Demorep's Example & Objection

[Mike Ossipoff]

First, I'd like to point out that Demorep's example is one 
in which not only is every alternative beaten, with sincere
rankings, but every altertnative has a full majority of all the
voters ranking something over it, sincrely. Demorep is talking
about a mighty hopeless, chaotic & ridiculous situation. 
Majority rule doesn't say who should win, since everything
has a majority preferring something else to it. The basic 
democratic principle that I named in a previous message can't
be complied with. And it isn't really meaningful to speak of
a lesser-of-2-evils problem under these conditions either.
This example is irrelevant. There's no right answer when
every alternative is beaten that badly by the sincere set of
rankings. Condorcet(EM) differs from other methods in not
unnecessarily violating that basic democratic principle that
I mentioned. Demorep has shown us an extreme and unlikely
example where no method can avoid violating it. So what?
 
Demorep said that his method isn't Instant Runoff (MPV,
the Alternative Vote, etc.). Oh yes it is, when there
are 3 alternativess. With 3 alternatives, Demorep's method
is identical to MPV. Since I've already posted bad-examples
for MPV, it isn't necessary to post one for Demorep's method,
but here's an example, the one I've most often used. Demorep's
method fails every one of the bad-examples that I've given
for MPV, Regular Champion, Young & Dodgson, & Simpson-Kramer.

Anyway, here's the example I've mosts often used:

40: Dole, Clinton, Nader
25: Clinton
35: Nader, Clinton, Dole

(We could have the Clinton voters divide their support between
Dole & Nader equally & that wouldn't affect the result wiin
Demorep's method)

If the Dole voters truncate, that creates a circular tie. Demorep
eliminates Clinton, who'd beat each one of the others in
separate 2-candidate elecions, and gives the election to Dole,
the only candidate with a majority against him.

Let me translate Demorep's example into a more familiar
language (but tell me if I've misinterpreted what your example is,
Demorep). 

Demorep is saying that A beats B 55 to 45, & B beats C 54 to
46, and that C beats A 56 to 44. No one has truncated.
The rankings are all sincere. These sincre rankings are
as follows (Because of the large number of voter groupings,
I've tried a columnar format. I haven't used that before in
e-mail, so I hope it posts ok):

Number of voters: 19 21  4 31 15 10
                   A  A  B  B  C  C
                   B  C  A  C  A  B

(Below each number of voters is the columnar ranking of those
voters, with their favorite on top, & their 2nd choice below).

***

Demorep says that 21 of the A voters, by voting sincerely, have
caused C to win, when if even 2 of those 21 had insincerely voted
B over C, then C wouldn't have won. Right. Who'd have won? B.
The order-reversal by those A voters would secure the election of
someone they like less. Bravo. 

In Demorep's 1st set of rankings, stated above, everyone has
voted sincerely, and the result is that the 2nd choice of those
21 A voters has won. Demorep is saying that they'd have an
incentive to change that so that their last choice instead of
their 2nd choice would win. Come again?

***

Then Demorep claims that voters will order-reverse in order
to maximize other candidates' votes-against. He proves that with
an example of how they'd do that:

All the A voters rank B 2nd. All the C voters rank A wnd. All
the B voters rank C 2nd.

Number of voters: 40 25 35
                   A  C  B
                   B  A  C

Now A wins instead of C. 

My main answer to this is that an example with everything 
sincerely beaten to this degree isn't of interest
in terms of the standards that I and many others consider important:
Getting rid of the lesser-of-evils problem, and protecting
majority rule. As I often say, the choice of methods simply
depends on what we want from a method.

The voters who are worse off because of this insincere voting
are all of the C voters, & the 31 B voters who prefer C to A.
Who gains? All of the A voters, and the 4 B voters who prefer
A to C.

So the voters who have incentive to give C's win to A are the
A voters & those 4 B voters.

The C voters, the main victims of the A voters' order-reversal,
have obligingly co-operated with the A voters' strategy, by
all voting A over B. Had they not done that, B would be beaten
by only 55 votes-against, and the A voters' order-reversal would
elect B, the last choice of the order-reversers. 

Demorep has simplistically suggested that everyone's interests
are served by order-reversal. It didn't help the C voters if
it made it possible for A voter order-reversal to steal the
election from them, electing the last choice of those C
voters.

A voters' motive for insincerely voting B over C is to prevent
C from winning. Even if it worsens the result for those A voters?
I doubt it.

But, as I said, this is a pointless example that doesn't relate
to the standards that many people, including me, consider
important.


Mike

 



--