[EM] What count means?
nkklrp at hotmail.com
Fri Jan 23 22:40:09 PST 2004
Mike Ossipoff wrote (many things, including):
>True, Approval doesn't let you vote all your preferences, but at least
>reliably counts all those that you vote. That can't be said for IRV.
What do we mean by "counts"?
Here we use the verb "count" in 2 different ways:
1. For a voting system, to count all the ballots means to use them to
determine the winner.
2. The standard dictionary definition of the verb "count" goes something
Let's define a number called "the count". Set the count equal to zero.
Increment it for each item that we want to "count". When that has been done,
we refer to the final value of the count as "the sum". Doing the
above-described process to obtain the sum is what it means to "count" the
In that standard dictionary sense, Approval counts every pairwise preference
that you vote. I've already stated a definiion of voting a preference for X
over Y. If more people have voted a preference for Smith over Jones than for
Jones over Smith, then Jones loses in Approval.
Obviously that isn't how an Approval count is done, but the result is as if
it were done that way.
Condorcet obvioiusly counts all pairwise preferences too, and uses the sums
for each X vs Y count for determining the winner.
In IRV, at any stage of IRV's procedure, if more people have ranked Smith
over Jones (and everyone else) than have ranked Jones over Smith (and
everyone else), then Smith doesn't lose that particular count. A candidate
loses that count if everyone beats Jones in that count in the sense that
Smith beats Jones in my example.
So, in IRV, at a particular stage of the the IRV process, the fact that a
voter voted Smith over Jones is counted only if that voter also voted Smith
over everyone else too. But if he did, that pairwise voted preference is
counted. As I said, if the number of voters who have voted pairwise
preferences for Smith over Jones that are counted is greater than the number
of voters who have voted pairwise preferences for Jones of Smith that are
counted, then Smith doesn't lose that count. There'll be one candidate for
whom it can't be said that he hasn't lost that coiunt. He is elminated.
Though the instructions for IRV doesn't read like that, the results are as
if they did. I've worded IRV & Approval as I did, so as to express their
counting instructions in terms of voted pairwise preferences.
So, when these methods instructions are worded in terms of pairwise
preference votes, it's correct to say that Approval and Condorcet reliably
counts every pairwise preference that you vote, while IRV doesn't.
That uses the ordinary, standard dictionary definition of the verb "count".
Sure, some wag could define a method that would count a pairwise preference
vote and then disregard it. Fine, but if the result is based on count sums,
and you don't even count a particular pairwise ipreference vote, that
ensures that it can't possibly affect the outcome. Then, counting a pairwise
vote is at least a requirement for giving it a possibility of affectng the
So, Jan, what do I mean by [the verb] "count"? I use the standard dictionary
definition of that verb.
You suggested that maybe I use an unusual or new definition of the verb
"count". I don't. It's in the dictionary.
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