At 11:04 AM 6/11/2005, Bart Ingles wrote:
There are four candidates, and the voters are in two groups:
Group I: a=b>c=d
Group II: c=d>a=b
If the two groups differ in size by more than one vote, an additional
voter cannot determine which group wins. If this voter's preference order
is a>b>c>d he should vote only for a and c. In other words, the voter has
incentive to reverse his preference order for b and c (never for a or d).
Just to keep things grounded, this analysis presumes a high degree of
polarization of the electorate such that the voter can predict with
extremely high precision what is given as a precondition.
In other words, what was mentioned earlier about this scenario being
"highly improbable" was an important fact to keep in mind. The voter has to
know that his vote for b will be useless, and that therefore d might win
over c.
Further, this scenario also presumes that, unlike everyone else, let me
emphasize *everyone* else, the voter has a preference between c and d, and
not only a preference, but a strong enough one to warrant the enduring the
distaste of skipping b. Seems an additional unlikelihood to me!
Further, the voter has to have precise knowledge of the classification of
all other voters infallible into two classes only, as described, as well as
knowledge that the difference between the groups is more than one vote. If
the voter has this knowledge, then, yes, the voter has an incentive to skip
a preferred candidate; indeed, if the voter is certain as to the margin
between the two groups, the voter would presumably know which group is
going to win. And therefore is really voting in a runoff election of a
sort, between the two candidates in the winning block. So, yes, of course,
with the preferences described, the voter would vote for c.
This kind of scenario has, it would seem, no application to real-world
conditions. From my point of view, if an election like this presented, and
there were this kind of knowledge in advance,
I don't want to say that this kind of theoretical analysis is useless, for
I don't think it is. But I do say that students of these methods should be
very careful about these borderland cases. They can confuse the debate over
methods. If someone says that Approval does not create situations where
voters have an incentive to vote contrary to preference, that statement, it
appears, would be true in substance even if there exists some exception
like this. Of course, a careful speaker will make a qualification like
"With rare and probably impossible exceptions, Approval Voting does not ...."
Unfortunately, people who speak like that tend to be rejected by voters as
too "nuanced." Yes, it is important that voters be educated as to the value
of trusting people who are careful not to lie to them, even in small ways,
but we have a ways to go to accomplish this! I certainly hope election
reform does not have to wait for this transformation of the electorate....
Note that in the scenario, not only does the additional voter have this
amazingly precise information in advance of the election, not only does
this voter have a unique preference for c over d, but the voter also has a
unique preference for a over b. Or else the voter would vote for a, b, and
c, and the election in one case would be a tie between a and b, or in the
other case, c would win. If the tie were resolved by a coin toss, the voter
might still experience the victory of his favorite....
It is not surprising that a pure approval system would fail to reflect
preferences within an approved group! Only a system which incorporates
expression of ranking would take these preferences into account. Yes,
pretty simple stuff, but than again I'm a rank beginner. :-)
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