Hi again,
I believe Stephane has erred below where he wrote that Condorcet methods
ensure a clone independent resolution. Perhaps his definitions of
Condorcet methods and/or clone independence and/or resolution differ
from what I believe are the standard definitions?
Condorcet methods are not necessarily independent of clone
alternatives. Some Condorcet methods are vulnerable to clones even when
no pairings are ties or have equal majorities, for examples Minmax
(which elects the candidate whose largest pairwise opposition in his/her
pairwise "defeats" is smallest) and Copeland (which elects the candidate
with the smallest number of pairwise "defeats"). Other Condorcet
methods, for examples MAM and Beatpathwinner, are clone independent when
no tiebreaking is needed and for complete clone independence rely on a
tiebreaker that is also clone independent.
(Briefly going off on a tangent... A simpler Minmax that is nearly
Condorcetian is the one that elects the candidate whose largest pairwise
opposition is smallest. It doesn't strictly satisfy the Condorcet
criterion if votes may be weak orderings, but it's simpler than the
Minmax defined in the previous paragraph and has similar properties.)
It matters that the tiebreaker be clone independent when the probability
of a tie is not negligible--in other words when the number of voters is
small--because otherwise there could *routinely* be farces where
factions nominate a huge number of clones in order to win if there is a tie.
I agree with Stephane about the desirability of being able to produce
the same winner each time the votes are tallied. From the standpoint of
electing the "best" alternative according to the votes, it doesn't
matter, since tied alternatives are equally good. But it may be
important in many circumstances for the outcome to be stable with
respect to recounts and verification tallies. It's a plus if every
voter can reach the actual outcome when s/he tallies the votes
independently.
I'm not sure what Stephane means when he says the tiebreaker should be
"equiprobable." I see nothing unfair about randomly picking a ballot
and using it to break ties. Yet it's possible that a majority of the
ballots rank one of the tied alternatives over the other, and in such a
case the two alternatives would not have an equal chance of being
selected by the random ballot tiebreaker. Why be concerned? According
to the votes the tied alternatives are equally good, so it doesn't
matter if one has an advantage in the tiebreaker.
Here's a reproducible way to "randomly" choose a tiebreaking ballot:
Keep track of when each vote is cast, and combine the tracked times to
make a seed to be used by a pseudorandom number generator. (My apologies
if this has already been proposed, or if a simpler/better technique has
already been proposed.)
I think Stephane's concern about influencing the chairperson is
overstated, since in the case of a tie every member is subject to influence.
Let's not forget how desirable it is that the tiebreaker (and voting
method) be fairly easy to understand by the voters. That's more
important than some of the criteria being discussed.
Regards,
Steve
----------------------------------------------
Stéphane Rouillon wrote:
I erred if I wrote it is ridiculous to nominate clones unless one can
predict before the election that a
tie will occur.
What I tough I wrote is : it is ridiculous to bother with an clone
independent tie-breaker if one considers a clone dependent electoral
system.
Using a Condorcet method for example ensures a clone independent
resolution, thus different computers should always end up to the same
winner despite ties if they both use the same reproductible (but
equiprobable or fair) tie-breaker.
Although I have a lot of admiration for Forest and Jobst work, I
cannot accept the use of random non-reproductible ballot selection for
tie-breakers (or for winner designation even more) because it kills
the validation of the process. If the process of designation of the
winner can be repeated ad nauseam, fraud can be achieved only by
corrupting the ballots database. It then becomes a lot easier for
electoral managers to ensure an honest result.
In the other case, anyone should be able to know in advance how the
random ballot is selected to thrust the electoral process. If it uses
a definite predictible and reproductible method, frauders will try to
get several favorable ballots as the tie-breaking numbered ballot. If
it uses a non-reproductible method, frauders will try to taint that
one time process. Thus I favor unpredictible but reproductible (but
still equiprobable) tie-breakers as the one presented previously,
which works for small groups and without any opportunity to influence
a chairperson. It is random only because it uses the election data
which nobody should know in advance.
From: Steve Eppley <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED]
Subject: Re: [EM] Random and reproductible tie-breaks
Date: Mon, 29 Sep 2008 06:36:50 -0700
Hi,
Raph Frank wrote:
Stéphane Rouillon <[EMAIL PROTECTED]> wrote:
-snip-
Tie-breakers have no need to be clone-independent. You cannot
predict a tie
will occur
before the election and it would be ridiculous to strategize on this
hypothesis.
In fairness, tie breaks are a low probability issue in any case. If
you are going to do them right, you might as well do them fully right.
Raph seems to be saying it's just an aesthetic value for the
tiebreaker to be independent of clones. I believe it's not just
aesthetic. Stephane erred when he wrote it is ridiculous to nominate
clones unless one can predict before the election that a tie will
occur. All that's needed for nominating clones to be strategically
sensible, assuming the cost of nominating clones is low, is that the
probability of a tie is not negligible. The probability of a tie is
typically not negligible when voting within small groups (committees,
councils, legislatures, etc.) and the cost of nominating clones in
small groups is typically tiny, which means it can be strategically
sensible to nominate clones if the tiebreaker is not independent of
clones. It's a form of insurance against a low probability undesired
event.
Even if one's focus is on large public elections, before asking the
public to adopt the method in public elections it may be crucial for
the voting method to first develop a track record of satisfaction
among many small groups. Hence the tiebreaker ought to be
independent of clones (or should be close enough to independent that
the probability of gaining by nominating clones is negligible).
I don't know that the tiebreaker used within small groups must be
identical to the tiebreaker that would be advocated for large
elections. For example, in small groups a seniority system is
common; typically a chairperson casts the tiebreaking vote.
Fortunately for us, that tiebreaker provides clone independence with
repeatability and no randomness.
Here's another tiebreaking option. It's typical for groups to choose
the status quo alternative when it's tied. Perhaps it would be
acceptable to break ties based on the order of nomination (treating
the status quo as first nominated, when it's an alternative). This
tiebreaker wouldn't provide a strict independence of clones, I think,
but it may be near enough to clone independent to make it
strategically hard or pointless to nominate clones. It too has the
desirable attributes of repeatability and non-randomness.
In a more recent message in this thread, Raph wrote:
Also, if there was a tie, then odds are that there is only 2 people
involved, so it doesn't really matter about clones.
I don't understand why Raph wrote that. Assume a tie involves two
alternatives, and assume the voting method (up to but not including
the tiebreaker) is independent of clones. By nominating clones of
one (or both) of the two tied alternatives, the tie can be changed so
it involves more than two. It follows that it can matter whether the
tiebreaker is independent of clones.
Regards,
Steve
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