[EM] question re: converting ballots into a matrix

[rob brown]

On 12/5/05, Dan Bishop <daniel-j-bishop at neo.tamu.edu> wrote:
>
> If Margins is used as the measure of defeat strength, then an A=B ballot
> is equivalent to the combination ½ A>B + ½ B>A, as they both have zero
> net contribution to the defeat strength.  This is what Kevin meant.


So a method that used margins would be unaffected (as I mentioned in my
post, "clearly some methods will be unaffected").  Others *would* be
affected, to some degree or another.

Isn't it reasonable to discuss *how* the methods that would be affected,
would be affected?

Since to me my method of creating the matrix is more logically consistant, I
would guess that the methods would be affected in a positive way, if
anything.  This is of course just a hypothesis based on nothing but
intuition.  Still I think it is worth considering.

This list has had lots of discussion on defeat strength; check the archives.
>
> > I guess my question was, for all of the above, doesn't it make more
> > sense to convert the ballots into a matrix as I described?
>
> Nope.  Even if you're using Margins, in which case it doesn't make a
> difference, your proposal, well, doesn't make a difference, so why spend
> the effort of adding half-votes to your matrix?


Your use of the word "even" above seems out of place, implying that margins
would be the most likely place for it to have a benefit.  But it makes no
difference on margins, as has been established.  It *does* make a difference
on other methods, maybe a positive difference.  You haven't addressed this.

As far as "effort" is concerned, I'm not sure what you mean.  Clock cycles
on a computer?  In the automated "ballot processor" I am making (it will be
added to the stuff at  http://karmatics.com/voting/testharness.html ), it's
most definitely not a problem.  Two extra lines of code, imperceptible time
difference even on ridiculously large numbers of ballots.

Regardless, I'm sure that for actual "calculation of the winner", you can
skip the step if it won't affect the result (such as if you are using
margins for the calculation), and if computing power is exceptionally
scarce.  That's not the point.  My point was that if you need to, say, show
the matrix to human eyes (for instance, as data returned to the public for
analysis of the election), the tiny amount of effort is well worth it since
it provides, in my opinion, a more accurate indication of how people
actually voted.  The simple fact that the matrix now contains an indication
of how many people voted seems a good thing to me, if nothing else.  Other
statistical calculations that are performed on the matrix data, it would
seem, would be more accurate and meaningful.

Also, I think there is a benefit to being able to say "your ballot affected
this matrix exactly equally in magnitude to each and every other ballot".
You cannot say that if using a traditional matrix.

And if you do have a
> reason for half-votes, you can always create a half-vote matrix from a
> traditional matrix, whereas the converse is not true.


I'm not sure I buy this.  How would you do that?

-rob
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