[EM] Siimpson-Kramer definition

[MIKE OSSIPOFF]

James--

You asked:

so what is Simpson-Kramer / minimax?

I reply:

To exactly quote the Nalebuff & Levin definition that Markus posted, I'd 
have to check the archives, but I believe that I can do a fair job:

The winner is the candidate whose greatest vote against him/her in a 
pairwise comparison (defeat or victory) is the least.

[end of Simpson-Kramer definition]


Now, I have to admit that I don't know whether or not Simpson-Kramer first 
seeks an unbeaten candidate and declares him/her the winner, and then 
applies the above rule only if there isn't an unbeaten candidate; or 
whether, instead, Simpson-Kramer applies that rule immediately.  If the 
latter, then Simpson-Kramer fails the Condorcet Criterion.The CW could have 
large-turnout pairwise comparisons, with big votes against him, and slightly 
bigger votes for him.

Nalebuff & Levin, at the beginning of their article, say that they aren't 
considering (or was it not talking about?) truncated rankings. There are 
several interpretations:

1. Simpson-Kramer is undefined unless everyone votes a complete ranking.

2. Simpson-Kramer is defined for truncated rankings too, but Nalebuff & 
Levin don't know that more general Simpson-Kramer definition.

3. Simpson-Kramer is defined for trunated rankings too, and Nalebuff & Levin 
know that more general definition, but aren't telling.

If the answer is #1, then Simpson-Kramer is obviously not PC, because PC is 
defined for truncated rankings too.

If the answer is #2 or #3, then it isn't known whether or not PC is 
Simpson-Kramer, and therefore it isn't justified to call PC Simpson-Kramer 
(or "minmax", which is a name that Nalebuff & Levin use for Simpson-Kramer).

That's based on the preceding. But, from what follows, Simpson-Kramer and PC 
are definitely not the same thing:

Either Simpson-Kramer is defined for truncated rankings or it isn't.

1. Say Simpson-Kramer is defined for truncated rankings: Obviously, when 
some rankings can be truncated, different results can be gotten by looking 
at greatest vote against in a (any) pairwise coimparison, including 
victories, as compared to looking only at greatest vote against in a 
pairwise defeat. So Simpson-Kramer is not PC.

2. Say Simpson-Kramer is not defined for truncated rankings: PC is defined 
for truncated rankings, and so obviously PC and Simpson-Kramer are not the 
same.

As I said, Nalebuff & Levin call Simpson-Kramer "minmax", which means that 
minmax can't mean PC, because PC and Simpson-Kramer aren't the same.

Now, you might say "What if someone else uses "minmax" to mean something 
else? What if someone else uses "minmax" to mean PC?". Well, if "minmax" is 
used to mean various different methods, then "minmax" doesen't mean anything 
at all. Then, minmax isn't the name of any voting system.

I'm going to post this message every time someone calls PC "minmax".

If people don't mind, I'd rather be the one who says what I mean by PC.

If you don't believe that Condorcet himself proposed PC (but can you not 
believe that after you read the translation of Condorcet's proposals?), then 
accept the fact that a number of authors have called PC "Condorcet" in 
journal articles. I believe that Fishburn is one of those, for instance.

Either Condorcet was the 1st proponent of PC, or else I and various journal 
authors have been callilng the method PC or "Condorcet" for a long time. 
That's it's name.

But maybe you want to change the name of PC. If you insist on changing PC's 
name, at least could you consider using a name that doesn't already belong 
to a different method?

As I said, I'll post this message every time someone calls PC "minmax" or 
"MinMax".

Mike Ossipoff

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