[EM] Answers to selected Steph statements

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Aug 27 20:21:42 PDT 2002

Steph has already been well-answered, and so I'll
limit myself
to a few brief comments on his letter:

First, this is what I, and all of us, mean by CW:

Candidate C is CW if and only if, for every candidate
Z who isn't
candidate C, the number of voters who prefer C to Z is
greater than
the number of voters who prefer Z to C.

[end of definition]

Note that "prefer" refers to sincere preferences, not
to votes.

Steph wrote:
1) Why is it that important that "truncation won't
steal the election
from a
majority-supported CW"?

I reply:

How about majuority rule? A majority indicate that
they prefer
X to Y, so shall we elect Y, if there is no beatpath of stronger
majority defeats contradicting that defeat?

For judging majority rule violations, I suggest that the most
useful definition is something similar to Markus' Beatpath GMC,
something that says:

Majority rule is violated if we elect a candidate who has a
majority defeat that isn't the weakest defeat in a cycle.

That could be called Qualitative or Comparative Beatpath GMC
(CBGMC). CBGMC is a criterion that is failed by methods that can
violate majority rule as defined in the previous paragraph.

It's ok that Plurality passes BGMC & CBGMC, because it's
accepted that Plurality doesn't violate expressed majority wishes.

CBGMC is a special case of Steve Eppley's BC. It's ok that Plurality
passes BC, because BC isn't used for comparing method merits, but
is only used for determining compliances with other criteria:
A rank method that meets BC also meets SFC, GSFC, WDSC, & SDSC.

I once defined GMC, saying that a we should never elect a candidate
who has a majority defeat if there's a candidate who doesn't.
Beatpath GMC improved on that, because it's reasonable that a defeat
loses some validity if it's part of a cycle of similar defeats.

I prefer CBGMC, because a defeat is more fairly nullified by
a beatpath that's stronger than the defeat. In that way, the criterion
only lets one candidate win in a Smith set cycle of majority

A good definition of majority rule is important, considering how
much the term is used, and how many people consider it an important

Also, I use that term in my definitions of offensive & defensive

Defensive strategy is voting that doesn't express all of the voter's
sincere preferences and is intended to protect the win of a CW,
or enforce majority rule.

Offensive strategy is voting that doesn't expres all of the voter's
sincere preferences and is intended to take victory from a CW, or
elect someone in violation of majority rule.

Steph continued:

For me if you change a set of ballots S1 into a new
set S2 by truncating
some ballots, it is quite possible and normal to
obtain a different
we have different ballots! Why would I preserve a CW
of S1 as a winner
if he is no more a CW of S2?

I reply:

He's still CW. Truncation doesn't change who's CW. CW
is about
sincere preferences, not votes. Nor does it
change the fact that a majority of all the voters have
indicated on
their ballot that they prefer one candidate to

Steph continued:

I do not think it is your goal since this is not
guaranteed to preserve
the winner if there is no


4) Thus, isn't the expression of sincere preferences
aimed to by using
dependent on having a CW and voters having no
sincerely truncated
preferences from the start?

I reply:

SFC, GSFC, WDSC, & SDSC don't depend on any assumption
that voters
have preferences among all the candidates. Check the
critia's wording.

As for your claim that the guarantees don't apply when
no CW, you've forgotten about GSFC:

If no one falsifies a preference, and if X is a member
of the sincere
Smith set, and Y is not, and if a majority of all the
voters prefer
X to Y, and vote sincerely, then Y shouldn't win.

[end of GSFC definition]

GSFC applies whether or not there's a CW.

The WV methods pass that criterion and have that
guarantee. The
margins methods don't.

Steph continued:

Since both conditions have no guarantee, I think
winning votes only
offer a partial
incentive toward sincere votes, and thus another
representing optimal fairness
(relative margins) should be considered.

I reply:

WV methods offer absolute guarantees, such as SFC,

Margins methods have situations in which all of the
Nash equlibria
are ones in which defensive order-reversal is used.

Steph doesn't think truncation will happen, but it
will be common
in rank-ballotings. It happened in all the
rank-ballotings that
I conducted or participated in. In one instance, a
voter indicated
strategic intent verbally when he voted.

Mike Ossipoff

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