[EM] SD & the defensive strategy criteria

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Mar 20 19:41:18 PST 2001

```
> > Say there are 3 candidates, and your favorite comes in "middle" in
> > the Approval count. Your favorite is B.
> >
> > B is sincere CW--is preferred to both A & C by more voters than
>vice-versa.
> > A pairwise beats C.
> >
>
>If B is the sincere CW under Condorcet, then she will win in Approval
>Seeded SP, at least my version. Whether B starts in the middle or the
>bottom of the seeded list, she will win every pairwise comparison all of
>the way to the top.

Certainly, if B is the _voted_ CW. But B could be the sincere CW
without being the voted CW. If the A voters truncate, and don't
vote B over C, then they can allow C to beat B, even if B is sincere CW.
Then B is out of the election.

And if A voters actually order-reverse against B, voting C over B,
then likewise they can make C beat B, even if the C voters strategically
refuse to vote C over B. C voters, in order to save B, could then have
to vote B over C, in violation of WDSC & FBC.

Either way, it's then between A & C, and A beats C under sincere
voting (by assumption). I could write an example in which the B voters then
can't prevent A from winning without insincerely voting C over A.

> > The Approval finishing order is
> > A, B, C. Some A voters truncate in the BC election. So, even though
> > B is sincere CW, B loses to C.
> >
> > When C goes agains A, A wins.
>
>In my version, A loses to B, so A stays at the bottom and is never
>compared to C.

But I'm saying the Approval finishing order is A, B, C. So the 1st
contest is between B & C. An example can be written in which truncation
or order-reversal by some A voters can allow or cause C to beat B, even
though B is sincere CW.

I admit that SFC, GSFC, FBC, & WDSC aren't criteria that you'll find in
journal articles, and so you might say that Approval-Seeded SD's
violation of those criteria isn't important. Not in the academic world.
But voters are very concerned about the lesser-of-2-evils problem, and
majority rule is a popular standard. I claim that the defensive strategy
criteria are the ones that best measure for both of those standards.

I should add the disclaimer that it's always possible that I don't
understand the method, or am making some other error. But it seems to
me that those criteria aren't met by that method.

those criteria aren't used in the academic world, but I claim that
they're about things that are important to voters.

In a meeting, when there's no computer, and a handraising vote is
desired, and there isn't time for any pairwise-count method,
then Sequential Pairwise isn't a bad solution, provided that people
are vigilant about order-reversal, and willing to retaliate against it
on a subsequent vote involving the reversers' alternative.  Approval
is a good way to seed SD. A quicker way is to write the alternatives on
the blackboard, in a vertical list, and flip a coin to decide whether to
start from the top or the bottom of that list.

Myself, I'd much rather use Approval than SD in a meeting, however,
because Approval is such a good public elections proposal that I'd want to
demonstrate Approval in the meeting.

Mike Ossipoff

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