Approval and LO2E

Mike Ositoff ntk at
Tue Nov 3 23:06:55 PST 1998

> If that isn't a criterion, perhaps it should be.
> >so I've quit using it, and I stick with the 1st Choice Criterion,
> >which says that there should never be a defensive strategic
> >need to vote a less-liked alternative over one's favorite
> >(weak form); or to vote a less-liked alternative equal to or
> >over one's favorite (strong form).
> I am having trouble defining the 1st Choice Criterion in a
> rigorous way based on your statement.  Here is one attempt
> There must be some way that the group of voter's whose first choice 
> is the sincere Condorcet Winner can fill out their ballots to ensure
> the election of their favorite and still rank this favorite alone in 
> 1st place.

That isn't it.

> I'm pretty sure that isn't satifiable though.  I guess I need a
> rigorous definition of "defensive strategic need."

Certainly. At the time I wrote my definition of the 1st Choice
Criterion, it did occur to me that I should include a definition
of defensive strategy. So here it is:

If voters, in order to ensure that a CW will win, instead of
someone they like less, do other than sincerely rank all of
the candidates, that's defensive strategy.

That's how I'll define defensive strategy if an exact
definition is needed. I've previously sometimes defined it
more broadly so that if a majority do other than sincerely
rank all the candidates in order to elect someone they
all like better than the person who'd otherwise have won,
then that too is defensive strategy. That would mean that
it would be meaningful to speak of defensive strategy in
a natural circular tie. For a working definition now, it
would probably be best to limit it to what I said in
the previous paragraph. It seems to me that both the broad
& narrow definitions worked with the statements I've made.

But I guess it complicates that definition if I have to
add that I call it "defensive strategy" also when people
do other than sincerely rank all the candidates to thwart
an effort by other voters to elect their candidate instead
of the CW. (in VA, when defending against order-reversal).
I'd call that "retaliatory defensive strategy", since it
doesn't protect the CW, except by deterring attempts to
steal its win.

So that's how I'm defining defensive strategy, in the paragraph
about protecting a CW's win, and in the above paragraph about
"retaliatory defensive strategy" that thwarts an attempt to
steal a CW's win but doesn't directly protect the CW's win.

The part about majority perhaps broadens the definition
undesirably, and should probably be left off. Maybe, with
that part added to the definition, it could be called
"broadly-defined defensive strategy".

> >
> >When we've used LO2E by itself, we're usually just referring
> >to a voters' problem, in general terms, the fact that voters
> >need to abandon favorites for compromises.
> >
> ...
> >
> >Approval:
> >
> >Voters may vote for 1 or more candidates, giving a whole vote
> >to each one they vote for. The candidate with the most votes
> >wins.
> >
> I think there are some different definitions of approval floating

There probably are, but the definition I stated here is the
one that describes the same method proposed by the person
who originated & named Approval. Demorep uses the term to
talk about Y/N voting, but that isn't how Approval's originator,
or subsquent writers, use the name.

Concluding this message, and will reply to the remainder
in a subsequent message in which paragraphs already replied-to
are deleted.


> around.  Anyway, my problem is this:  Consider an election with
> a united but minority totalitarian movement and a fragmented
> democratic movement.  A and B will be the democrats.  C will
> be the totalitarian.  The public will be 55% democratic, 45%
> totalitarian.  The totalitarians will likely all vote for C
> alone.  Voter preferences are as follows:
> 30 A B C
> 25 B A C
> 45 C A=B
> Now if not enough A and B voters compromise the result could be 
> like this
> 25 A
> 10 A B
> 20 B
> 45 C
> A 35
> B 30
> C 45
> With C winning easily
> On the other hand, one of the A or B groups could stare down the other
> side, using its fear of C to force it to compromise.
> 35 A B
> 20 B
> 45 C
> A 35
> B 55
> C 45
> Here B won because the C voters panicked.  This is what I mean by
> government of the stubborn.
> If both A and B compromise the results could look like this
> 50 A B
> 3 A
> 2 B
> C 45
> A 53
> B 52
> C 45
> See how compromise can result in the election between A and B being
> made by a few people who don't compromise.
> This is in contrast to Smith//Condorcet, Tideman, Schulze (VA and Margins) 
> and AV/IRO, where the democratic voters can prevent the election of C 
> just by ranking C last.  And the C voters have no way to use insincere 
> voting to get C elected.
> This is of course related to my problems with Approval and Clones,
> since A and B are clones as far as their sincere rankings in this
> example.
> ---
> Blake
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