Approval and LO2E

[Blake Cretney]

On Fri, 30 Oct 1998 18:53:14   Mike Ositoff wrote:
>> 
>> On Wed, 28 Oct 1998 18:18:10   Mike Ositoff wrote:
>> >
>> >> I think it's worth pointing out that Approval's LO2E assurance
>> >> is rather different from the ranked methods'.  That is, in the
>> >
>> >I haven't made a secret of that, Blake: Approval doesn't assure
>> >you that you'll never have strategic need to vote a less-liked
>> >alternative equal to your favorite--but then neigher does
>> >Margins :-)
>> 
>> Of course, that isn't what LO2E says.  If I remember, LO2E says
>> that the majority has a way to prevent the election of a candidate,
>> without voting insincerely except with respect to this candidate.
>
>That wasn't how it went, but someone, maybe you, found a problem
>with LO2E-2, which is the one you're probably referring to, and

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.

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

>
>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
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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