Paul--
I'd said:
"The winner is the candidate whose greatest vote against him/her in a pairwise comparison (defeat or victory) is the least."
You say:
If there's anything that's going to keep an improvement in election methods from being accepted by the people who have to vote for a change it is language like this.
I reply:
I've got news for you: I'm not proposing Simpson-Kramer to the public. In fact I'm not proposing Simpson-Kramer at all.
I was briefly stating Simpson-Kramer's definition. I don't know if Nalebuff's and Levin's definition is different from what I posted. Someone could look it up, because Markus posted it some weeks ago.
For best un-ambiguity, a much wordier definition is better. This time, for this, I chose the brief definition, partly because it isn't a proposal of mine.
You continued:
I had to read that sentence three times and vote on which of the three interpretations was most likely the correct one.
I reply:
You forgot to tell us what your 3 interpretations are. Would you like to post them?
You continue:
I am not at all sure that any of my interpretations are what the author meant.
I reply:
So let's find out. Post your 3 interpretations of my wording of Simpson-Kramer's definition.
We'll find out if any of your 3 interpretations is what Nalebuff & Levin meant, and we'll find out if any of your 3 interpretations is what I meant. Of course Nalebuff and Levin aren't the author: They're the authors.
When you say that you don't understand a definition, it helps if you say which part of it you didn't understand. Which different meanings you found, in a part that you specify.
But I'm going to re-copy the wording that I posted here, and then I'll define it more unambiguously:
Here's what I'd posted:
"The winner is the candidate whose greatest vote against him/her in a pairwise comparison (defeat or victory) is the least."
Now let me try to write it more unambiguously:
(I hope that my indentations post ok, but I can't guarantee that. But pay attention to the "endwhile"s).
Let each candidate in turn be referred to as i.
While a particular candidate is being referred to as i:
Let each candidate other than i, in turn, be referred to as j
While a particular candidate is being referred to as j:
Record the number of people who voted for j over i. Call that "the [put j's name here] votes
against number for i".
endwhile
i now has, for each of the other candidates, a votes-against number labeled with that other candidate's name.
Find which of those votes-against numbers of i is the largest. Call it "i's greatest votes against number".
endwhile
After the above has been done for each candidate in turn, declare, as the winner, the candidate whose greatest votes-against number is less than the greatest votes-against numbers of the other candidates.
[end of Simpson-Kramer instruction]
Again, I don't know whether the above is done immediately, or whether Simpson-Kramer first looks for a candidate with no pairwise defeats, and elects him/her if s/he exists.
So you can very reasonably have two different interpretations of my previously posted definition (and also of the definition posted here), based on the matter in the paragraph before this one.
I don't know if you'll find the Simposon-Kramer definition in this posting clearer than my briefer one int he previous posting. But if you feel that the Simpson-Kramer defintion that I stated in this posting has more than one interpretation, don't hesitate to say what they are.
Mike Ossipoff
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