-------------------------------------------------------------------------------- Jan said:
Mike Ossipoff wrote (many things, including):
True, Approval doesn't let you vote all your preferences, but at leastit
reliably counts all those that you vote. That can't be said for IRV.
What do we mean by "counts"?
I reply:
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 like this:
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 items.
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 outcome.
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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