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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