[EM] To Martin re: SFC

[Martin Harper]

Hi Mike. How was your weekend?


Let's compare this to the Independance from Clones Criterion. Blake's 
defn of this is the following (with appropriate defns of clone set, 
eliminated, etc):

 >>>>> "If there are alternatives X1, X2 ... Xn that are a clone set, 
and if one of these clones is eliminated from every ballot, then, if the 
winner for the old ballots was in the clone set, the winner for the new 
ballots must also be in the clone set. If an alternative outside the 
clone set won for the old ballots, the same alternative must win for the 
new ballots."

Now, we could rephrase this using your type of wording, and the first 
clause would be replaced with:

"If there are alternatives X1, X2 ... Xn that are a clone set, or are 
close enough to a clone set, and..."

But what does "close enough" mean? Well, exactly the same as your "on a 
scale sufficient": it might mean a single voter who votes them 
non-adjacently, or it might mean lots of voters voting them non-adjacently.

Here's another example: "IRV elects the Condorcet winner, provided that 
third parties do not occur on a scale sufficient to change the outcome." 
- an absolutely true statement. But if you check it, all it's actually 
saying is that IRV elects the Condorcet winner, provided there are only 
two parties in the election.

Now, you claim that for the wv methods you propose, the typical levels 
of falsification will be typically unable to stop SFC's gaurantees from 
working. That's all very well and good - but it's just a claim, and it 
is entirely possible for a method to pass SFC, but to fail this further 
claim.

So what I'd really like is to have some evidence for your claim. I'd 
also like to see both instances of "typically" given values: for 
example, in terms like "if the CW beats B by X%, then falsification can 
occur on a scale of up to Y%, and B will still not be elected." 
(provided the rest of the conditions hold.


Incidentally, you criticise my example methods somewhat. The point here 
is that they were examples. I like to keep my examples simple. I thought 
it was fairly obvious that they weren't serious proposals, given how 
they involved oracles, devils, and similar such things.

I came up with these two methods, both of which pass SFC, in order to 
contrast the different meanings of "and that falsification doesn't occur 
on a scale sufficient to change the election outcome" in each case. In 
the first method, that phrase means one voter, in the second case that 
phrase means any number of voters. Hence, my reasoning went, the phrase 
is essentially meaningless.

Hope this clarifies things... :)