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Technical discussion of election methods

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Just a thought

KM
Kristofer Munsterhjelm
Fri, Apr 19, 2024 4:10 PM

Is Woodall the same as Smith,IRV? (And thus Schwartz-Woodall the same as
Schwartz,IRV?)

Here's my thinking: Suppose that the IRV order is A>B>C>D>E and the
Smith set is {B, C, D}. Woodall's rules say: keep eliminating until only
one of the initial Smith set members is left.

So first eliminate E. The remaining members are {B, C, D}
Then eliminate D: {B, C}
Then eliminate C: {B} - and B is elected.

At each step, we subtract from the Smith set the k last ranked
candidates on IRV's social order (which are those who were eliminated
before round k). We then increase k until the set difference produces a
single candidate.

But this candidate is the Smith set member who is highest ranked on
IRV's elimination order. Hence it is the winner of Smith,IRV.

Sounds about right?

-km

Is Woodall the same as Smith,IRV? (And thus Schwartz-Woodall the same as Schwartz,IRV?) Here's my thinking: Suppose that the IRV order is A>B>C>D>E and the Smith set is {B, C, D}. Woodall's rules say: keep eliminating until only one of the initial Smith set members is left. So first eliminate E. The remaining members are {B, C, D} Then eliminate D: {B, C} Then eliminate C: {B} - and B is elected. At each step, we subtract from the Smith set the k last ranked candidates on IRV's social order (which are those who were eliminated before round k). We then increase k until the set difference produces a single candidate. But this candidate is the Smith set member who is highest ranked on IRV's elimination order. Hence it is the winner of Smith,IRV. Sounds about right? -km
CL
Closed Limelike Curves
Fri, Apr 19, 2024 7:58 PM

IRV fails ISDA, so removing all non-Smith members can affect the
IRV-ordering of Smith set members.

IRV fails ISDA, so removing all non-Smith members can affect the IRV-ordering of Smith set members.
KM
Kristofer Munsterhjelm
Fri, Apr 19, 2024 8:21 PM

On 2024-04-19 21:58, Closed Limelike Curves wrote:

IRV fails ISDA, so removing all non-Smith members can affect the
IRV-ordering of Smith set members.

Yes. I don't think Woodall was claimed to be ISDA.

James Green-Armytage gives the following election:

6: D>A>B>C
5: B>C>A>D
4: C>A>B>D

and says that Woodall elects B whereas Smith//IRV elects A. Since
Woodall restricted to the Smith set is just IRV, this shows that Woodall
fails ISDA. Benham also elects B, thus failing ISDA as well.

-km

On 2024-04-19 21:58, Closed Limelike Curves wrote: > IRV fails ISDA, so removing all non-Smith members can affect the > IRV-ordering of Smith set members. Yes. I don't think Woodall was claimed to be ISDA. James Green-Armytage gives the following election: 6: D>A>B>C 5: B>C>A>D 4: C>A>B>D and says that Woodall elects B whereas Smith//IRV elects A. Since Woodall restricted to the Smith set is just IRV, this shows that Woodall fails ISDA. Benham also elects B, thus failing ISDA as well. -km