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Re: Tideman's Tiebreaker
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Blake Cretney
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Sep 30, 2001 14:29 PDT
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On Sat, 29 Sep 2001 05:43:47 +0000
Rob LeGrand <honk-@aggies.org> wrote:
| | Using the tiebreaking procedure I proposed, when A>C and C>D were
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You don't suggest a name, so I'll call it TBRC-lower for now.
| | considered, only the defeated candidates of the pairs, C and D,
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would be
| | compared in the TBRC. D loses to C in the TBRC, so C>D would have
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been
| | locked instead of A>C, and C would have gone on to win the election.
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| | This makes more sense to me. Plus it's simpler! Let's just hope it
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has
| | the same desirable properties (clone-independence, etc.) as the
Zavist/Tideman tiebreaker.
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First, you've noted in the past that TBRC-lower is more likely to give
the result the TBRC wants. On the other hand, it isn't clear that a
randomly picked ballot should get its way. Randomly picking a ballot
to increase its value, and randomly picking a ballot to decrease its
value seem equally justifiable to me. As well, neither Zavist/Tideman
nor TBRC-lower will always give the best result possible to the TBRC
voter, so neither can be used if this is required.
TBRC-lower certainly passes clone independence.
On the other hand it fails my recently suggested pairwise dominance
criterion from "Tiebreaker Correction". The criterion is plausible,
but perhaps not a knock-down argument.
You've recently suggested constructing a TBRC by successively going
through random ballots to construct a full ranking. If you're going
to do that anyway I don't see any further arguments for Zavist/Tideman
over TBRC-lower. On the other hand, I'm starting to see this as a lot
of unnecessary work. And if you randomly complete the TBRC ranking
(as Tideman and Zavist suggest in their 1989 paper), then TBRC-lower
violates Pareto, which is the criterion that says that if some one
prefers A to B, but no one prefers B to A, B should not win. On the
other hand, this doesn't occur in examples I would consider very
likely.
Zavist/Tideman passes Pareto even if the TBRC is completely random, or
the result of some other process, like the order in which the
proposals are made. So, it allows maximum compromise of clone
independence in favour of practicality, while still maintaining a
strict adherence to Pareto.
Why am I becoming so relaxed with regard to clone independence and so
strict with regard to Pareto? Here's my thinking. In the clone-tie
examples, I don't think that a random candidate order provides a worse
result than a random ballot. The argument really is that the method
is more affected by strategy. But when you consider that the effect
of this strategy is less than a single vote, I don't see this as a
major issue. As well, if voters ever rank a preference when they have
none between two candidates, we're sunk anyway with regard to this
strict level of clone independence.
But Pareto is so obviously right that violating it, or even the
possibility of violating it, would be a significant embarrassment.
And a result that did would appear to be clearly wrong.
It should be noted that Schulze's method is in much the same situation
as ranked pairs with the TBRC-lower tiebreaker. That is, it passes
Pareto if you get a complete ranking solely from drawing ballots, but
otherwise it doesn't.
---
Blake Cretney
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