One does not need to meet the different criteria fully. One could say
that it may be enough if it is better to vote as if some criterion
was true. It could be e.g. that even if monotonicity would be
guaranteed only with 51% probability voters would vote as if the
method was monotonic.
In practice there are cases where one gan guarantee some property
with 95% probability and that may be enough. Even though there is no
election method that would meet all the wanted criteria there may be
one that meets all those criteria well enough.
There are also criteria that should be respected in most situations
but not necessarily in all. Then meeting some criterion in 99% of the
cases is actually the target. There are e.g. cases where it could be
better not to meet Smith set, Condorcet loser and independence of
clones. This of course depends on what kind of social utility
function one wants to implement with the election method.
(Example: Ranked votes where three candidates form a strong loop and
some fourth candidate loses only very little to all the three looped
candidates (that are possibly but not necessarily clones). The last
candidate could well be the best (for some needs). This situation is
very exceptional and may never happen in real elections. But if this
happens it could be good not to respect the three mentioned criteria.)
In summary, often it is enough to respect some criteria only in most
cases, and sometimes this can be even what one wants.
Juho
On Jan 10, 2008, at 5:09 , daniel radetsky wrote:
On Jan 1, 2008 1:15 PM, Steve Eppley <[EMAIL PROTECTED]>
wrote:
Are monotonic methods less manipulable than non-monotonic methods?
I've
never heard any evidence of that.
I'm going to assume that you are not asking something like "For all
possible voting methods and some reasonable manipulability metric,
is the average manipulability of the monotonic methods lower than
the average manipulability of the non-monotonic methods?" For if a
method is non-monotonic, this means that there is a way to
manipulate it. If you are asking whether given the choice between
(say) a monotonic, non-clone-independent method and a non-
monotonic, clone-independent method, all else being equal, then
perhaps as you suggest, clone-independence is more important.
However, I was under the impression that one of the goals of
studying voting methods was to avoid having to make this choice.
In any case, resistance to manipulability is not the only reason to
desire a particular property for a voting system. Another important
quality is transparency: does casting a vote do what the voter
thinks it does? A voter thinks that when he increases his vote for
X (whatever "increases" means in the system in question), he is
helping X win. In a non-monotonic system, he's wrong, or at least
not guaranteed to be right. This is bad. Right?
Daniel
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