Abd ul-Rahman Lomax wrote:
If you don't want to use the term "sincere" here, that's fine by me;
let's use something else. Let's find some term that describes an
ideal method in which a voter can express his true (dictatorial,
perhaps benevolently so, perhaps not) preferences without worrying
that there's some way of voting otherwise to achieve a better result.
Well, there is such a method, actually. First of all, you've got to
collect the necessary data, and the only ballot that does that is a
Range ballot. But you can analyze a Range ballot as if it were a
preference ballot with equal ranking allowed. There are two ways to
go: with sufficient resolution, it can be a simple Range ballot,
because a voter can maintain a preference of only one rating step,
which is really pretty small if it is Range 100. It's still pretty
small with Range 10! However, if the resolution is low, the device
would be used of having a preference indicator that does not alter
the Range vote. I.e., you could vote two candidates as perfect 10s
but still prefer one.
But, it turns out, you would be unlikely to actually do that, in what
I propose. Basically, the ballots are analyzed two ways: sum of
votes, which determines a "Range nominee," and pairwise. If the Range
winner is the Condorcet winner, and if the rules allow a victory by a
plurality (I don't like that), then the election is over. There is no
question about "plurality" if the Range winner is preferred by a majority.
But if the Range winner is beaten by another candidate, pairwise by
preference, then there is a runoff.
At 11:03 AM 10/9/2007, Chris Benham wrote:
Abd,
What do you propose if the Range winner is pairwise beaten by more
than one candidate?
Chris Benham
Abd ul-Rahman Lomax wrote:
An obvious question of great interest to election methods experts. Not
of much interest practically speaking. If it is sum-of-votes range,
which I highly recommend, such a situation would be extraordinarily
rare. But a complete method must address it. There is a simple
solution, and it does not have to be perfect.
The contest is between the Range winner and any candidate who beats
the Range winner. If there are more than two, then there are
possibilities:
(1) (Preferred) The Condorcet winner among the set, (Range Winner,
those who beat the Range winner).
(2) If there is a whole condorcet cycle beating the Range winner, then
the one with the lowest Range score is eliminated and the contest is
between the Condorcet winner remaining.
(The Range winner is guaranteed to be in the runoff. We can, thus,
exclude the Range winner from any cycle, if the Range winner is a
member of a Condorcet cycle.)
This, then, always reduces to two candidates which can be resolved in
a single runoff.
Abd,
Probably this or something like it would work ok in practice, but it
doesn't fill the bill as an
ideal method in which a voter can express his true (dictatorial,
perhaps benevolently so, perhaps not) preferences without worrying
that there's some way of voting otherwise to achieve a better result.
We know that Condorcet methods are vulnerable to Burial and Compromise,
and that Range is vulnerable to Burial and what has been called
Compromise-compression
(incentive to falsely vote one or more candidates equal-top alongside
the voter's true strict favourite).
The final runoff component means that in addition the composite method
is vulnerable to Pushover. Voters who are confident that their
favourite will be one of the finalists
could have incentive to vote to try to promote a "turkey" as the other
finalist. Voting sincerely could cause their sincere favourite to face a
strong candidate and lose in the runoff.
Chris Benham
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