[EM] Description of "Median," my Approval variant

[Kevin Venzke]

 --- Forest Simmons <fsimmons at pcc.edu> a écrit : 

>How about subtracting the approval score from twice
the max opposition score and going with 
>the smallest result? 

Whew.  That might work, as well (and not require a
calculator).  The main thing is that if the final
score represents something you can picture, it's
easier to explain the system to uninterested people,
and convince them that we would not be at the mercy of
potentially random results.  (I've had a couple of
people charge that the system is not deterministic, as
though I were looking at a spectrum and saying, "That
guy looks like the median; let's see what we can do to
get him elected.)

Originally I was trying to design a system where
center candidates could "acquire" other candidates'
votes in proportion to their overlap.  I had to
abandon it because the overlap matrix would need a
number of dimensions equal to the number of candidates
you could vote for, in order to avoid double-counting
(i.e., a candidate "acquires" the votes of two other
candidates, but they actually represent some of the
same voters).  Also, vote-acquisition could be
criticized for making assumptions about what is
"actually" acceptable to a voter.

I always used to factor in Approval with Median.  The
final score was (Approval minus Median score), but I
changed the "minus" to "divided by" because it seemed
more fair to candidates with less approval.  E.g., if
you use subtraction, 50 approval with 40 GCD
("greatest constructive disapproval") would tie with
40 approval, 30 GCD.  If you divide, the latter is
more electible (sp?), and I think it should be.

>I have another suggestion. If I understand correctly,
you chose the word "median" because of 
>the centrality of the position that is least far from
the most distant of the other positions. But 
>technically (at least for linearly ordered point
sets) the position closest to the most distant of 
>the other positions is the midrange position, the
position halfway between the extremes. 
>What complicates things is that your measure of
"distance" is based on numbers of voters in
> various subsets, so that creates a resemblance with
median calculations where numbers of 
>voters on each side are the determining factor.

This latter "complication" is the view I take of it. 
It seems to me that we can't talk about the "midrange
candidate" because that candidate might not exist (the
distances aren't uniform).  I actually don't mean to
refer to the "median candidate," but the "median
voter," as you noted, which should be equivalent to
the "midrange voter."  The "median candidate" is not
the same thing at all, for instance if one side of the
spectrum is littered with candidates in comparison to
the other.  (Major clone problems if you elect the
literal "median candidate.")

>Of course you can name your method anything you want
to, but (1) "median" is already 
>overworked, and (2) "median" isn't sexy enough for
the public. 

I can definitely see that.  I originally called it
Approval/LUB, with the slash indicating division, and
LUB standing for "largest unrepresented bloc."  Later,
for quite awhile, I called it CDV for "constructive
disapproval voting."  I think that's a reasonably sexy
name...  I went to "Median," though, because it seems
to contain, right in the name, its justification.  It
takes some additional effort to explain why
"constructive disapproval" is better (or aims at
something different than) "approval."

>If we write the opposition scores as percentages of
the total number of ballots, and then 
>subtract from 100%, we could call the result
"satisfaction" and call the method "Max 
>Satisfaction."

I think that would end up annoying a lot of voters,
since they could vote against the winner but still be
counted in the "satisfaction" score if their votes
weren't the largest bloc of disapproval.  Except for
that, that kind of score could at least satisfy people
who want "large score" to mean "good."

>There's also the possibility that somebody else has
already named the corresponding method 
>based on pairwise matrices derived from fully ranked
preference ballots. It would be 
>interesting to see how they described it and what
they named it, as well as any properties that 
>your version would naturally inherit. 

Yes, that would be pretty interesting.  I'm having
some difficulty imagining how it would work with
ranked ballots, though...  I conceive of my system as
roughly estimating Condorcet without requiring
thought-out rankings.  Thus if it translates into
something quite different from Condorcet, when applied
to ranked ballots, I'd be quite surprised.

Kevin Venzke


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