candidate is elected.<br>
3: If, after one or more eliminations, there are ballots that no longer
make any approval distinction between the remaining<br>
candidates, then those ballots that approve none of the remaining candidates
shall be counted as approving the highest-ranked<br>
of them and those ballots that approve all of them will be counted as
approving all but the lowest-ranked.<br>
<br>
This last feature is my new idea. Ranking but not approving a candidate
can never harm an approved candidate, so voters<br>
can have as much Later-no-harm as they want.<br>
Without this feature, AER and other methods that use an approval cutoff
give too big an advantage to well-informed<br>
strategic voters. My idea is that as and when a voter's approval cutoff
in it's original position becomes redundant/useless<br>
(because it no longer distinguishes between the remaining candidates), it
is moved the minimum distance neccessary for<br>
this to be not the case.<br>
Some people who are not Condorcet fans have been down on the idea of a
"low utility" CW with very few first preferences<br>
winning. They can be reassured that with this method such a candidate cannot
win unless they are explicitly "approved" by<br>
a significant proportion of the voters.<br>
This method can easily be adapted to elect more than one winner by PR.<br>
It doesn't meet the Condorcet Criterion, but that is incompatible with
Later-no-harm.<br>
A while ago (Sat.Apr.13,2002) Adam Tarr posted something on "Approval-Completed
Condorcet".<br>
In his example, these were the sincere preferences:<br>
<pre>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
</pre>
<br>
</body>
</html>