[EM] Re: Simpson-Kramer definition

[MIKE OSSIPOFF]

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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