[EM] question re: converting ballots into a matrix

[rob brown]

On 12/5/05, Kevin Venzke <stepjak at yahoo.fr> wrote:
>
> Rob,
>
> --- rob brown <rob at karmatics.com> a écrit:
> > Because it makes it so that each
> > voter's ballot counts exactly the same (as far as magnitude) as every
> > other voter's.
>
> I guess you assume that a voter wants this?


It does seem to me consistant with the "one person one vote" concept that
each voter should have equal influence in that respect.  Except that here
it's more like "one person, (numCandidates*(numCandidates-1))/2 votes" or
something. :)

It also seems rather expected and reasonable that if two voters express
 A>B=C>D
that it should have the exact same effect in the end as if one of them voted
 A>B>C>D
and the other voted
 A>C>B>D

I suppose one could say that in the first case, the voters did not express
their feelings regarding A vs. B, while in the second case they did.  I
might argue that the voters in the first case explicitly stated that they
considered B and C to be equal.

Of course this is different than the implicit equality from truncated
ballots, in which case my argument is a harder one to make.

> I'm making no guarantees that the result will be "better" in those
> > methods
> > if half votes are counted.  Maybe it will, maybe not.  I'm only
> > hypothesizing that it will.
>
> Well, at least if we're talking about actual election methods and their
> results, this has already been debated to death. I'll be surprised if
> something new can be said on this topic.


Ok, as long as we're talking about the methods themselves, I am convinced
that this does nothing new.

I'm less convinced that for output, showing a matrix "normalized" or
"balanced" in this way (neither are quite the right term) doesn't make
sense.

> As a simple example, if you wanted to use the matrix to answer the
> > question
> > "how many (or what percentage of) people ranked this candidate as their
> > top
> > choice", I believe you could do it if you had a matrix where equals were
> > treated as half votes.  Not so otherwise.
>
> You say this becomes possible by *discarding* information?


Well, I now understand that as long as we store the number of ballots in
addition to the data in the matrix, there is all the data I need.
Otherwise, I don't see how you can do something as simple as a borda count
with the data in a traditional matrix.

-rob
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