[EM] Woodall's Whacky & Zany Criteria

[MIKE OSSIPOFF]

The other day I  mentioned how, in a vote between X & Y, with 2 voting X 
over Y, and 1 voting Y over X, and 98 refusing to express a preference, 
symmetric completion would give us a majority vote for X over Y.  A 
majority, when only 2/100 people voted X over Y.

If you think that's funny, then what abouit this?: Chris claims that if 
symmetiric completion isn't a good thing, that doesn't mean that the 
Symmetric Completion Criterion isn't a good thing. No, the SCC just says 
that a method should either do symmetric completion, or else give the same 
results as if it did symmetric completion. :-)

To Chris, that criterion's merit is independent of the desirability or 
undesirability of symmetric completion.

What about Later No Harm (LNH)? As I understand LNH, it says that adding B 
to your ranking, below A, shouldn't be able to keep A from winning.

But what's the point of adding B to your ranking? To keep someone worse than 
B from winning.  But, for instance, with IRV, your pairwise preference for B 
over C, when ranking B in 2nd place, might not even be counted (by that 
word's dictionary definition, Jan Kok). Sometimes, if you actually want to 
keep C from winning, you have to put B in 1st place, over A, in IRV. And 
that _can_ harm A. It only takes half as many mistaken compromisers to give 
away A's win in IRV as it would require in Approval.

So this freedom to rank B without harming A is rather hollow, since B in 2nd 
place doesn't reliably give the method anything that will be counted against 
C.

We don't rank B because we're there to make B win. We'd rather that A win. 
We rank B to keep someone worse than B from winning. Hey, wait a minute, 
that's what the majority defensive strategy criteria say too. As opposed to 
the more cosmetic act of merely ranking B.

And what about the criteria's requirements? LNH says that we don't want to 
harm A. FBC speaks of not having incentive to vote someone over your 
favorite. My original definition of voting X over Y said:

A voter votes X over Y if s/he votes in such a way that it's possible to 
contrive a configuration of other people's ballots such that if we delete 
everyone but X & Y from the ballots, X is the unique winner if & only if we 
count that voter's ballot.

[end of definition]

Since there are only 2 candidates left on the ballot, we could say "...X is 
the unique winner instead of Y".

Though that definition specifies removing everyone but X & Y from the 
ballot, it's obvious that voting in that way could also probably just as 
likely change the winner from Y to X even without removing everyone else 
from the ballot. That removal was mainly motivated to make the definition 
apply as expected to nonmonotonic methods.

So then FBC, and the other defensive strategy criteria are also requiring no 
harm to one's favorite, or no harm in the form of changing the winner from a 
more preferred candidate to a less preferred one.

So, what I'm saying is that if we change LNH so that it makes more sense, so 
that it speaks of keeping someone worse than B from winning instead of the 
hollow goal of merely ranking B, then we get the defensive strategy 
criteria, or something very similar to them.

This suggests that the defensive strategy criteria do a better job of 
measuring for the standard(s) that, consciously or unconsciously LNH is 
based on.

Mike Ossipoff

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