[EM] Proposal: Majority Enhanced Approval (MEA)

[Juho]

On May 9, 2010, at 2:34 AM, fsimmons at pcc.edu wrote:

Here are some more late comments (I was busy with some other  
activities for a while).

> Juho,
>
> Thanks for your interest and input.
>
> Having an approval cutoff to rank just like the candidates is a good  
> idea.  On ballots where the cutoff is
> ignored (i.e. truncated) then all ranked candidates are ranked above  
> the cutoff.
>
> In general, I don't think that voters will truncate a decent  
> Condorcet candidate, since voters will tend to rank
> the lesser evil last and truncate the greater evil when they think  
> no really good candidate has a decent
> chance of winning.

I was thinking about situations where both left and right wing have a  
good compromise candidate. Let's say that both wings have one extreme  
and one moderate candidate (XL, ML, MR, XR) and the extreme ones have  
more support within their wing.

Let's first assume that left wing voters will not rank (nor explicitly  
approve) the right wing candidates and vice versa (but most of them  
rank candidates of their own wing).
As a result one of the extreme candidates (let's say XL) will probably  
have greatest approval, and XL will pairwise beat ML.
- If left wing has majority then XL will win
- If right wing has majority then XL is probably covered by both right  
wing candidates and XR will win

Conclusion:  We need more approvals and/or rankings across the border  
line between the two wings if we want to elect good compromise  
candidates in this set-up. Voters must use the implicit approval  
cutoff so that they "approve" also candidates that they may strongly  
dislike and that are the strongest competitors of their own favourite   
candidates. The supporters of the extreme candidates may need to rank  
both their first compromise candidate and also the compromise  
candidate of the other wing (if there are not many enough supporters  
of the moderate candidate to do the job).

(One could also generalize this so that any Condorcet method that  
encourages truncation to separate one's favourites and those that are  
not carries a risk of making the sincere Condorcet winner lose.)

Let's then assume that sufficient number of left wing voters will rank  
the moderate right wing candidate and vice versa so that the moderate  
candidates will pairwise beat the extreme candidates of their own wing  
(ML>XL, MR>XR). In this case we will probably have a Condorcet winner  
(ML or MR).

Then let's try to see what will happen when there is a top cycle (and  
the approvals may influence the outcome of the election). Let's say we  
have a third wing with candidates MT and XT. We also assume that  
voters will rank the moderate candidates of the other wings  
sufficiently so that they will both beat and cover the extreme  
candidates. The winner must be one of the moderate candidates then.  
The moderate candidates are looped, so none of them cover any of the  
others.

In this situation any approval that a voter gives to the moderate  
candidate of some other wing increases the probability that the winner  
will be that candidate and decreases the probability that the moderate  
candidate of one's own wing will win. It seems that a good strategy  
(with explicit approval cutoff) could be to approve some of the  
expected frontrunners (that might become looped) (not all of them, not  
none of them). If one wants to use an implicit cutoff, then maybe  
something like "approve all but the last ranked candidate(s)" could  
work. Or maybe "approve all but the last two ranked candidates" since  
the size of the cycle is at least three and this might often enough  
lead to a bullet approval vote to one's favourite among the three  
frontrunners. If voters know that there is such an approval cutoff  
they might also give fuller rankings (good!) since they would now  
happily rank also the compromise candidates of the other wings as  
"ranked but not really approved" (and ranking one of the favourites  
just above the truncated / tied last candidates would carry a flavour  
of not approving them).

(Another psychological trick would be to use ballots that have a  
"green" section to rank the nicest candidates and a "red" section to  
rank the less liked candidates. It would feel natural to fill also the  
"red" section. Also here I try to get full rankings of all the  
potential winners.)

(And yet one more and more complex approach would be to have also a  
third neutral section that could be used in Bucklin style to find the  
most approved candidate when there are too few "green" approvals.)

> Now, changing the subject slightly, remember DMC?   In that method  
> if the second place approval candidate
> beat the approval winner pairwise, then that was enough to keep the  
> approval winner from being elected.  In
> MEA tha's not enough, but if the second place approval candidate  
> covers the approval winner, that is enough
> to keep the approval winner from being elected.  So MEA takes  
> approval somewhat more seriously than
> DMC.

Both DMC and MEA are based on a serial process. What do you think of  
comparing directly the uncovered candidates and their approval levels?  
Does the serial process that is used in MEA improve the results when  
compared to jumping directly to the uncovered candidates?

My proposals on explicit cutoffs are problematic in the sense that in  
real life elections most decisions would probably be done based on  
rankings only, and therefore the approval cutoffs are just extra work  
to the voters in most elections. Maybe explicit cutoffs would provide  
at least some interesting statistical data. And they might encourage  
voters to rank also other candidates than their favourites.

Juho



>
> Forest
>
>> From: Juho
>> To: EM Methods
>> Subject: Re: [EM] Proposal: Majority Enhanced Approval (MEA)
>> Message-ID:
>> Content-Type: text/plain; charset=WINDOWS-1252; format=flowed;
>> delsp=yes
>>
>> You seem to use implicit approval cutoff at the end of the
>> ranked
>> candidates (since you say "based on ranked ballots with
>> truncations
>> allowed"). How about using explicit cutoff? Would that take away
>>
>> something essential? I'd like the left wing voters rank also the
>> right
>> wing candidates and vice versa. Otherwise we might easily lose a
>>
>> sincere Condorcet winner.
>>
>> Juho
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